Message Legislation and the Politics of Virtue Signaling

Abstract

Message bills are hopeless legislation constructed not to change public policy but instead to signal desirable attributes of incumbents to constituents-virtue signaling. Well-known examples are the repeated hopeless attempts to repeal the Affordable Care Act during the 113th and 114th Congresses. To explore the logic of message legislation, we create a formal principal-agent model of electoral accountability. The theory makes explicit predictions about who signals, on what kind of issues, and when. Then, using novel and extensive data on bill locations and status quo locations, we test the predictions. The data suggest that most introduced bills are not viable. Who messages and on what topics appear consistent with the theory; the evidence is less supportive on when members message. We further show that the patterns predicted for non-viable message bills do not hold in viable bills. We briefly discuss the normative implications. Message legislation helps voters select zealous representatives , but perhaps at the cost of lower quality policy-making.

Full text

Message Legislation
and the Politics of Virtue Signaling
-----
Daniel Gibbs*Jesse M. Crosson†Charles M. Cameron‡
Princeton University Trinity University Princeton University
April 1, 2021
Abstract
Message bills are hopeless legislation constructed not to change public policy but instead to signal
desirable attributes of incumbents to constituents – virtue signaling. Well-known examples are the
repeated hopeless attempts to repeal the Affordable Care Act during the 113th and 114th Congresses.
To explore the logic of message legislation, we create a formal principal-agent model of electoral ac-
countability. e theory makes explicit predictions about who signals, on what kind of issues, and
when. en, using novel and extensive data on bill locations and status quo locations, we test the
predictions. e data suggest that most introduced bills are not viable. Who messages and on what
topics appear consistent with the theory; the evidence is less supportive on when members message.
We further show that the patterns predicted for non-viable message bills do not hold in viable bills.
We briefly discuss the normative implications. Message legislation helps voters select zealous repre-
sentatives, but perhaps at the cost of lower quality policy-making.
*Daniel Gibbs is Ph.D. Candidate at Princeton University’s Department of Politics.
†Jesse M. Crosson is Assistant Professor at Trinity University.
‡Charles M. Cameron is Professor of Politics and Public Affairs at Princeton University.
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is is now the pattern of business in the House of Representatives: Spend most of the time
passing bills designed not to become law but to satisfy the ideological desires of conservative
voters. And block bills that actually need to get passed.
—Editorial, “e Bills to Nowhere,” New York Times, June 7, 2012
Introduction: The Bills to Nowhere
In every Congress from the 112th to the 116th (2011 to 2020), Congressman Rob Woodall, a Georgia
Republican representing a suburb of Atlanta, introduced H.R. 25, which he dubbed “e Fair Tax Act.”
e bill would have repealed the federal income tax, abolish the Internal Revenue Service, and create a
national sales tax. If enacted, the Fair Tax Act would have been the boldest revision to the federal fisc since
the 16th Amendment to the Constitution in 1913, creating the federal income tax. Not surprisingly, the
congressman’s bill never went anywhere. Indeed, Woodall was not even a member of the House Ways
and Means Committee, which commands the tax code. Despite his very modest success as a legislator,
Woodall faced no serious primary opponent after his initial election, until his announced retirement in
2019. In 2020, the district elected a Democrat.
In the 115th Congress (2017-2018), Representative Mark Pocan, a Democrat representing the fa-
mously liberal college town of Madison, Wisconsin, introduced H.R. 6361, the “Establishing a Humane
Immigration Enforcement System Act.” e bill would have abolished ICE, the Immigration and Customs
Enforcement agency, without establishing any replacement. Doing so would arguably open America’s bor-
ders to illegal immigrants. Pocan’s effort at government reorganization went to the relevant committees
of the House, where it promptly died. After his initial election in 2012, Rep. Pocan has won more than
99% of the primary vote in his district, considered a safe Democratic seat.
ese bills exemplify clearly hopeless legislation, introduced in Congress despite a manifest inability
to secure a majority or overcome the opposition of critical veto players. ey were “bills to nowhere,” in
the apt words of the editorial quoted above. Perhaps the most spectacular of the bills to nowhere were the
legislative vehicles offered by House Republicans during the 113th and 114th Congresses to “repeal and
replace” the Affordable Care Act, Obamacare. In this period, Barack Obama controlled the presidential
veto while congressional Democrats, who supported the ACA, had sufficient numbers in the Senate to
deny Republicans filibuster-proof and veto-proof majorities. Hence, the actual enactment of any “repeal
and replace” legislation was a mathematical impossibility. Republicans nonetheless essayed the attempt,
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not once but over and over and over. ough less spectacular, Democratic attempts to de-fund the Iraq
War during the Bush Administration were equally futile, yet the target of doggedly repeated efforts.
Why do members of Congress introduce and devote time and effort to clearly hopeless bills? One
answer is that the bills are “message bills.” As described by Frances Lee in a prominent study, such bills
encompass “an attractive-sounding idea with the following characteristics: (1) its members support it; (2)
the other party opposes it; and (3) it is not expected to become law” (Lee, 2016, 143). But, what is the
message in message bills? One possibility involves blame game politics. In other words, the bills may try to
force members of the opposition party to cast electorally damaging votes (Groseclose and McCarty, 2001;
Gilmour, 1995). Another possibility, however, is virtue signaling: the bills convey a positive attribute
of their authors and co-sponsors to constituents. If constituents find the signal credible, the incumbent
becomes more attractive as a representative, thereby boosting his or her re-election prospects, perhaps
especially in primaries. Such bills are pure position-taking, in Mayhew’s (1974) famous phrase.
Virtue-signaling message bills raise important and intriguing questions. First, why would voters believe
the message sent in bills doomed to failure, especially if voters understand that politicians are just using
the bills to message? Second, how frequent are non-viable bills? ird, which members of Congress write
and sponsor virtue-signaling message bills, in what topical areas, and when do they do it? Finally, what
are the consequences for governance? What happens when legislators devote a great deal of their time and
effort to fake rather than real legislating?
In this paper, we attempt to answer the first three of these questions. Our approach is both theoretical
and empirical. First, to clarify the logic of message legislation, we create a formal game-theoretic model.
e model adapts principal-agent models of electoral accountability to this specific legislative setting. Our
approach complements Patty (2016) which employs a costly signaling model to develop a theory of why
legislators obstruct bills that they know will inevitably become law. Our model studies legislators who
introduce bills that they know will inevitably fail. While a similar costly signaling mechanism makes virtue
signaling credible in both models, there is an important distinction between these two legislative settings.
Virtue signaling through hopeless obstruction requires opposition legislators to wait for the majority to
introduce a bill that the majority is willing to defend against obstruction. Virtue signaling through message
bills is a tactic available to any legislator willing to take time to develop and introduce a piece of legislation.
Our theory makes clear empirical predictions about what type of issues are attractive venues for message
bills, which members of Congress find it more attractive to engage in messaging, and when they are more
likely to do so.
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Actually testing these predictions requires new and extensive data on bill locations and status quo
locations, as well as more-standard data on ideal points and the attributes of congressional districts. To
derive the critical bill and status quo locations, we employ data from Crosson, Furnas and Lorenz (2019).
eir approach extends the analysis in Peress (2013) by jointly scaling roll call data, bill sponsorship data,
and interest group position-taking data to recover plausible bill and status quo locations. (ieme (2020)
uses a similar approach at the state level.) e data provide locations for 1007 bills introduced between the
110th and 114th Congresses. ese offer sufficient observations to detect whether or not the non-viable
bills display the patterns predicted by the theory. In addition, the viable bills allow a robustness check, to
determine whether only the non-viable bills display the predicted message-sending patterns.
Our main findings are as follows. First, the bulk of introduced bills appear to be non-viable – their
spatial locations relative to the status quo indicate they could not command a majority and over-come
the opposition of critical veto players. Second, as predicted, topical areas that are highly salient in specific
congressional districts are much more likely to draw non-viable legislation drafted or sponsored by repre-
sentatives from those districts. ird, as predicted, members whose ideal points lie far from the status quo
are more likely to engage in messaging. However, in contrast to the theory’s prediction, the likely opening
of policy windows in the near future did not stimulate statistically significantly more message bills be-
forehand. Fourth, only non-viable bills display the patterns predicted for message legislation. Viable and
non-viable bills are quite different from one another.
e prevalence of message legislation raises possibly disturbing implications about Congress’s policy
making capacity in the current age. Space does not allow us to pursue these implications fully, but we
touch on relevant points in the Discussion.
Theory
We develop a principal-agent model of electoral accountability to construct a theory of message legislation
and derive empirical implications. e players are a voter and an incumbent legislator.1e voter dislikes a
status quo policy and desires its repeal. e voter suffers a loss of λ > 0if the status quo is not repealed. e
disutility from the status quo, λ, represents the distance between the status quo and the voter’s preferred
policy. ere are two types of legislators, slackers and zealots (Gailmard and Patty, 2007), who differ in
the intensity of their desire to repeal the status quo. Like the voter, a zealot receives a payoff of −λif the
1Consistent with convention in the principal-agent literature, we use the pronouns “she/her/hers” for the voter (principal)
and “he/him/his” for the legislator (agent).
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status quo is not repealed. e slacker cares less about the status quo than the zealot and voter. e slacker
receives a policy payoff of 0whether or not the status quo is replaced.
Both slackers and zealots earn a payoff of b > 0from holding office. e office benefit absorbs all
office benefits not pertaining to legislator preferences over the particular status quo that the voter and
zealot intensely dislike. is includes both material benefits of holding office as well as policy influence
that a legislator can assert in other policy areas he values. With this interpretation of b, the slacker is not
necessarily a single-minded seeker of material office rents. We only require that the slacker cares less about
repealing the particular status quo in question than the zealot and voter. e legislator’s type is private
information. It is common knowledge that the legislator is a zealot with probability 1/2.
e game is played with the following sequence of moves. First, Nature selects the legislator’s type.
e game then enters a legislative phase. We assume that a veto player blocks any effort by the legislator to
change the status quo. Both the voter and incumbent know that any attempt to change the status quo is
futile. e legislator can, however, exert doomed effort to repeal and replace the status quo. e legislator
can attempt to replace the status quo any number of times. We denote the number of times the legislator
chooses to attempt repeal with n∈N.2Attempting to repeal the status quo requires scarce time and
resources. Each attempt costs the incumbent k > 0.3
After the legislative phase, the voter observes the incumbent legislator’s attempts to repeal and replace
the status quo, n, with probability ζ. With probability 1−ζthe voter is inattentive and does not observe
n. e ζparameter represents the salience of an issue to the voter. A voter is quite likely to know whether
or not her representative attempts to change a status quo that directly affects her such as one regulating
the industry in which she works. She is less likely to pay attention to the legislator’s activities in policies
areas that do not affect her personally.4
e voter then chooses between the incumbent and a challenger in an election. Because legislators
vary in terms of the intensity of their preferences, it is natural to conceive of the challenger as a primary
rather than general election challenger. Like the incumbent, the challenger is a zealot with probability
1/2. In addition to the policy consequences of reelecting the incumbent versus the challenger, we assume
2In a previous version of the model, the incumbent also selects a spatial location for each bill where the status quo is λand
voter and zealot’s ideal points are 0. In this earlier version of the model, the veto player blocks any change to the status quo less
than λ. We therefore lose little generality with respect to this alternative model by restricting the incumbent’s strategy here to
complete repeal. Details are available upon request.
3We model legislation as a discrete choice rather than as continuous effort in order to capture the empirical phenomenon
we are studying: observable instances of non-viable legislation.
4Additionally, ζmay capture features of the media landscape. e presence of cable news, the internet, and social media
intuitively make a legislator’s actions more visible to the voter.
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that voter takes into account additional factors unrelated to the policy issue in question when making her
decision. Prior to the election, the voter observes a private independent taste payoff from voting for the
incumbent, ω, drawn from a continuous and strictly increasing distribution, F. We assume that the mean
of Fis zero and that its density, f, is symmetric.5
e winner of the election is appointed to the legislature. Following the election, the policy window
opens with probability ρ. If the policy window opens, the veto player accepts repeal of the status quo.
For simplicity, we model a second period of legislative action in reduced form. We assume that the status
quo is successfully repealed at no cost to the legislator if and only if the policy window opens and the
second-period legislator is a zealot.6
e game then ends and payoffs for the legislator and voter are realized as follows.
uL=b(legislator is reelected)−λ(legislator is a zealot and status quo not repealed)−nk
uV=ω(voter reelects incumbent)−λ(status quo not repealed)
Both types of incumbent legislators receive −nk from their failed legislative effort prior to the election
and earn the office payoff bif and only if they are reelected. A zealot who loses the election continues to
care about policy and receives a payoff of −λif the status quo is not repealed after the election.7e voter
receives −λif the status quo is not repealed and receives ωif and only if she reelects the incumbent.
Equilibrium
Our solution concept is a pure-strategy undefeated sequential equilibrium (Mailath, Okuno-Fujiwara and
Postlewaite, 1993).8We are interested in identifying the conditions under which we should expect to
observe non-viable legislation and the conditions under which this constitutes message legislation. To this
end, we consider a separating equilibrium in which the zealot legislates a positive number of times, n∗>0,
5is implies that F(0) = 1/2 and F(−x) = 1 −F(x). An example of such a distribution is a normal distribution with
mean zero.
6If the second legislative period is explicitly modeled, this is the unique equilibrium outcome if the cost of viable legislation
is sufficiently low.
7is distinguishes a zealous legislator from a policy-minded implementer who may avoid some or all of the distress and
shame of carrying out a detested policy by quitting the job, a “clean hands” phenomenon (Cameron and de Figueiredo, 2020).
8Sequential equilibrium requires that for each nthat at least one type of legislator selects in equilibrium, if the voter observes
n, her posterior belief about the legislator, µ(n), satisfies Bayes’ rule. e undefeated refinement places a requirement on µ(n)
for each nthat neither type selects in equilibrium. Consider an equilibrium σwith posterior beliefs µ(·)in which neither type
selects n. Now consider an alternative equilibrium σ′with posterior beliefs µ′(·)that satisfies two properties: i) at least one
type selects nand ii) the set of types who choose nis precisely the set of types who prefer σ′to σ. If σ′exists and µ(n)̸=µ′(n),
then σ′defeats σ. e equilibrium σis undefeated if and only if either µ(n) = µ′(n)or no σ′exists.
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and the slacker does not legislate. In this equilibrium, costly non-viable legislation reveals the zealot’s type
to the voter and functions as an effective message. We therefore refer to this equilibrium as a messaging
equilibrium.9
In a messaging equilibrium, voter reelects the incumbent if and only if she weakly prefers the incum-
bent to the challenger given her beliefs. Let µ(n)denote the voter’s posterior belief that the incumbent
is a zealot when she observes n. If the voter reelects the incumbent, she receives the taste payoff ωand
suffers policy loss of λunless both the policy window opens and the incumbent is a zealot. Her expected
payoff from reelecting the incumbent when she observes nis therefore −λ(1 −µ(n)ρ) + ω. If she elects
the challenger, she does not receive ωand suffers policy loss of λunless both the policy window opens
and the challenger is a zealot. Because the challenger is a zealot with probability 1/2, her expected payoff
from electing the challenger is −λ(1 −ρ/2). Comparing these two payoffs, if the voter observes n, she
reelects the incumbent if and only if
λρ
2[2µ(n)−1] + ω≥0
By Bayes’ rule, if the the voter observes n∗, she believes the incumbent a zealot: µ(n∗) = 1. us if she
observes n∗, she reelects the incumbent if and only if
λρ
2+ω≥0
With ω∼F, the probability that the incumbent is reelected when the voter observes n∗is F(λρ
2)>1/2.
If the voter does not observe the legislative stage, she believes the incumbent is a zealot with probability
1/2 by Bayes’ rule. In this case she reelects the incumbent if and only if her private taste payoff from
reelecting the incumbent is non-negative: ω≥0. She therefore reelects the incumbent with probability
F(0) = 1/2 if she does not observe n. Because the voter observes nwith probability ζ, the equilibrium
probability that an incumbent is reelected if he chooses n∗is
P∗(ζ, λ, ρ)≡ζF (λρ
2) + (1 −ζ)
2
If the voter observes the legislative stage and sees that the incumbent does not legislate, she believes the
incumbent is a slacker by Bayes’ rule: µ(0) = 0. We assume that in a messaging equilibrium, if the voter
9We provide a complete formal definition of a messaging equilibrium in the Appendix.
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observes an unexpected amount of legislation less than n∗, she believes the incumbent is a slacker. us if
the voter observes n < n∗, she reelects the incumbent if and only if
−λρ
2+ω≥0
It follows that an incumbent who chooses n < n∗, is reelected with probability 1−P∗(ζ, λ, ρ)in a
messaging equilibrium.
If an incumbent selects n∗, we say that he “messages” or is “messaging.” In equilibrium, messaging
raises the incumbent’s probability of reelection by
2P∗(ζ, λ, ρ)−1
relative to no messaging, n= 0.10
e gain in reelection probability that messaging affords an incumbent is increasing in ζ,λ, and ρ.
If the voter is likely to be attentive to the incumbent’s legislative actions, messaging becomes more likely
to be observed and rewarded. Failure to message also becomes more likely to be observed and punished.
If it is likely that the policy window opens and the voter strongly dislikes the status quo, the voter places
greater weight on the intensity of her representative’s preference for repealing the status quo (relative to
taste payoff ω) when choosing between the incumbent and challenger.
For a messaging equilibrium to exist, the slacker must prefer not to message. e slacker only values
reelection in order to earn the office benefit, b. Let
B∗≡b(2P∗(ζ, λ, ρ)−1)
denote the office value of messaging. e slacker is unwilling to pay more than nk =B∗to receive this
benefit of messaging. We now define n∗explicitly as the minimum amount of legislation such that the
slacker prefers not to message, as equilibrium requires:
n∗≡ ⌈B∗
k⌉
10Because legislation is costly and all n < n∗yield the same probability of legislation, an incumbent who chooses not to
message is best off choosing n= 0. Similarly, all n > n∗are equilibrium dominated by n∗because P∗(λ, ρ, ζ)maximizes an
incumbent’s probability of reelection.
8

