Rhetoric in Legislative Bargaining with Asymmetric
Arizona State University
H¨ ulya Eraslan
Johns Hopkins University
June 22, 2010
1We thank Ming Li and Jack Stecher for helpful comments and stimulating conversa-
tions, along with seminar participants at the Carnegie Mellon University, University of British
Columbia and Quebec Workshop on Political Economy. Any errors are our own.
In this paper we analyze a legislative bargaining game in which parties privately in-
formed about their preferences bargain over an ideological and a distributive decision.
Communication takes place before a proposal is offered and majority rule voting deter-
mines the outcome. When the private information pertains to the ideological intensities
but the ideological positions are publicly known, it may not be possible to have informa-
tive communication from the legislator who is ideologically distant from the proposer,
but the more moderate legislator can communicate whether he would “compromise” or
“fight” on ideology. If instead the private information pertains to the ideological po-
sitions, then all parties may convey whether they will “cooperate,” “compromise,” or
“fight” on ideology. When the uncertainty is about ideological intensity, the proposer
is always better off making proposals for the two dimensions together despite separable
preferences, but when the uncertainty is about ideological positions, bundling can result
in informational loss which hurts the proposer.
JEL classification: C78, D72, D82, D83
Legislative policy-making typically involves speeches and demands by the legislators
that shape the proposals made by the leadership. For example, in the recent health care
overhaul, one version of the Senate bill included $100 million in Medicaid funding for
Nebraska as well as restrictions on abortion coverage in exchange for the vote of Nebraska
Senator Ben Nelson. As another example, consider the threat by seven members of the
Senate Budget Committee to withhold their support for critical legislation to raise the
debt ceiling unless a commission to recommend cuts to Medicare and Social Security is
approved.1Would these senators indeed let the United States default on its debt, or
was their demand just a bluff? More generally, what are the patterns of demands in
legislative policy-making? How much information do they convey? Do they influence
the nature of the proposed bills? Which coalitions form and what kind of policies are
chosen under the ultimately accepted bills?
To answer these questions, it is necessary to have a legislative bargaining model in
which legislators make demands before the proposal of bills. One approach is to assume
that the role of demands is to serve as a commitment device, that is, the legislators refuse
any offer that does not meet their demands.2While this approach offers interesting
insights into some of the questions raised above, it relies on the strong assumption
that legislators commit to their demands.3In this paper, we offer a different approach
that allows legislators to make speeches but do not necessarily commit to them when
casting their votes. The premise of our approach is that only individual legislators know
which bills they prefer to the status quo. So even if the legislators do not necessarily
undertake what they say, their demands can be meaningful rhetoric in conveying private
information and dispelling some uncertainty in the bargaining process.
We model rhetoric as cheap-talk messages as in Matthews (1989). In our framework
2This is the approach taken by Morelli (1999) in a complete information framework. He does not
explicitly model proposal making and voting stage. As such, the commitment assumption is implicit.
3Politicians often carry out empty threats, for example, http://thehill.com/homenews/news/14312-
(1) three legislators bargain over an ideological and a distributive decision; (2) bargainers
other than the proposer are privately informed about their preferences; (3) communica-
tion takes place before a proposal is offered; (4) majority rule voting determines whether
the proposal is implemented. By introducing communication into legislative bargaining,
our goal is take a step towards answering fundamental questions of political economy,
“who gets what, when and how” (Lasswell, 1958), together with fundamental questions
of communication theory, “who says what to whom in what channel with what effect”
We begin by analyzing the case in which the legislators’ positions on a unidimensional
ideological spectrum are publicly known, but their trade-offs between the ideological
dimension and the distributive dimension are private information. So the proposer of
a bill (also referred to as the chair) is unsure how much private benefit he has to offer
to a legislator to gain support on a policy decision. When no equilibrium coalition is
a surplus coalition (i.e., at most one legislator other than the proposer gets positive
private benefit), we obtain two main findings: (1) the rhetoric of the legislator who is
ideologically more distant from the proposer is not informative in equilibrium; (2) it is
possible for the more moderate legislator to have meaningful rhetoric.
