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Extreme Districts, Moderate Winners: Same-Party Competition in Washington and California's Top-Two Primaries

  • Trinity University

Abstract and Figures

In an effort to break the link between districts' lack of competitiveness and election of ideologues, Washington and California have recently adopted the top-two primary election system. The reform came in direct response to a Supreme Court challenge that struck down Washington's long-standing ``blanket'' primary, a system that California had copied and implemented in the late 1990s. Among other features, the top-two primary, allows members of the same party to run against each other in the general election. Though proponents argue that this system should encourage the election of more moderate candidates in highly partisan districts, early studies have uncovered little evidence to this effect. This study disentangles the conditions under which one should expect such primaries to encourage the election of more moderate candidates, and is the first to provide evidence of this connection. Using election returns data from the 2008, 2010, and 2012 elections, I find that districts facing same-party competition elect more moderate legislators than similar districts not subject to same-party competition.
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Extreme Districts, Moderate Winners
Same-Party Challenges and Deterrence
in Top-Two Primaries*
Jesse M. Crosson
Princeton University and Trinity University
In an effort to break the link between districts’ lack of competitiveness and the election of ideologues,
Washington and California recently adopted the “top-two” primary election system. Among other features,
the top-two primary allows members of the same party to run against one another in the general election.
Although proponents argue that this system encourages the election of more moderate candidates in highly
partisan districts, early reports have uncovered mixed evidence of this effect—despite the fact that reformers
insist the system is working. is study addresses this puzzle by first disentangling the conditions under
which one should expect such primaries to encourage the election of more moderate candidates. Using
election returns data from the 2008 through 2014 elections, I find that districts facing same-party general-
election competition do elect more moderate legislators than similar districts not subject to same-party
competition. However, using an application of a common regression discontinuity diagnostic test, I also
find that elite actors appear able to strategically avoid this kind of competition—partially explaining why
broader effects of the top-two have not been uncovered. e findings contribute not only to ongoing
debates about the effectiveness of the top-two primary, but also to our understanding of how political
elites may maneuver institutional changes to their own benefit.
Keywords: primary election reform; polarization; top-two; parties
*Conditionally Accepted at Political Science Research & Methods. e author wishes to thank George Tsebelis, Doug Ahler,
Seth Masket, Justin Kirkland, Boris Shor, participants at the 2018 State Politics and Policy Conference, and two anonymous
reviewers for helpful feedback and counsel.
Fellow, Center for the Study of Democratic Politics, Princeton University; Assistant Professor, Trinity University
e author may be reached at
For years, western states like Washington and California have pioneered electoral reforms. Many such
states, for example, were among the first to adopt term limits in the 1980s and 1990s, open primary
elections throughout the latter half of the twentieth century, and online voter registration in the early
2000s. While the goals of these reforms have varied, ranging from increasing accountability to decreasing
legislative polarization, they have boasted wide-ranging levels of effectiveness and have become the sub-
ject of intense popular and academic scrutiny. In their latest electoral reform, California and Washington
made headlines in the late 2000s for their adoption of a new kind of primary election, the “top-two” pri-
mary. In these primaries, candidates of all parties compete against one another in a single “primary” or
“first-round” election, from which the two general-election candidates are selected. Under this system,
districts may experience an extreme oddity in American politics: same-party competition in the general
election. Policymakers and good-government advocates hope that these same-party general elections—
and candidates’ anticipation thereof—will lead to the election of more moderate candidates, particularly
in partisan-homogenous districts. Rather than perpetuating extremist control of partisan-homogenous
districts, proponents argue that the top-two primary provides a means for encouraging meaningful, mod-
erate challenges in these districts.
But while advocates and pundits have touted these potential ramifications, quantitative evidence has
provided far less reason for optimism. Indeed, to date, scholarly investigations of the top-two primary have
uncovered little to no evidence of a widespread moderating effect following the reform’s institution. Ahler
and colleagues (2016), for example, use field-experimental methods to demonstrate that voters struggle
to distinguish between moderate and extreme candidates (particularly of the same party), casting doubt
on their ability to demand and select more moderate candidates within the top-two system. Other obser-
vational studies, such as those by McGhee and Shor (2017) and Smith (2016), find the system’s effects
on winning candidates to be quite limited and the effect on candidates in general to be negligible. Some
studies even add that the introduction of the top-two primary may have harmed the representativeness of
the legislature (Phillips et al. 2016).