where ⌈·⌉ is the ceiling function which returns the smallest integer greater than or equal to its argument.
e zealot must prefer to message for the equilibrium to exist. If the zealot messages, he receives the
office value of messaging, B∗. e cost of messaging, kn∗=k⌈B∗
k⌉, however, (weakly) exceeds B∗. We
refer to the difference
k⌈B∗
k⌉ − B∗≥0
as the “net cost of messaging” (with respect to the office benefit of messaging). In order for a messaging
equilibrium to exist, the policy value of messaging to the zealot must must exceed the net cost of messaging.
From the zealot’s perspective, reelection ensures that the status quo is successfully repealed if the policy
window opens. His expected policy payoff conditional on reelection is therefore −λ(1 −ρ). If he loses
the election, the status quo is repealed only if the policy window opens and his replacement is a zealot.
His expected policy payoff if he is not reelected is −λ(1 −ρ/2). e policy value of reelection for the
zealot is therefore λρ
2. Multiplying the policy value of reelection by the gain in probability of reelection
that messaging affords yields the policy value of reelection to the zealot,
g(ζ, λ, ρ)≡λρ
2[2P∗(ζ, λ, ρ)−1]
e policy value of reelection, g(ζ, λ, ρ), is increasing in each of its arguments. We establish above that
the equilibrium probability of reelection when the incumbent messages, P∗(ζ, λ, ρ), is increasing in each
argument. Additionally, the policy value of reelection to the zealot, λρ
2, is increasing in both λand ρ. If
the zealot strongly disfavors the status quo and the opportunity to repeal the status quo is likely to arise
after the next election, the policy value of reaching the second period is high. We will use these properties
of g(ζ, λ, ρ)below to derive empirical implications from the model.
Remark 1. The policy value of messaging to the zealot, g(ζ, λ, ρ), is increasing in ζ,λ, and ρ.
Comparing the zealot’s policy value of legislation to the net cost of messaging reveals that the zealot
prefers to message if and only if
g(ζ, λ, ρ)≥k⌈B∗
k⌉ − B∗(1)
us a messaging equilibrium exists if and only if (1) is satisfied. Note that k⌈B∗
k⌉ − B∗< k if and
only if ⌈B∗
k⌉ − B∗
k<1. It is a property of the ceiling function that for any x∈R,⌈x⌉ − x∈[0,1).
erefore the net cost of messaging to the zealot is bounded above by the cost of legislating once, k. e
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cost of legislating once is a strict upper bound on the net cost of messaging to the zealot because n∗is
defined as the minimum amount of legislation that makes the slacker (weakly) prefer not to message. us
a sufficient condition for a messaging equilibrium to exist is
g(ζ, λ, ρ)≥k(2)
In the Appendix we show that the messaging equilibrium is the only undefeated separating equilibrium.
is rules out any separating equilibrium in which the zealot legislates more than the minimum amount
required for legislation to send a credible message, n∗.
In addition to the messaging equilibrium, there may exist a pooling equilibrium in which neither type
of incumbent legislates. We refer to this as a no legislation (NL) equilibrium.11 In a NL equilibrium, the
voter learns nothing new about the incumbent, regardless of whether she observes the legislative phase or
not. e incumbent is therefore reelected with probability 1/2. In addition to the NL equilibrium, other
sequential pooling equilibria may exist in which both types of the incumbent legislate a positive number
of times. Such equilibria require that the voter punishes the incumbent for not legislating even though
legislation is uninformative to the voter. We show in the Appendix that these pooling equilibria do not
survive our refinement; the NL equilibrium is the only undefeated pooling equilibrium.
Our refinement therefore leaves two possible pure strategy equilibria, the messaging equilibrium and
the NL equilibrium. In the Appendix we establish that if the messaging equilibrium does not exist, the NL
equilibrium exists. us if (1) fails, the unique equilibrium is NL. We now derive a sufficient condition
for the messaging equilibrium to be unique.
In a NL equilibrium, the slacker receives a strictly positive expected payoff, b/2. By the definition of
n∗, the slacker receives a non-positive payoff if he chooses n∗in the messaging equilibrium. e slacker
therefore prefers no legislation in the pooling equilibrium to n∗in the messaging equilibrium. In the
NL equilibrium, the zealot receives an expected payoff of (b+λρ
2)1
2. In a messaging equilibrium, the
zealot receives and expected payoff of (b+λρ
2)P∗(ζ, λ, ρ). e zealot therefore prefers n∗in a messaging
equilibrium to no legislation in the NL equilibrium if and only if
g(ζ, λ, ρ)>2k⌈B∗
k⌉ − B∗(3)
Note that (3) implies (1), the necessary and sufficient condition for a messaging equilibrium to exist.
11We provide a complete formal definition of a NL equilibrium in the Appendix.
10