To establish these results, we first explore the legislators’ expected payoffs in different
coalitions. Suppose one legislator is offered positive private benefit while the other is
offered none (call this a minimum winning coalition). Then the legislator who is excluded
strictly prefers the status quo and will vote against the proposal whereas the legislator
who is included becomes pivotal and hence can guarantee a payoff at least as high
as the status quo. Alternatively, suppose no legislator is offered private benefit (call
this a minority coalition). Then the chair’s optimal proposal is the one that makes
the moderate legislator just willing to accept. Hence in a minority coalition the more
moderate legislator gets a payoff equal to the status quo but the more distant legislator
is made worse off than the status quo. It follows that the more distant legislator would
like to maximize his chance to be included in a coalition, thereby undermining the
credibility of his rhetoric. As to the more moderate legislator, it is possible for him to
have (at most) two equilibrium messages signaling his ideological intensity. When he
puts a relatively high weight on the ideological dimension, he sends the “fight” message,
and the chair responds with a minority coalition that excludes both legislators as their
demands indicate that there is no room for making a deal. When he puts a relatively
low weight on the ideological dimension, he sends the “compromise” message and the
chair responds by offering some private benefits in exchange for moving the policy closer
to his own ideal. The threshold type is indifferent between sending the “fight” and the
“compromise” messages because either way he gets a payoff equal to the status quo, and
a single-crossing property of the utility function guarantees that other types’ incentive
constraints are satisfied as well. It is impossible for even the moderate legislator to
convey more precise information about his ideological intensity. In particular, once the
chair believes that the moderate legislator puts a relatively low weight on ideology and
hence includes him in a minimum winning coalition, the legislator now has the incentive
to exaggerate his ideological intensity and demand a better deal from the chair, but
this undermines the credibility of his demands. Somewhat ironically, the proposal of a
minority coalition induced by the “fight” message always passes in equilibrium, but the
minimum winning coalition induced by the “compromise” message may fail to pass.
Next, we consider the case in which the legislators’ ideological intensities are known,
but their ideological positions are uncertain. The setup is related to Matthews (1989)
which models presidential veto threats as cheap talk in a bilateral bargaining game over
a unidimensional policy and assumes that the president’s position is his private infor-
mation. Our model differs from Matthews (1989) by having multiple senders and a
distributive dimension in addition to an ideological dimension. In this case, we find that
equilibrium demands from either legislator may convey limited information about their
preferences. In particular, legislators can signal whether they will “cooperate,” “com-
promise” or “fight.” If either legislator makes a cooperative speech, the chair responds
by proposing his ideal policy and a minority coalition in which he extract all the surplus
. If both legislators make tough demands by sending the “fight” message, the chair gives
up on the ideological issue and again does not give out any private benefits. Otherwise,
he proposes a compromise policy, which depends on whether one or both legislators sig-
nal willingness to compromise. Again, only the minimum winning coalition induced by
rule such that mi(ti) = m1
iif t ∈ [τ1
i], mi(ti) = m2
iif t ∈ (τ2
i] where τ1
i= −2 <
and he proposes a compromise policy y if both legislators send m2
i= 2; the chair proposes his ideal ˆ y0if at least one of the legislators send m1
i. The indifference
condition of type τ2
iimplies that τ2
i≈ −0.81. If both legislators send m2
i, the chair
responds with the proposal y ≈ −0.62, and the legislator i votes for the proposal if
and only if ti≤
payoff on the policy dimension is −0.36. Since he keeps the whole cake, his payoff on the
distributive dimension is 1. So the chair’s total expected payoff is 1−0.36 = 0.64, higher
than his expected payoff (= 0.56) in the size-three equilibrium if the two dimensions are
≈ −0.31. Calculation shows that the chair’s expected equilibrium
bundled together in negotiation. The reduction of payoff from bundling comes from the
loss of the cake when the legislators fail to reach an agreement, which happens when
both legislators send the “compromise” message but their ideological positions are too
far from the chair’s for them to find the resulting proposal attractive enough. Although
failure to reach an agreement also happens even if the legislators negotiate the ideological
dimension separately, the distributive dimension is shielded from such failure.