In spite of these findings, proponents insist that the system has functioned as intended (Reed 2017).
In this paper, I address this puzzle by disentangling the conditions under which moderation under the
top-two primary ought to occur and demonstrating that these conditions do not obtain as frequently as
reformers have hoped. More specifically, I test and find support for the hypothesis that same-party general
elections are a necessary condition for the election of more moderate candidates, and that candidates’ and
parties’ avoidance of these contests helps to explain the limited effectiveness of the reforms. To do so, I use
three different comparison groups for same-party contests to demonstrate that moderate candidates fair
better in same-party general elections than they do in similarly situated two-party contests. Drawing on
elections and ideology data from all legislative races in Washington (2008-2012) and California (2010-
2014), as well as randomly selected U.S. legislative elections over the same time period (2008-2014), I
show that winners in same-party general elections are more moderate overall than winners in similar two-
party races. In spite of this finding, however, I use a diagnostic test for precise control over exposure
to treatment (in this case, same-party general-election competition) to demonstrate that political actors
appear able to systematically avoid same-party general elections—offering an explanation for why the top-
two primary has not had wider moderating effects. I conclude by exploring channels by which same-party
competitions are avoided, and by suggesting how future research may further examine party power in the
top-two primary.
e findings in this paper therefore contribute not only to scholarship evaluating the top two primary
and its ramifications, but also to the execise of party power in the face of institutional challenges. e
top-two primary presented party leaders with a historic challenge to their electoral power, as their nearly
ten-year legal battle over the system and its constitutionality attests. Indeed, the system weakens parties’
ability to control the use of their brand name, and it enables potentially contentious campaigns to arise
in otherwise “safe” districts. Nevertheless, reformers appear to have relied upon a somewhat deterministic
link between district extremity and the incidence of same-party general-election competition. By demon-
strating that the actual occurence of such competition appears to be subject to some level of precise control,
this study underscores the importance of accounting for elite response when designing primary election
reform policy. Moreover, in using a regression discontinuity diagnostic test as a tool for detecting such
control, the study posits a means for examining difficult-to-observe responses to institutional changes in
other settings.
e Mechanics of the Top-Two Primary
According to proponents of the top-two primary, the partisan-neutral, two-stage nature of the system
leverages the participation of minority party voters in safe districts in order to elect more moderate win-
ners. In first-past-the-post elections, when one party is particularly strong within a district, the votes of
the minority party matter very little: in general elections, the “out-partys” candidate stands little chance
of winning, given the district’s partisan make-up. Moreover, in many cases, out-party voters cannot par-
ticipate in the majority party’s primary elections because of state laws about primary participation. Even
in open-primary states, minority party members often must forfeit their ability to vote in their own party’s
primary if they want to participate in the majority-party primary. In closed-primary states, they are for-
bidden from participating in the majority-party primary altogether.
In the top-two primary, however, the votes of minority party members matter just as much as the votes
of the majority party. During the first round, voters are free to vote their affiliation: if a Democrat in a
majority-Republican district still desires to vote for a Democrat, she is free to do so. But if the district is
sufficiently Republican, the Democrat may fail to reach the general election. In this case, the Democrat
must choose among two different Republican candidates—one ostensibly more moderate than the other.
If proponents of the top-two primary are correct, the moderate candidate should win the election in most
cases, because she will win the votes of the minority party members.
is dynamic, in fact, was crucial for the top-two’s architects and their case for reform. For example,
appearing before the Republican caucus in the Washington House and Senate during legislative debate
about the top-two, Washington Secretary of State Sam Reed—the primary creator of Washington and
Californias current primary election system—underscored the importance of leveraging out-party votes.
Figure 1 depicts a small portion of Reed’s speech notes from one such meeting.1During his remarks,
Read (himself a Republican) stressed the importance of ”electing moderates in Urban [sic] areas,” where
Democrats dominate legislative elections. As the smaller party statewide, Reed argued, Republicans would
be harmed if the state transitioned to a traditional “pick-a-ballot” primary, all but guaranteeing the election
of strongly progressive candidates in districts throughout the state.