erefore if (3) is satisfied, the undefeated refinement requires that in a NL equilibrium, the voter believes
the incumbent is a zealot with probability one if she unexpectedly observes n∗. Given this off-path belief
in a NL equilibrium, deviation to n∗yields the same expected payoff to the zealot as his equilibrium payoff
in a messaging equilibrium. From (3), this deviation is profitable. erefore if (3) is satisfied, the unique
undefeated equilibrium is the messaging equilibrium. It is straightforward to check that the maximum
value of 2k⌈B∗
k⌉ − B∗is 2k. erefore the messaging equilibrium is unique if
g(ζ, λ, ρ)≥2k(4)
Proposition 1.
If g(λ, ρ, ζ)≥k, the messaging equilibrium exists.
If g(λ, ρ, ζ)≥2k, the messaging equilibrium is unique.
If the messaging equilibrium does not exist, the no-legislation equilibrium exists and is unique.
Empirical Implications
We now use Proposition 1 and Remark 1 to derive empirical implications from the model. From Proposi-
tion 1, if the policy value of messaging to the zealot, g(λ, ρ, ζ), is sufficiently low, a messaging equilibrium
may not exist. As g(λ, ρ, ζ)rises, a messaging equilibrium first becomes guaranteed to exist and then be-
comes the unique equilibrium as g(λ, ρ, ζ)rises further. We therefore expect to observe a higher prevalence
of message legislation as g(λ, ρ, ζ)rises. From Remark 1, g(λ, ρ, ζ)is increasing in each argument. We
therefore expect expect the prevalence of message legislation to be positively associated with λ,ρ, and ζ.
Hypothesis 1: Issue Salience
The probability of messaging is increasing in issue salience, ζ.
Hypothesis 2: Opening of Policy Window
The probability of messaging is increasing in the probability that the policy window opens, ρ.
Hypothesis 3: Distance from Status Quo
The probability of messaging is increasing in a legislator’s ideological distance from the status quo, λ.
Data, Measurement, and Specification
Before detailing the data collected to test each of the above hypotheses, we first preface the basic empirical
design we use to test our hypotheses. ereafter, for each construct included in our empirical setup,
11

we detail the measurements necessary to capture the construct and the data we use to generate those
measurements.
Design
In order to test our hypotheses, we estimate a series of models that incorporate each of ζ,ρ, and λjointly.
Our decision to do so reflects our desire to maintain congruence between our theoretical and empirical
models: our belief is that each factor influences the observed outcomes simultaneously. However, before
proceeding, it is worth noting that we do make one small empirical departure from our theoretical setup:
namely, we measure the existence rather than the volume of messaging as our outcome variable. As we
discuss below, we do so because of nature of our underlying data sources; however, given that our theoretical
expectations in the messaging equilibrium hinge upon the zealot crossing a messaging threshold, we do not
believe this decision alters the appropriateness of our empirical tests.
In general, then, our models take the following form:
P r(Mijt = 1) = µ+αj+δt+β1ζijt +β2ρjt +β3λij t +Xβ+ϵit
where Mijt represents legislator i’s decision about whether or not to message on issue jduring congress
t,ζijt represents the salience of issue jto member i’s district in congress t,ρjt represents the likelihood
that the policy making window for issue jwill open in congress t+ 1,12 and λijt represents legislator
i’s distance from issue j’s status quo location in congress t. e specification also includes issue- and
session-level effects (αjand δt, respectively), as well as a vector of control variables X.
As the specification makes clear, we test each of our hypotheses at the member-issue-congress level,
leveraging within-issue variation on virtue-signaling behavior. We operationalize our hypotheses at the
issue-level for several reasons. Practical considerations, such as the measurement of particular independent
variables like salience, render an issue-level analysis more tractable than other alternatives. ese practical
advantages notwithstanding, though, our primary reason for our level of analysis is rather straightforward:
although members’ policy making behaviors are typically observed at the bill-level, recovering a relevant
alternative to messaging (i.e., the choice against messaging) in a manner interpretable across member-
offices is impossible at the bill-level. at is, unless two legislators choose to sponsor legislation on precisely
12at is, the probability, measured in Congress tthat the future policy making window will open.
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the same topic area, thereby addressing precisely the same status quo, one would be unable to assess why
one legislator chose to message while another did not. By aggregating to the issue level, we circumvent
this problem: all members face a choice about whether to message on a more general issue area such as
education or defense policy, and they must allocate their attention accordingly. us, as we detail below,
all of our variables are aggregated to one of twenty policy issue areas, drawn from the Comparative Agendas
Project.
In what follows, we detail our means of capturing both the dependent variable and independent vari-
ables that lie at the center of our theory of virtue-signaling.
Data and Measurement
Decision to Message (Mijt ). Member i’s decision to message on issue jconstitutes the most central
concept and measurement in the empirical tests of our theory. Conceptually, we define message bills as
legislation written for the purpose of signaling, with no chance of actually passing into law. Empirically,
we classify any bill as “messaging” if, by virtue of its spatial location, the location of its associated status
quo, and the location of pivotal actors in Congress, the bill would fail to pass into law. Formally, we define
a bill bas messaging if the following conditions obtain:
Mbt =




1|qbt −Vt| ≤ |pbt −Vt|
0|qbt −Vt|>|pbt −Vt|
where pbt and qbt represent a bill b’s proposal and associated status quo location, respectively, and Vt
represents the pivotal actor in Congress tnearest to qbt. In order to aggregate to the issue level, we define
Mijt = 1 if a member chose to sponsor any piece of messaging legislation within issue area jin Congress
t. Formally,13
Mijt =