Another, perhaps less obvious, disadvantage of bundling is the information loss that
may result from bargaining the two dimensions together (or, as another interpretation,
the chair’s lack of commitment of not using private benefit in exchange for votes on
ideological decisions). This matters even if there is no risk of “losing the cake.” To
illustrate, suppose c = 0, so the break-down of agreement does not result in the dissipa-
tion of private benefits. In this case, we can interpret bundling of the two dimensions
together as (the possibility of) using side payments to gain support on an ideological
decision and separation of the two dimensions as the unavailability of side payments.
As shown in the previous paragraph, if no side payments are allowed, then there exists
an informative equilibrium in which the legislators send m1
iif tiis below τ2
iif ti is above τ2
i. When side payments are allowed, however, this is no longer an
equilibrium strategy if the chair puts a relatively low weight on the distributive dimen-
the argument provided in Matthews (1989) to show that each legislator’s message rule has at most
size two when they bargain over just the ideological dimension. Because it does not provide much new
insight, we omit the details of the modified argument here.
sion. For example, suppose θ0= 9, but keep all the other parametric assumptions in
Example 2 unchanged. If the legislators were to follow the message rule with the cutoff
i= −0.81, then, upon receiving m2
respond by proposing y equal to his ideal point ˆ y0and a side payment (= 3.8415) to one
ifrom both legislators, the chair would optimally
of the legislators. But this undermines the legislator i’ incentive to send m1
induces the chair’s ideal without the possibility of getting any side payment whereas the
other message m2
iinduces the chair’s ideal with a side payment as well. Indeed, in this
example there exists no informative equilibrium when the chair can use side payments in
his proposals. Because of this informational loss, the chair’s equilibrium payoff is lower
when side payments are allowed.18
5 Concluding remarks
In this paper, we develop a new model of legislative bargaining that incorporates pri-
vate information about preferences and allows speech making before a bill is proposed.
Although the model is simple, our analysis generates interesting predictions about what
speeches can be credible even without commitment and how they influence proposals
and legislative outcomes. We are also able to provide new insight into when legislators
should make proposals for different issues together and when they should make proposals
We believe that both private information and communication are essential elements of
the legislative decision making process. Our paper has taken a first step in understanding
their roles in the workings of a legislature. There are many more issues to explore and
many ways to generalize and extend our model and what follows is a brief discussion of
some of them.
Our motivation for incorporating private information into legislative bargaining is
that individual legislators know their preferences better than others. Another possible
18Harstad (2007) shows in another bargaining game that side payments may be harmful because
they increase conflict of interest and incentive to signal, resulting in more delay. The reason for side
payments to be harmful is different here.
source of private information is that some legislators may have better information (per-
haps acquired through specialized committee work or from staff advisors) regarding the
consequences of certain policies, which is relevant for all legislators. Although the role
of this kind of “common value” private information in debates and legislative decision
making has been studied in the literature (e.g. Austen-Smith (1990)), it is only in the
context of one-dimensional spatial policy making. It would be interesting to explore it
further when there is trade off between ideology and distribution of private benefits.
In our model the chair does not have private information about his preference, con-
sistent with the observation that bill proposers are typically established members with
known positions. But sometimes legislators can be uncertain about what exactly the
legislative leaders’ goals are, in particular, how much compromise the leaders are willing
to make to accommodate their demands in exchange for their votes. In this case, apart
from speeches, the proposal that the chair puts on the table may also reveal some of his
private information. This kind of signaling effect becomes particularly relevant when the
legislators have interdependent preferences or when the proposal is not an ultimatum
but can be modified if agreement fails.
We have focused on a specific extensive form in which the legislators send messages
simultaneously. It would be interesting to explore whether and how some of our results
change if the legislators send messages sequentially. In that case, the design of the
optimal order of demands (from the perspective of the proposer as well as the legislature)
itself is an interesting question. Another design question with respect to communication
protocol is whether the messages should be public or private. Although this distinction
does not matter for our model because we assume simultaneous speeches and one round
of bargaining, it would matter if either there were multiple rounds of bargaining or the
preferences were interdependent.