Same-party, general-election competition is therefore central to the potential moderating effect of the
top-two primary. However, if such competition fails to occur, the moderating effect is more ambiguous.
On one hand, it is possible that even absent same-party competition, the top-two primary system could
moderate candidates: the mere threat of same-party general elections could induce incumbents (and other
candidates) to adjust their ideological position-taking before the general election ever takes place. On
the other hand, party loyalty could simply lead voters in top-two elections to vote for their co-partisan
candidate, regardless of whether she is the more moderate candidate in the election. While I address this
possibility below, this ambiguity thus focuses my scope to same-party cases. Specifically, I test whether the
moderating mechanism of the top two—same-party, general-election competition—actually leads to the
1Facsimiles of this document, and many others like it, are located at the Washington State Archive, Olympia, WA. Appendix
B displays a facsimile of the entire document presented here, captured in an authorized photocopy by the author.
Figure 1: Speech Notes from SOS Sam Reed.
Presented in private meeting to legislative Republicans.
election of a more moderate general election candidate, as intended. Not only is the theoretical connection
between same-party competition and moderation stronger than in traditional two-party races, but also such
competition was central to reformers’ own understanding of how the system would generate moderation.
As noted earlier, previous empirical investigations of the top-two primary have found mixed evidence
regarding the systems moderating effects 7. Anecdotal examinations of post-reform Washington and Cal-
ifornia (e.g., Cohn 2014, Walters 2014, Sinclair 2015) underscore the ability of the top-two primary to
encourage the election of moderates. In addition to these qualitative studies, Grose (2014) finds that legis-
lators in post-reform California were more moderate and the parties overall were less extreme. In the most
thorough examination of the top-two primary to date, however, McGhee and Shor (2016) find only par-
tial support for the hypothesis that the top-two primary leads to the election of more moderate candidates.
According to their findings, the reforms have had the intended effect for California Democrats, but not
for California Republicans (nor for either party in Washington). Further still, other studies find little to no
support for the moderating effect of the top-two primary. Smith (2016) finds that, on average, candidates
in Washington and California were no more moderate overall after reform than they were before. Kousser
et al. (2016) even find suggestive evidence that the top-two primary elects legislators more extreme than
their district. Finally, Ahler et al. (2016) use experimental evidence to call into question the ability of
voters to distinguish between extreme and moderate candidates altogether.
While these studies provide important information about the aggregate impact of top-two primaries in
California and Washington, one possible reason for these mixed findings derives from the fact that previous
studies do not examine the influence of same-party competition specifically. McGhee and Shor (2016), for
example, examine whether legislators were, on average, more moderate before and after reform (broken
down by party and incumbency status), and whether legislators elected in California were, on average,
more or less moderate than their counterparts from similar districts in other states. Here, the outcome of
interest is the ideology of winning candidates—irrespective of the ideology of the winner’s opponent and
the partisan dynamics of the general election. Were same-party competition sufficiently widespread, this
broad focus may not matter: the potential moderating effect of same-party competition may be strong
enough to influence the results of aggregate studies like that of McGhee and Shor. However, without
examining the influence of same-party competition specifically, it is difficult to know whether same-party
competition is effective but insufficiently widespread, or whether the top-two system as a whole simply fails
to elect more moderate candidates. us, in the foregoing analysis, I examine two main questions. First,
does same-party competition encourage the election of more moderate candidates than similarly situated
two-party contests? Second, if such competition does lead to moderation, does it occur as frequently
and deterministically as reformers had hoped? ese questions not only interrogate the effectiveness of
arguably the most important feature (same-party general-election competition) of one the United States
most notable electoral reforms in recent history, but they also point to the importance of understanding
how adversely affected political actors may work to resist reform efforts.
Exploring Same-Party Competition: Empirical Strategy and Data
At the most basic level, this study relies upon a quantitative comparison of electoral outcomes between
two groups—a “treated” group (districts subject to same-party elections) and a “control” group (those not
subject to such elections)—to test the aforementioned hypothesis concerning same-party competition.