1Mibt = 1
0otherwise
In order to capture these messaging sponsorships, we require three sets of measurements. e first,
of course, is the spatial location of the proposal itself; however, this information is not enough to isolate
which bills are actually “hopeless.” Instead, we also require a measurement of the bill’s associated status
13Technically, one could conceive of this as a count rather than a binary variable. However, due to data limitations and the
general rarity of messaging within particular issue-congresses, we focus our analysis on the binary operationalization.
13

quo (qbt) and the locations of relevant pivotal actors or veto players in the legislature (Vt)—all on the same
scale. We draw these measurements from a new dataset, called cIGscores, developed by Crosson, Furnas
and Lorenz (2019). Crosson et al. generate their estimates by jointly scaling cosponsorship, roll call, and
interest group position-taking data throughout the legislative process.
As (Clinton, 2017) summarizes in his review of strategies for measuring the content and direction of
policy changes, common methodologies for generating ideal point estimates (e.g. Poole and Rosenthal,
1997; Clinton, Jackman and Rivers, 2004) fall short of producing reliable estimates for prosposal and
status quo locations. More specifically, while legislators’ ideal points and bill’s cutpoints (i.e., the spatial
dividing line between yay and nay votes) are well identified using existing methods, identification of the
proposal locations (and, relatedly, the status quo positions) is fragile and relies upon the curvature of the
legislators’ assumed utility functions. is fragile identification, per Poole and Rosenthal’s (1991) initial
warning, has traditionally prevented legislative scholars from using proposal and status quo estimates in
analyses of policymaking. In response, Crosson et al. develop their measurements using an adaptation first
developed by Peress (2013) and applied at the state level by ieme (2020). Peress’s general approach allows
for the identification of proposal locations alone using cosponsorship data, by modeling the cosponsorship
decision as proximity-based. us, by jointly scaling cosponosorship decisions with roll call decisions and
identifying bill-specific cutpoints simultaneously, the methodology allows for the identification of proposal
locations, status quo locations, and legislator ideal points on the same scale.
As both ieme and Crosson et al. underscore, however, the methodology is limited by the timing of
roll call votes, which overwhelming occur after a bill has changed substantially from the time of introduc-
tion to the voting stage. To address this problem, both studies jointly scale interest group position-taking at
the time of introduction with roll call and cosponsorship data, in order to identify proposal and status quo
locations for bills as they are introduced. us, not only does the method place interest group ideal points on
the same scale as bill scores and legislator ideal points, but it vastly expands the number of scoreable bills.
Given our focus on the U.S. Congress (ieme’s study focuses on state legislatures), we make use of the
data provided by Crosson, Lorenz, and Furnas, which includes scores for 1,007 bills introduced between
the 110th and 114th Congresses.14 eir scores are generated using interest-group position-taking from
the non-profit MapLight, which has compiled over 110,000 instances of interest-group position-taking in
the specified Congresses (Lorenz, Furnas and Crosson, 2020).
ese measurements enable us to measure messaging decisions at the legislator-issue-congress level for
14Some summary statistics and visualizations of these data are presented in Supplemental Information A.
14

Figure 1: Messaging Legislation by Issue Area, 2009-2016
the 110th through 114th Congress (2009 to 2016). Supplemental Information A provides additional on
the distribution of the outcome variable, but Figure 1 underscores the prevalence of message legislation in
recent Congresses. Indeed, across most issue areas, the majority of bill sponsorships constitute relatively
hopeless pieces of legislation, providing some quantitative support for recent journalist accounts about
“bill to nowhere” (The Bills to Nowhere, 2012). However, as the figure also depicts, there is considerable
variation in messaging rates across issue areas. It is this variation that we ultimately exploit in our empirical
tests.
Issue Salience (ζijt ). According to Hypothesis 1, the probability of messaging should be increasing
in issue salience. at is, as the likelihood that constituents learn about a member’s messaging, ζ, increases,
members should grow more likely to message. In order to capture the salience of legislating to a member’s
district, we argue that constituencies will be most attentive when the an issue area affects a significant
15

portion of the local economy. More specifically, we argue that the larger the percentage of a district
employed in an industry relevant to issue j, the greater the salience of policymaking in that issue area to
legislator i’s district.
In order to measure the percentage of each congressional district employed in industries relevant to
particular issues, we begin with district-level NAICS employment statistics reported in the Census’s Amer-
ican Community Survey and County Business Patterns dataset. Since 2013, the Census has reported
these statistics directly at the district level, providing exactly the kind of information necessary to measure
salience. However, prior to 2013, the closest available data captures the number of industry-relevant estab-
lishments in each Zip Code Tabulation Area (ZCTA). Fortunately, the establishments are classified by num-
ber of total employees, allowing for a translation from establishment numbers to employment numbers by
industry in each ZCTA. Using a ZCTA-to-congressional district crosswalk generated by the Missouri Cen-
sus Data Center’s Geographic Correspondence Engine http://mcdc.missouri.edu/applications/
geocorr2014.html, we then generated district-level estimates of employment for the years prior to 2013.
To ensure this estimation procedure reasonably approximated the post-2013, we double-coded the year
2013, demonstrating a strong correlation in industry employment between the two measurements. e
results of this validity check are found in Supplemental Information B.
After assembling district-level employment data, we converted the employment statistics into salience
measures by creating a crosswalk between the NAICS industry classification system and the Comparative
Agendas Project’s major issue topic codes. e crosswalk, reported in Supplemental Information B, links
each policy topic with all industries to which it is relevant. For example, a district with a large automobile
manufacturing presence would, according to our coding scheme, register as attentive to labor issues and
foreign trade, among other issues. By contrast, a poor, urban district with larger-than-average numbers of
social service employees may register as attentive to social welfare issues. Table TK list the issue of highest
salience to each district, after standardizing employment percentages by issue area.
Opening Policy Window (ρijt). According to Hypothesis 2, the probability of messaging should
be increasing in the probability that the policy window opens in the immediate future for issue j. at is,
presuming that policy change is not possible for issue jin the present congress t, members should be more
likely to message when they believe that the policymaking window will open in the upcoming congress. In
order to capture these expectations, we require contemporaneous measurements of members’ expectations
about the probability that legislation can move in a given policy area in the near future. While many
16

factors influence members’ beliefs about this probability, we argue that a precondition for major policy
change in the contemporary U.S. Congress is majority control of one’s own chamber. at is, without
majority control, the likelihood of passing meaningful legislation is low. However, if a member expects
that her party will gain majority status in after the upcoming election, she may believe that policy in her
issue area will move (ρis high) and message within the current congress accordingly.
We therefore operationalize ρijt as the probability that i’s party will gain majority control after the up-
coming election. To measure this quantity, we make use of Crosson’s (2019) interpolated Iowa Electronic
Market (IEM) share prices. e IEM has, since the mid 1990s, solicited investments from private citi-
zens on a wide variety of political outcomes, including whether particular parties will control the House,
Senate, and presidency. Most crucially for measuring contemporaneous beliefs about electoral outcomes,
IEM functions as a futures market, meaning that participants’ relative willingness to invest money in spe-
cific outcomes reflects their beliefs regarding which electoral outcome is most likely. Because contracts
are priced within [$0, $1], the price of a contract can be interpreted directly as a probability associated
with the object of the contract.15 As Crosson notes, while political scientists have used these data in the
past, such studies typically assess the markets as prospective predictors of electoral outcomes—and not as
a measure of how electoral expectations might influence the policymaking process. However, given that
the IEM is typically active only during election years, Crosson interpolates between election years by fit-
ting average monthly share prices using a variety information that may have informed politicians’ beliefs
regarding probabilities of partisan control. is information includes economic indicators such as unem-
ployment rates and consumer sentiment, baseline political information such as the size of a party’s majority
and (in the Senate) the number of a party’s members up for reelection, and granular political data such as
presidential and congressional approval rates—in addition to generic congressional vote ballot polls.16
Figure 2 depicts monthly interpolated share prices for Republican and Democratic majority control
in the House and Senate. Unsurprisingly, these probabilities vary considerably both within and across
congresses, providing the variance necessary to test Hypothesis 2 with the data. However, it is important
to note that given our operationalization of ρas the probability that one’s party gains majority control,
our empirical tests of Hypothesis 2 only apply to current members of the minority party. Put differently,
if member iis currently in the majority and the policy window is nevertheless closed, it is not clear that
retaining majority control will have an appreciable influence on the likelihood that the policy window
15For more information, see https://iemweb.biz.uiowa.edu/about/
16For more detailed information, see Crosson (2019), Appendix D
17

Figure 2: Predicted Probabilities of Majority Control by Republicans (Red) and
Democrats (Blue)
(a) House
(b) House
Interpolated IEM scores by presidency, indicating the expected probability that each party will hold the majority after the upcoming
election. Vertical ticks indicate the date of each upcoming election (after which point the probabilities “reset” and refer to the next
election thereafter).
18

opens. For these reasons, using these electoral data, we test Hypothesis 2 using only members of the
minority party.
Member Proximity to the Status Quo (λijt). Finally, according to Hypothesis 3, we should
observe that members whose preferences differ most from the status quo will most frequently message.
In order to test this hypothesis, the ideal measurement would compare each member i’s ideal point with
the status quo location associated with issue j. Unfortunately, while cIGscores do provide status quo
estimates and legislator ideal points on the same scale, the method generates status quo estimates at the
bill level—and not the issue level. us, in order to measure λ, we need to make some assumptions about
the distribution of status quo policies facing members of Congress.
Generally speaking, according to veto players/pivotal politics theory (Krehbiel, 1998; Tsebelis, 2002),
policy should, on average, move to toward the center of the political spectrum over time. at is, because
out-of-equilibrium status quo policies lie near the fringes of the political distribution while gridlocked
status quos near the center remain immovable, policy changes over time lead policy to amass in the cen-
ter of the distribution over time. is is especially true for political systems with large numbers of veto
players, such as the United States, as such systems have large gridlock intervals or cores—meaning that
movable status quo policies are the those that lie at the farthest reaches of the political spectrum. Moreover,
once moved, these policies are not likely to be moved again for a considerable amount of time (Tsebelis,
2002; Tsebelis, Money, Jeannette et al., 1997). e resulting distribution may then resemble the hypo-
thetical distribution depicted in Figure 3a, wherein most status quo policies lie toward the center of the
distribution, with only a out-of-equilibrium status quo policies lying to the far right and left.
If the distribution of status quo policies appears as in Figure 3a, then we should expect that members
of Congress with ideal points farthest from the center of the political distribution will, on average, find
themselves far away from most status quo policies. Consequently, we hypothesize that, consistent with
Hypothesis 3, members of Congress lying farthest from their respective chamber medians should, overall,
message more so than do members located closer to the center of the political spectrum.
Of course, as many past studies of Congress have underscored, agenda-setters do not target status quos
randomly. Instead, particularly if one conceives of the majority party as Congress’s agenda-setters (Cox and
McCubbins, 1993, 2005; Lee, 2016), status quo policies are likely selected so as to maximize policy gains
for the majority party (and minimize fracturing of the caucus). If this is the case, then the distribution of
targeted status quos within congress twill differ considerably from the overall distribution of status quos.
19