 A. Ambrus and S. Takahashi. “Multi-Sender Cheap Talk with Restricted State
Space,” Theoretical Economics, 3, 1-27, 2008.
 D. Austen-Smith. “Information Transmission in Debate,” American Journal of Po-
litical Science 34,1 , 124-152, 1990.
 D. Austen-Smith. “Interested Experts and Policy Advice: Multiple Referrals Under
Open Rule,” Games and Economic Behavior 5, 3-43, 1993.
 D. Austen-Smith. and J. S. Banks. “Elections, Coalitions, and Legislative Out-
comes,” American Political Science Review 82 , 405-422, 1988.
 J. S. Banks and J. Duggan. “A Bargaining Model of Collective Choice,” American
Political Science Review, 94, 73-88, 2006.
 D. P. Baron. “A Spatial Bargaining Theory of Government Formation in Parlia-
mentary Systems,” American Political Science Review, 85, 137-164, 1991.
 D. P. Baron and J. A. Ferejohn. “Bargaining in Legislatures,” American Political
Science Review, 83, 1181-1206, 1989.
 M. Battaglini. “Multiple Referrals and Multidimensional Cheap Talk,” Economet-
rica, 70, 1379-1401, 2002.
 Y. Breitmoser. “Demand Commitments in Majority Bargaining or How Formateurs
Get Their Way,” International Journal of Game Theory, 38, 2, 183-191, 2009.
 V. Crawford and J. Sobel. “Strategic Information Transmission”, Econometrica 50,
6, 1431-1451, 1982.
 D. Diermeier and A. Merlo. “Government Turnover in Parliamentary Democracies,”
Journal of Economic Theory, 94, 46-90, 2000.
 J. Farrell and R. Gibbons. “Cheap Talk Can Matter in Bargaining,” Journal of
Economic Theory, 48, 221-237, 1989.
 T. Gilligan and K. Krehbiel. “Asymmetric Information and Legislative Rules with
a Heterogeneous Committee,” American Journal of Political Science 33, 2, 459-490,
 B. Harstad. “Harmonization and Side Payments in Political Cooperation.” Ameri-
can Economic Review, 97, 3, 871-889, 2007.
 M. Jackson and B. Moselle. “Coalition and Party Formation in a Legislative Voting
Game.” Journal of Economic Theory, 103, 49-87, 2002.
 V. Krishna and J. Morgan. “Asymmetric Information and Legislative Rules.” Amer-
ican Political Science Review 95, 2, 435-452, 2001.
 H. D. Lasswell. Politics: Who Gets What, When, How? New York: Meridian, 1958.
 H. D. Lasswell. The Structure and Function of Communication in Society. In L.
Bryson (Ed.), The Communication of Ideas. New York: Harper. p.117., 1948.
 S. Matthews. “Veto Threats: Rhetoric in a Bargaining Game,” Quarterly Journal
of Economics, 104, 2, 347-369, 1989.
 S. Matthews and A. Postlewaite. “Pre-play Communication in Two-Person Sealed-
Bid Double Auctions,” Journal of Economic Theory, 48, 1, 238-263, 1989.
 M. Montero and J. J. Vidal-Puga. “Demand Commitment in Legislative Bargain-
ing,” American Political Science Review, 101, 4, 847-850, 2007.
 M. Morelli. “Demand Competition and Policy Compromise in Legislative Bargain-
ing,” American Political Science Review, 93, 4, 809-820, 1999.
 T. S. Tsai. “The Evaluation of Majority Rules in a Legislative Bargaining Model,”
Journal of Comparative Politics, 37, 4, 674-684, 2009.
 T. S. Tsai and C. C. Yang. “On Majoritarian Bargaining with Incomplete Informa-
tion,” International Economic Review, forthcoming.
 T. S. Tsai and C. C. Yang. “Minimum Winning versus Oversized Coalitions in
Public Finance: The Role of Uncertainty,” Social Choice and Welfare, forthcoming.
 J. J. Vidal-Puga. “Bargaining with Commitments,” International Journal of Game
Theory, 33, 1, 129-44, 2004.