Figure 3: Overall and Targeted Distributions of Status Quo Policies
(a) Hypothetical Overall Distribution of
Status Quos
(b) Actual Distribution of Targeted Status
Quos
Left panel depicts hypothetical distribution of all status quo policies at any given point in time, based on general predictions provided
by veto players and pivotal politics theory. The right panel compares that overall distribution with the actual distribution of status
quos targeted by Republican- and Democratic-sponsored bills in our data.
More specifically, partisan agenda-setters face incentives to focus their policymaking on status quos that
lie farthest from their party median. Indeed, not only are changes to these status quo policies least likely
to fracture the caucus, but they also carry with them the largest spatial improvements to policy.
If agenda-setters do target status quo policies in this fashion, the distribution of targeted status quo
policies is likely to lean leftward or rightward, based on majority control of the chamber. In fact, Crosson,
Lorenz, and Furnas’s data provides some direct evidence to this effect. In Figure 3b, two actual status
quo policy densities are overlaid on the hypothetical distribution in Figure 3a. As the figure plainly de-
picts, Republican members overwhelmingly target left-leaning status quos in their bill sponsorship, while
Democratic members clearly favor conservative ones. Assuming partisan agenda-setters behave similarly,
then, our measure of λshould incorporate this information in some fashion. us, we include a term in
our regressions that captures a member’s distance from the majority party median.
Unlike the coefficient on overall extremity (distance from chamber median), we expect the coefficient
on distance from the majority party median to be negative: members farthest from the majority median are
actually closest to the center of distribution of targeted status quos. In other words, a left-leaning Democrat
should expect that the status quo policies of interest to a Republican majority will lie quite proximate to
her own ideal point, lowering her probability of messaging. To be clear, we do not believe that this
20

dynamic will overcome the general tendency for extremists to message more frequently overall. Instead,
conditional on overall ideological extremity (which we believe will always encourage messaging behavior
in our framework), there are conditions under which some extremists should be expected to message less
frequently than others: namely, members who lie far from the majority median should message less often
than those who lie closer to it.
Confounds. In order to remain as true as possible to the parameters of the model, we have generally
refrained from introducing a large vector of control variables to our models. Instead, we include both
issue- and congress-level fixed effects, to at least partially address unobserved confounds by time period
and issue area. However, we do include one member-level covariate—Seniority—in each of our models.
We do so because we believe seniority may map onto one of the parameters of our model for which we
have not generated hypotheses, namely the cost of messaging (k). Indeed, it is entirely possible that more
seniors members of Congress have not only amassed the legislative experience necessary to efficiently and
effectively offer message legislation, but they may even have the ability to recycle language from previous
messaging bills into their current bill introductions. Given the role that kplays in the dynamics of the
model, and given the general importance of seniority to many facets of congressional politics, we therefore
include it in all of our regressions. We draw these data from the Center for Effective Lawmaking (www
.thelawmakers.org).17
Taken together, our measurements result in the following model specification, which will serve as the
basis for our empirical tests:
P r(Mijt = 1) =µ+αj+δt+β1ζijt +β2ρijt +
β3|ℓi−mc|it +β4|ℓi−mm|it +Xβ+ϵit
In this specification, λis simply decomposed into two parts, legislator i’s (ℓi) distance from the chamber
median (mc) and her distance from the majority median (mm). Based on our hypotheses, we expect β1
and β3to be positive for all members, β2to be positive for members of the minority, and β4to be negative.
17It is worth noting here that we did incorporate other member-level covariates from the Center for Effective Lawmaking
dataset, to ensure the robustness of our results. ese inclusions did not influence the substantive results of our hypothesis tests.
21

Inference and Results
As noted above, we report results from a series of regressions, which model member i’s decision to mes-
sage on issue jas a function of a variety of parameters of our theoretical model. Before executing those
regressions, however, we must first confront one final methodological challenge—namely, a selection issue
generated by our measurement of messaging legislation.
In order to capture cutpoints on bills as introduced, which provides the basis for identifying both
proposal and status quo locations, Crosson, Lorenz and Furnas rely upon early-stage position-taking by
interest groups. In spite of the methodological usefulness of this position-taking, however, the measure-
ments’ reliance on this phenomenon necessarily implies that not all instances of messaging are detected
using this measurement strategy. Put differently, a failure to observe messaging in issue jcould be due
to either a member’s decision against messaging—or simply the fact that the measurement strategy did
not detect messaging that actually did occur. If these errors were randomly distributed, this issue would
not be especially problematic. However, assuming these errors are not randomly distributed, our empir-
ical specification requires a correction that addresses this selection issue. at is, we require an empirical
approach that effectively distinguishes between actual decisions against messaging and simple missingness
due to measurements strategy.
We believe that Heckman-style selection models provide a framework addressing for this issue. at
is, because we understand that interest group bill attention generates our selection issue, it is possible
to specify a series of models that capture and address biases arising from interest group issue attention.
us, we adopt a two-stage estimation approach that first models members’ decisions to sponsor legislation
on issue jand in congress t—a necessary condition for messaging in our model—and then adjust the
estimation of our messaging model accordingly.
More specifically, we estimate a first-stage model of bill sponsorship as:
P r(Sijt = 1) = (Zγ+ϵ)
where Sijt represents i’s decision to sponsor in issue jduring Congress tand Zcaptures variables influenc-
ing Sijt . In our models of bill sponsorship, we include variables for the number of bill sponsorships that
member ioffered in congress t, the number of interest groups active in issue j, issue-level fixed effects, and
congress-level fixed effects. By estimating this model, we are then able to estimate the following modified
22

specification of our base model:
P r(Mijt = 1|S = 1) = Xβ+rσu
1
h(x)(Zγ)
where requals the correlation between ϵand unobserved determinants uof M,σurepresents the variance
of u,1
h(x)represents the inverse Mills ratio, and Xβcaptures the base model specification of messaging
decision detailed above. Below, we present the results of this portion of the estimation.18 Results from the
selection stage, as well as from the “naive” models (which exhibit substantively similar results), are available
in Supplemental Information C.
Findings
Using this specification, we find consistent evidence in favor of two of our three hypotheses. Our results
are reported in Table 1. As the table depicts, Salience to Constituency (ζ) is positively associated with
messaging behavior, as predicted in Hypothesis 1. Of note, however, the table also underscores that this
association is driven in large part by members of the minority party. Indeed, the second and third models
of the table rerun our regressions using only majority and minority member data, respectively, allowing us
to examine whether dynamics differ based on this important factor. Our results indicate that salience is
especially important to members of the minority, as they decide whether or not to message on a particular
issue.
With regard to our two measures of λor a member’s distance from the average status quo policy
(both targeted and non-targeted), we find similar support consistent with the claims of our hypotheses.
In this case, consistent with Hypothesis 2, a legislator’s distance from the chamber median is strongly and
positively associated with messaging. Also consistent with our expectations, controlling for distance from
chamber median, distance from the majority median is negatively associated with messaging activity. In
both cases, if status quo policies are distributed as we argue, we find evidence that distance from status
quo policies is positively associated with virtue signaling.
For both ζand λ, our results are not only statistically significant but also substantively notable. Figures
5a and 5b depict predicted probabilities of messaging for different values of salience, distance from chamber
median, and distance from majority median, holding all other variables at their means or modal values.
As the figures depict, a shift from low to high values of each variable corresponds with notable changes in
18We opt for linear probabilities in our main analysis, for ease of interpretation. Results are substantively similar when
modeling the binary nature of the data directly.
23

Figure 4: Salience (ζ) and Predicted Probability of Messaging
Figure depicts predicted probability of messaging, holding all other variables at their means or modal values. The shaded area does
not depict confidence intervals. Rather, it represents the range of predicted values if one generates predictions for each of the congress-
and issue-level fixed effect values. Predictions are from the full model in Table 1.
24

Table 1: Models of Messaging, 109th - 114th Congresses
P r(Mijt = 1|S = 1)
(All) (Majority) (Minority)
Salience to Constituency 0.514∗∗ 0.235 0.793∗∗∗
(0.231) (0.339) (0.277)
Pr(Opening Policy Window) −0.005 −0.015 0.004
(0.012) (0.021) (0.019)
|ℓi−mc|0.071∗∗∗ 0.086∗∗∗ −0.039
(0.022) (0.028) (0.057)
|ℓi−mm| −0.095∗∗∗ −0.058 0.010
(0.017) (0.036) (0.054)
Member Seniority 0.002∗∗∗ 0.003∗∗∗ 0.001
(0.0005) (0.001) (0.001)
Constant −0.044∗−0.031 −0.084∗∗
(0.026) (0.040) (0.034)
Observations 40,972 22,697 18,275
Heckman’s rho 0.078 0.086∗∗ 0.115
Inverse Mills Ratio 0.019∗∗∗ 0.021∗∗∗
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
messaging probability. As the figures demonstrate, absent changes in the variables of interest, the baseline
probability for messaging in any given issue area is close to zero. However, in the case of issue salience,
for example, minority members (depicted in blue) at the highest levels of issue salience message with
a probability of nearly twenty percent. Likewise (though to a smaller extent), a movement from the
smallest to largest distance from the chamber median in our data is associated with an increase in messaging
probability—in this case, approximately seven percent. Conversely, a shift from the nearest proximity
to the majority median to the farthest is associated with a roughly nine percent decrease in messaging
probability.
Unlike with ζand λ, it is important to note that the results for ρwere much less strong. As noted above,
our predictions about ρ, as measured, apply only to the third model in Table 1 (minority party cases).
Here, although the coefficient on probability of gaining majority status lies in the expected (positive)
direction, it fails to achieve standard levels of statistical significance. One possibility for this weakened
result derives from the indirect nature of our measurement: that is, while our model parameterizes the
probability of the policy window opening for a particular issue area, our measurement captures a single
probability of gaining majority status. Moreover, even if one gains majority status, divided government,
divided legislatures, or general bargaining failures always have the potential to stymie policy changes—a
component of the “policy window” that our measure also does not capture. Nevertheless, we cannot reject
25

Figure 5: Distance to Status Quo (λ) and Predicted Probability of Messaging
(a) |ℓi−mc| (b) |ℓi−mm|
Figure depicts predicted probability of messaging, holding all other variables at their means or modal values. The shaded area does
not depict confidence intervals. Rather, it represents the range of predicted values if one generates predictions for each of the congress-
and issue-level fixed effect values. Predictions are from the full model in Table 1. The left panel depicts the first term associated with
distance from the status quo, Distance from Chamber Median, while rightward panel depicts the second term, Distance from
Majority Median.
the null that ρ, as measured, is statistically indistinguishable from zero.
Viable Proposals as a Robustness Check
Generally speaking, the results presented above provide support for our theory of message legislation and
virtue signaling. is support notwithstanding, one may levy the reasonable objection that the patterns
we uncover are emblematic of bill sponsorship patterns generally—and not messaging sponsorship specif-
ically. To address this concern, we conclude by re-estimating the above models, this time using viable bill
sponsorships, instead of non-viable, messaging ones. By viable legislation, we simply mean the inverse of
messaging legislation: legislation that would be expected to pass into law, were it brought up for a vote.
us, viable legislation is defined simply as:
Vbt =




1|qbt −Vt| ≥ |pbt −Vt|
0|qbt −Vt|<|pbt −Vt|
26

with issue-level viable legislative defined as
Vijt =




1Vibt = 1
0otherwise
We believe that, should we observe similar empirical results modeling viable legislation as non-viable
(using the above selection adjustments), such a result would cast doubt on the specificity of our messaging
results. Instead, such a result might indicate that factors such as salience and extremity are more general
predictors of prominent bill sponsorships. Inasmuch as viable proposals do not follow these patterns,
however, such a result would lend greater credibility to our messaging-specific results.
Table 2: Models of Viable Legislating
Probability of Offering Viable Bill
(All) (Majority) (Minority)
Salience to Constituency 0.161 0.161 0.238
(0.279) (0.435) (0.268)
Pr(Opening Policy Window) 0.022∗0.008 0.004
(0.013) (0.026) (0.017)
|ℓi−mc| −0.072∗∗∗ −0.027 −0.020
(0.011) (0.034) (0.016)
Member Seniority 0.002∗∗∗ 0.004∗∗∗ −0.001
(0.001) (0.001) (0.001)
Constant −0.029 −0.059 −0.036
(0.032) (0.053) (0.032)
Observations 36,250 19,742 16,508
Heckman’s rho 0.077 0.077∗0.120
Inverse Mills Ratio 0.016∗∗ 0.016∗
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Table 2 depicts the results of these regressions. As the table depicts, the results for models of viable
legislation differ considerably from those in the messaging models. With regard to salience, for example,
the results fall far short of reaching standard levels of statistical significance. Moreover, with regard to
member extremity, the association with viable legislating is negative—opposite its association with mes-
saging legislation. Given these relatively stark difference from messaging dynamics, we believe these results
provide additional evidence regarding the validity of the tests of our theory.
27

Discussion
Seasoned observers of Congress have long appreciated how members use roll-call votes and bill introduc-
tions to engage in position-taking (Mayhew 1974). New theory and new data allows us to gauge the
extent of and systematic variation in an important form of legislative position-taking, congressional mes-
sage legislation—hopeless bills that signal to constituents a desirable trait, policy making zeal, in their
representative.
e principal empirical findings of this research are:
1. Message legislation is extraordinarily pervasive. Our empirical measures indicate that the majority
of introduced bills are not viable.
2. Message legislation tends to address highly salient topics in the member’s district. is is particularly
true for minority party members.
3. Messagers tend to be ideological extremists – a legislator’s distance from the chamber median is
strongly and positively associated with messaging.
4. Members whose preferences likely accord with status quo policies targeted by the majority party tend
to message somewhat less in those policy domains.
5. e volume of minority-party message legislation does not measurably increase in anticipation of
the minority party gaining control of Congress.
6. Viable legislation displays quite different empirical patterns than non-viable legislation.
With the exception of the fifth pattern, these empirical findings follow closely from or are compatible with
our theory of message legislation.
e sheer volume of “bogus’’ rather than “bona fide’’ lawmaking raises serious normative questions
about the institutional performance of Congress. An in-depth exploration of this theme lies outside our
scope here, but the theoretical model identifies three factors that are important in a normative assessment
of message legislation.
First, message legislation helps voters select zealous representatives. is zeal may prove advantageous
to constituents should their representative ever be in a position to influence real policy-making, rather
than to pantomime policy-making. Perhaps contrary to one’s initial expectation, then, message legislating
can actually boost voter welfare by improving the selection of representatives with valued traits.
28

Second, however, fake policy-making is not cost-free: it comes at the expense of other activities. If the
alternative uses of time and effort have negligible value, then the cost of virtue signaling is small. But if
those activities are precious, as previous research such as Hall (1996) suggests, then the cost can be very high
indeed. More than that, the activities most likely to be sacrificed in favor of public signaling are those “work
horse’’ style activities (Hall, 1996) that voters cannot immediately perceive (Holmstrom and Milgrom,
1991). Examples include painstaking investment in institutional knowledge and personal relationships,
careful and extended investigation of genuine social problems, the construction of thoughtful and effective
legislative remedies, and the dutiful oversight of bureaucratic performance. Here, the implications of a
maelstrom of nonviable lawmaking are disturbing.
ird, if message legislation actually helps voters retain policy zealots, then the composition of the
legislature may shift over time. To be sure, the implications are not entirely clear. However, selection for
policy zealots may build cadres of hard-edged lawmakers who eschew compromise with the opposition,
and who scorn or defy their own party leaders. Tea Party legislators and the left-leaning “squad” may
provide recent examples. is institutional evolution may result not just in a decline in comity, but more
troubling, in the degradation of legislative capacity.
Conclusion
Modern accountability theory identifies several perverse incentives created by representation. ese in-
clude “pandering’’—the knowing selection of popular but harmful policies whose ill consequences fall
beyond the next election; “blame-game politics’’—the deliberate construction of policies whose main in-
tent is to cast opponents in an ill light; and biased representation—deliberate favoritism aimed at the
organized and knowledgeable.19 In this paper, we construct new theory and develop new data to study a
phenomenon distinct from these perverse incentives: namely, virtue signaling via hopeless message bills.
e theory puts new flesh on the bones of Mayhew’s path-breaking analysis of legislative position-taking,
while the data underscore the pervasiveness of message legislation in recent congresses and highlight previ-
ously unnoted empirical regularities. Our analysis complements recent studies of hopeless obstructionism
in the form of doomed filibusters and vetoes.20
We only scratch the surface of a rich topic. Extensions to the theory, here kept simple in order to
ground the empirical investigation, would allow a more detailed exploration of the normative implications
19See, respectively, Canes-Wrone, Herron and Shotts (2001), Groseclose and McCarty (2001), and Achen and Bartels (2017).
20See Patty (2016) and Cameron and Gibson (2020).
29

of message legislation. Empirically, historical evidence on the incidence of message bills over time, and
of bona fide legislating, would be valuable in assessing the dynamics of institutional change. Although
we focus here on Congress, purely performative politics can be found in many other settings as well.
An obvious venue is state legislatures, where newly developed estimates of bill locations make feasible
empirical studies similar to ours (ieme, 2020). Further afield, elected state attorneys general often sue
the federal government, sometimes in hopeless or near frivolous lawsuits, perhaps endeavoring to display
their zealousness to state voters (Dean, 2021). Interest group leaders sometimes “tilt at windmills,’’ for
example, submitting likely ineffectual amicus briefs to high courts or demonstrating over symbolic goals,
perhaps in an effort to display policy zeal to donors and members. Nor are such examples restricted to the
U.S. One may observe likely examples across representative democracies. New perspectives on the theory
and empirics of performative politics and political virtue signaling may prove useful in understanding these
phenomena too.
Acknowledgements
We thank seminar participants at Princeton and the University of California at San Diego, especially Seth
Hill, Frances Lee, Nolan McCarty, Tom Romer and particularly Federica Izzo, for helpful comments and
suggestions.
30

References
Achen, Christopher and Larry Bartels. 2017. Democracy for realists. Princeton University Press.
Cameron, Charles M. and John M. de Figueiredo. 2020. “Quitting in Protest: Presidential Policymaking
and Civil Service Response.” Quarterly Journal of Political Science 15(4):507–538.
Cameron, Charles and Nathan Gibson. 2020. “New Directions in Veto Bargaining: Message Legislation,
Virtue Signaling, and Electoral Accountability.” The SAGE Handbook of Research Methods in Political
Science and International Relations p. 224.
Canes-Wrone, Brandice, Michael C Herron and Kenneth W Shotts. 2001. “Leadership and pandering:
A theory of executive policymaking.” American Journal of Political Science pp. 532–550.
Clinton, Joshua D. 2017. “Coding the Ideological Direction and Content of Policies.” Annual Review of
Political Science 20(1):433–450.
Clinton, Joshua, Simon Jackman and Douglas Rivers. 2004. “e statistical analysis of roll call data.”
American Political Science Review 98(2):355–370.
Cox, Gary W and Mathew D McCubbins. 1993. Legislative Leviathan: Party Government in the House.
Berkeley: University of California Press.
Cox, Gary W and Mathew D McCubbins. 2005. Setting the agenda: Responsible party government in the
US House of Representatives. Cambridge University Press.
Crosson, Jesse. 2019. Agenda Control and Policy Change in American Legislatures: How Partisan Unity
and Electoral Competition Encourage Change and Stasis in US Politics PhD thesis.
Crosson, Jesse M, Alexander C Furnas and Geoffrey C Lorenz. 2019. “Estimating Pro-
posal and Status Quo Locations for Legislation Using Cosponsorships, Roll-Call Votes, and
Interest Group Bill Positions.” Massachusets Institute of Technology, Cambridge, Massachusets.
https://polmeth.mit.edu/sites/default/files/documents/Jesse_Crosson.pdf .
Crosson, Jesse M, Alexander C Furnas and Geoffrey M Lorenz. 2020. “Polarized Pluralism: Organizational
Preferences and Biases in the American Pressure System.” American Political Science Review .
31

Dean, Julian. 2021. “How State Attorneys General Use Litigation Against the Federal Government to
Seek Re-election.” Working Paper, Department of Politics, Princeton University.
Gailmard, Sean. and John W. Patty. 2007. “Slackers and Zealots: Civil Service, Policy Discretion, and
Bureaucratic Expertise.” American Journal of Political Science 51(4):873–889.
Gilmour, John B. 1995. Strategic Disagreement: Stalemate in American Politics. Pittsburgh: University of
Pittsburgh Press.
Groseclose, Tim and Nolan McCarty. 2001. “e politics of blame: Bargaining before an audience.”
American Journal of Political Science pp. 100–119.
Hall, Richard L. 1996. Participation in congress. Yale Univ Pr.
Holmstrom, Bengt and Paul Milgrom. 1991. “Multitask principal-agent analyses: Incentive contracts,
asset ownership, and job design.” JL Econ. & Org. 7:24.
Krehbiel, Keith. 1998. Pivotal politics: A theory of US lawmaking. University of Chicago Press.
Lee, Frances E. 2016. Insecure majorities: Congress and the perpetual campaign. University of Chicago Press.
Lorenz, Geoffrey M, Alexander C Furnas and Jesse M Crosson. 2020. “Large-N bill positions data from
MapLight. org: What can we learn from interest groups’ publicly observable legislative positions?”
Interest Groups & Advocacy pp. 1–19.
Mailath, George, Masahiro Okuno-Fujiwara and Andrew Postlewaite. 1993. “Belief-Based Refinements
in Signalling Games.” Journal of Economic Theory 60:241–276.
Mayhew, David. 1974. Congress: The Electoral Connection. New Haven: Yale University Press.
Patty, John. 2016. “Signaling through Obstruction.” American Journal of Political Science 60(1):175–189.
Peress, Michael. 2013. “Estimating proposal and status quo locations using voting and cosponsorship
data.” The Journal of Politics 75(3):613–631.
Poole, Keith T and Howard Rosenthal. 1991. “Patterns of congressional voting.” American journal of
political science pp. 228–278.
32

Poole, Keith T and Howard Rosenthal. 1997. Congress: A political-economic history of roll call voting.
Oxford University Press.
The Bills to Nowhere. 2012. The New York Times .
URL: https://www.nytimes.com/2012/06/08/opinion/the-bills-to-nowhere.html
ieme, Sebastian. 2020. “A Direct Test of Legislative Gatekeeping.” Legislative Studies Quarterly .
Tsebelis, George. 2002. Veto players: How political institutions work. Princeton University Press.
Tsebelis, George, Jeannette Money, George Money Jeannette et al. 1997. Bicameralism. Cambridge
University Press.
33

Supplementary Materials
Message Legislation and the Politics of Virtue Signaling
Daniel Gibbs, Jesse M. Crosson, and Charles Cameron
Contents
A Measurement and Visualization of Dependent Variable SM—2
A.1 Additional Information on cIGscores . . . . . . . . . . . . . . . . . . . . . . . . . . SM—2
A.2 OutcomeVariable .................................... SM—4
B Measurement of Salience SM—5
B.1 Validity check for Bridging pre- and post-2013 employment data . . . . . . . . . . . . SM—5
B.2 Industry to Issue-Area Crosswalk . . . . . . . . . . . . . . . . . . . . . . . . . . . . SM—6
C Alternative Specifications and Details from Model Estimation SM—7
C.1 Models of Sponsorship Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SM—7
C.2 “Naive” Models of Messaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SM—7
D eory SM—9
D.1 StrategiesandBeliefs................................... SM—9
D.2 Messaging Equilibrium Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . SM—9
D.3 No-legislation Equilibrium Definition . . . . . . . . . . . . . . . . . . . . . . . . . . SM—10
D.4 ProofofProposition1.................................. SM—10
SM—1

A Measurement and Visualization of Dependent Variable
A.1 Additional Information on cIGscores
Below, we include several visualizations of cIGscores, as provided by Crosson, Lorenz and Furnas. Figure
A.1 compares the distribution of legislator ideal points in the data (ℓiin our model, dotted lines in the
graphs) with the distribution of proposal locations (pbt, shaded regions). For both ℓiand pbt, red represents
Republicans (either Republican ideal points or Republican-sponsored bill locations) and blue represents
Democrats.
Figure A.1: cIGscores for Proposals and Ideal Points
0.00
0.25
0.50
0.75
1.00
-3 -2 -1 0 1 2 3
Ideological Location
Democratic Members
Republican Members
Democratic Sponsored Bills
Republican Sponsored Bills
Figures A.2 and A.3 depict cIGscores for legislators and interest groups in relation to other measures
of those actors’ preferences. Figure A.2 demonstrates that the inclusion of cosponsorship data into the
estimation matrix did not appreciably change the recovered IGscores (Crosson, Furnas and Lorenz, 2020)
for interest groups and legislators. Likewise, the inclusion of both interest groups and cosponsorships
resulted in similar ideal points as generated by NOMINATE, depicted in Figure A.3.
SM—2

Figure A.2: cIGscores v. IGscores
-2.5
0.0
2.5
5.0
-2 0 2 4
cIGscore
IGscore
Interest Group?
0
1
Figure A.3: cIGscores v. NOMINATE
-2
-1
0
1
2
-2 -1 0 1 2
cIGscore
Mean DW-NOMINATE Score
SM—3

A.2 Outcome Variable
Figure A.4: Distribution of Messaging by Issue Area
Decisions to message in each issue area by members of Congress who messaged in at least one issue area during a given Congress.
Points are jittered around 1 and 0, which correspond to the decision for/against messaging in the given issue area.
SM—4

B Measurement of Salience
B.1 Validity check for Bridging pre- and post-2013 employment data
Below, Figure B.1 depicts the correlation between district employment in 2013, using the Census-provided
estimates (y axis) and our zip-based estimates (x-axis). Here, the unit of analysis is the NAICS industry-
district. As the figure depicts, although differences are not uncommon, the correlation between the two
measures remains strong. is correlation, not depicted here, notably increases when NAICS industry are
crosswalked to issue codes, as used in the main analysis. Particularly when combined with the congress-
level fixed effects we employ in our models, these measurements provide a viable means of extending the
Census’s estimates backward in time
Figure B.1: District-Level versus Adjusted Zip-Code Level Estimates of Employment
SM—5

B.2 Industry to Issue-Area Crosswalk
NAICS Sector Name Policy Agendas Topic
Agriculture, forestry, Environment,Public Lands and Water Management;
fishing and hunting Agriculture; Immigration, Labor and Employment
Mining, quarrying and oil and Energy; Environment; Public Lands and Water
gas extraction Management
Utilities Energy; Environment
Construction Labor and Employment; Transportation;
Community Development and Housing Issues;
Environment; Government Operations;
Public Lands and Water Management
Manufacturing Labor and Employment; Environment; Energy;
Foreign Trade; Banking, Finance, and Domestic
Commerce; Macroeconomics
Wholesale trade Banking, Finance, and Domestic Commerce;
Foreign Trade; Macroeconomics; Transportation
Retail trade Banking, Finance, and Domestic Commerce,
Foreign Trade; Macroeconomics; Labor and Employment
Transportation and warehousing Energy; Transportation; Labor and Employment
Information Space, Science, Technology, and Communications
Educational services Civil Rights, Minority Issues, and Civil Liberties;
Education
Finance and insurance Macroeconomics; Community Development and
Housing Issues; Foreign Trade; Banking, Finance,
and Domestic Commerce; International Affairs and
Foreign Aid
Real estate and rental and leasing Civil Rights, Minority Issues, and Civil Liberties;
Community Development and Housing Issues;
Public Lands and Water Management; Banking,
Finance, and Domestic Commerce
Professional, scientific, and technical Space, Science, Technology, and Communications;
services Foreign Trade; Defense; Health; Education;
Immigration; Law, Crime, and Family Issues;
Civil Rights, Minority Issues, and Civil Liberties
Management of companies Macroeconomics; Education; Banking, Finance, and
Domestic Commerce; Foreign Trade
Administrative support, waste Public Lands and Water Management; Government
management, and remediation service Operations; Environment; Health
Health care and social assistance Health; Social Welfare
Arts, entertainment, and recreation Education
Accommodation and food services Agriculture; Health; Immigration;
Labor and Employment
Other services (except public admin.) Civil Rights, Minority Issues, and Civil Liberties;
Law, Crime, and Family Issues; Social Welfare
Public Administration Government Operations
SM—6

C Alternative Specifications and Details from Model Estimation
Below, we present the results of the model of sponsorship that precedes our adjusted models of messaging
decisions. According to the results of this model, many issue areas themselves appear to attract dispro-
portionately high or low sponsorship activity. Issue areas with especially high numbers of interest groups
appear to be more likely to experience sponsorship activity. Moreover, members who are legislatively active
overall appear more likely in general to engage in bill sponsorship within particular issue-congresses.
C.1 Models of Sponsorship Selection
Table C.1: Results from Selection / Bill-Sponsorship State of Estimation
Dependent variable:
Sponsored Bill in Issue-Congress
Total Number of Bill Sponsorships in Congress t0.053∗∗∗
(0.001)
Groups Active in Issue j0.0003∗∗∗
(0.0001)
Fixed EffectsaIssue, Congress
Observations 51,082
Log Likelihood −29,070.160
Akaike Inf. Crit. 58,192.320
aSignificant issue-area fixed effects include: Civil Rights (-), Health (+), Agriculture (-), Labor (-), Environment (-), Immigration (-), Transportation (-), Social
Welfare (-), Community Development (-), Banking (+), Defense (+), Science and Technology (-), International Affairs (-), Foreign Trade (-), Government Operations
(+), Public Lands (+). Significant session fixed effects include: 112th (-), 113th (-), and 114th (-) Congresses.
C.2 “Naive” Models of Messaging
In Table C.2, we present results from our main models, estimated without any adjustments for selection. As
the table depicts, the results are substantively similar to those presented in the main text, with both salience
and distance from status quo policies correlating positively and significantly with messaging behavior.
SM—7

Table C.2: Base Models of Messaging, Not Accounting for Selection
Dependent variable:
(All) (Majority) (Minority)
Salience to Constituency 0.291∗∗∗ 0.173 0.399∗∗∗
(0.104) (0.157) (0.120)
Pr(Opening Policy Window) −0.012∗∗ −0.040∗∗∗ 0.011
(0.005) (0.010) (0.009)
|ℓ−mc| 0.037∗∗∗ 0.041∗∗∗ −0.014
(0.010) (0.013) (0.029)
|ℓ−mm|−0.050∗∗∗ −0.021 0.003
(0.008) (0.016) (0.028)
Member Seniority 0.001∗∗∗ 0.002∗∗∗ 0.0003
(0.0002) (0.0003) (0.0003)
Constant −0.006 0.027 −0.030∗∗
(0.012) (0.019) (0.015)
Observations 21,805 13,096 8,709
R20.020 0.025 0.016
Adjusted R20.018 0.023 0.013
Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
SM—8

D Theory
D.1 Strategies and Beliefs
Let γ∈Γ = {s, z}denote the incumbent legislator’s type. A pure strategy for the legislator is a mapping
from his type into the number of times he chooses to make a non-viable attempt to change the status quo
n: Γ →N
e voter’s decision depends on her beliefs given the legislator’s actions in the first period and the
private utility shock, ω, she receives from voting for the incumbent. We assume that the distribution of
taste shocks, F, is symmetric and absolutely continuous. Let fdenote the density that Fadmits and Ω
denote the support of f. Formally, symmetry assumes that F(−y) = 1 −F(y)for all y∈Ω.
With probability ζ, the voter observes n, the number of times the incumbent legislates. With proba-
bility 1−ζ, the voter does not observe n. Let jdenote the voter’s information from the legislative stage. If
the voter observes the legislative stage, j=n. If the voter does not observe the legislative stage, let j=∅.
An information set for the voter is a pair, (j, ω). Let ϕdenote an information set for the voter and let
Φ = (N∪ ∅)×Ωdenote the set of all possible information sets. A pure strategy for the voter prescribes a
choice between the incumbent and challenger at each information set. e voter’s beliefs are a mapping
µ: Φ →[0,1]
where the voter believes the incumbent is a zealot with probability µ(ϕ)at information set ϕ.
D.2 Messaging Equilibrium Definition
We formally define a messaging equilibrium below. In the main text we define n∗≡ ⌈bζ[2F(λρ
2)−1]
k⌉as
lowest nsuch that the slacker weakly prefers no legislation and reelection probability 1−P∗to n∗and
reelection probability P∗.
Definition 1 (Messaging Equilibrium).In a messaging equilibrium,
SM—9

• slackers do not legislate: n∗(s) = 0
• zealots legislate n∗times: n∗(z) = n∗
• for all ϕsuch that j=n≥n∗
µ(ϕ) = 1
the voter reelects the incumbent if and only if λρ
2+ω≥0
• for all ϕsuch that j=∅
the voter reelects the incumbent if and only if ω≥0
µ(ϕ) = 1/2
• for all ϕsuch that j=n < n∗
µ(ϕ) = 0
the voter reelects the incumbent if and only if −λρ
2+ω≥0
D.3 No-legislation Equilibrium Definition
Definition 2 (No-legislation equilibrium).In a no-legislation equilibrium,
• neither type legislates: n∗(s) = n∗(z) = 0
• for all ϕ,
µ(ϕ) = 1/2
the voter reelects the incumbent if and only if ω≥0
D.4 Proof of Proposition 1
We derive the necessary and sufficient condition for the messaging equilibrium to exist, (1), in the main
text and show that (2), implies (1). We now prove that the messaging equilibrium is the unique undefeated
equilibrium. In any separating equilibrium, the voter learns the incumbent’s type if she observes n. us
in any separating equilibrium, the slacker is reelected with probability 1−P∗(ζ, λ, ρ)and the zealot with
probability P∗(ζ, λ, ρ). Because 1−P∗(ζ, λ, ρ)minimizes the incumbent’s probability of reelection, the
slacker must not legislate in any separating equilibrium. It follows that the slacker’s equilibrium expected
SM—10

payoff is the same in any separating equilibrium as it is in the messaging equilibrium. To prevent the
slacker from profitably imitating the zealot, the zealot must legislate at least n∗times in any separating
equilibrium. Because the zealot’s probability of reelection is the same in any separating equilibrium, his
equilibrium expected payoff varies across separating equilibria only through the cost he incurs from leg-
islating. is cost is minimized in the messaging equilibrium. erefore if any separating equilibrium
exists, a messaging equilibrium exists. Moreover, the zealot receives a strictly higher payoff from n∗in
the messaging equilibrium than from the greater amount of legislation prescribed by any other separating
equilibrium. e undefeated refinement therefore requires that the voter believes that the incumbent is a
zealot with probability one in any separating equilibrium when she observes n∗. But a separating equilib-
rium in which the zealot legislates more than n∗requires that the voter believes the incumbent is a zealot
with less than probability 1/2 if she observes n∗(otherwise the zealot can profitably deviate to n∗). e
messaging equilibrium thus defeats all other separating equilibria.
In the main text we show that a NL equilibrium is defeated by a messaging equilibrium if and only if
(3) is satisfied. We now show that (3) implies that no other pooling equilibrium is undefeated. Consider
a pooling equilibrium in which incumbents choose ˜n > 0. In any pooling equilibrium, the incumbent is
reelected with probability 1/2. In order for this equilibrium to exist, the slacker must weakly prefer ˜nto no
legislation. e worst payoff the slacker can earn from deviating to no legislation is realized when the voter
believes the incumbent is a slacker with probability one when she observes no legislation. e minimum
deviation payoff is therefore equivalent to his payoff from no legislation in the messaging equilibrium.
erefore if a pooling equilibrium with ˜n > 0exists, the slacker earns a higher payoff from choosing ˜n
in the pooling equilibrium than from n∗is the messaging equilibrium. e zealot earns a payoff in the
pooling equilibrium of
(b+λρ
2)1
2−˜nk
e zealot therefore strictly prefers n∗in the messaging equilibrium to ˜nin the pooling equilibrium if and
only if
g(ζ, λ, ρ)+2k˜n > 2k⌈B∗
k⌉ − B∗
which is implied by (3). erefore the voter must believe µ(n∗) = 1 off path in the pooling equilibrium.
SM—11

But the pooling equilibrium requires µ(n∗)<1to prevent deviation by the zealot. erefore (2) implies
that the unique undefeated equilibrium is the messaging equilibrium.
It is straightforward to check that neither type of incumbent can profitably deviate from an NL equilib-
rium given the voter’s off-path beliefs specified in the definition of a NL equilibrium. At every information
set, the voter believes the incumbent is a zealot with probability 1/2. Deviations therefore do not raise the
incumbent’s probability of reelection but cost more. us if (3) fails, the NL equilibrium exists. Moreover,
because (3) implies that all pooling equilibria are defeated by the messaging equilibrium, the NL equilib-
rium exists and is undefeated by the messaging equilibrium if any pooling equilibrium is undefeated by
the messaging equilibrium.
We now prove that the NL equilibrium defeats all other pooling equilibria. In order for a pooling
equilibrium with legislation to exist, the voter must reelect the incumbent with less than probability 1/2 if
she unexpectedly observes no legislation. is requires that she believes the incumbent is more likely to be
a slacker when she observes no legislation. Both types of incumbent strictly prefer no legislation in the NL
equilibrium to any equilibrium amount of legislation in some other pooling equilibrium. e undefeated
refinement therefore requires that in any pooling equilibrium, the voter believes the incumbent is a zealot
with probability 1/2 when she observes no legislation. us the NL equilibrium is the only undefeated
pooling equilibrium. It follows that if the messaging equilibrium does not exist, the NL equilibrium the
unique undefeated equilibrium. □
SM—12