Treated districts should elect more moderate candidates than those districts in the control group. us,
the first and perhaps most important step of the analysis comes in defining these groups. Defining the
treatment group, races in California and Washington that resulted in same-party general elections, is rela-
tively straightforward. According to electoral results compiled from the Secretaries of State in Washington
and California, 82 elections in California and Washington’s state legislatures and congressional delega-
tions experienced same-party general elections in the time period covered in this study (2008-2012 in
Washington and 2012-2014 in California).2ese cases serve as the treatment group in our comparison.3
Defining the relevant comparison group is slightly more complicated. Should one compare results
from similar districts pre- and post-reform? Or between similar same-state districts that nevertheless did
not experience same-party competition? Further still, should one turn to similar districts outside the state
that did not face a top-two primary system at all? Each approach entails a variety of advantages and disad-
vantages. First, comparing results pre- and post-reform carries with it the potential to hold district charac-
teristics (mostly) constant. However, because the implementation of the top-two primary also coincided
with the rollout of new legislative districts in 2012, such an approach faces serious challenges—particularly
in California, which introduced a new, independent redistricting commission in 2010.
Another possible approach might be to compare districts with same-party competition to similar dis-
tricts in the same state that did not face such competition. Doing so allows one to hold state-level factors
2CFscores for Washington legislators in 2014, necessary for the following empirical tests, are not yet available. 82 elections
out of the nearly 800 contested elections over the same time period represents roughly 10 percent of all state legislative and
Congressional races.
3Some of these cases have missing data for key variables, so the actual number of treated cases in the empirical analysis is
constant. However, this approach may obfuscate the impact of year- or cycle-specific factors on the election
of moderates. To address such concerns, a final approach compares districts facing same-party competi-
tion with similar districts outside the top-two states. is approach allows one to account for potential
nationwide electoral trends. However, such a design may mask key cross-state factors that influence the
election of moderates.
Given these advantages and disadvantages, I make use of versions of all three comparison groups. First,
I compare similar pre- and post-reform districts within the same state, testing whether exposure to 1) the
top-two primary in general and 2) same-party competition specifically are associated with 1) the election of
more moderate candidates and/or 2) an increased probability that the more moderate between the general-
election candidates wins. Second, I compare similar post-reform districts within the same state to examine
how same-party competition is associated with winning candidates’ ideologies and election rates for the
more moderate candidate. Finally, I compare districts in Washington and California with similar districts
in other states—first to establish whether same-party competition is associated with moderate candidate
election, and then to explore whether the top-two primary itself appears to be associated with higher
moderate win rates.
Data and Methods
Before discussing findings from each of these tests, I first detail my measurement strategy, data sources,
and empirical methodology. I measure the two main outcome variables in the following way. To measure
the first outcome variable, Winner Extremism, I make use of Adam Bonica’s CFscores, from his Database
on Ideology, Money in Politics, and Elections (DIME).4ese data rely upon campaign donations from
various interest groups and committees to generate ideal point estimates for every candidate who received
donations within a given election cycle.5Because Bonicas scores are centered near 0, the outcome variable
in my models is measured simply as |ideologyw inner |. e second outcome variable, Election of Moderates,
is defined as a “success” (coded as a ‘1’) if the most moderate candidate within a district’s general election
wins, and a “failure” (coded as ‘0’) otherwise. Formally, Election of Moderate takes on the value ‘1’ if
|ideologyw inner |<|ideologyloser|and zero otherwise. Because Bonicas CFscores provide a means for
4I choose CFscores as my measure of candidate preferences for both theoretical and practical reasons, which I detail at
greater length in Appendix A. ere, I also retest the main findings presented below, using a measure of legislator preferences,
DW-DIME, more directly tied to roll call behavior.
5For each test, I ensure that exposure to same-party competition is not also predictive of donation totals for candidates,
which could pontentially create measurement bias. In each case, I fail to uncover such problematic patterns. Results from these
tests may be found in Appendix A.
measuring the ideology of all candidates for office, including both the winner and losers in each election,
these scores are ideal for testing this study’s basic race-level hypotheses.
I label the primary explanatory variable of interest as Same Party. is variable takes on the value ‘1’
if the general election involved a two-way race between members of the same party and zero otherwise. I
anticipate that races with same-party general-election competition will be more likely to result in both more
moderate candidates winning, as well as the more moderate of the two general-election candidates winning.
ese data are drawn from official election returns from the Secretary of State offices in Washington and
In addition to these primary variables, each of my models also include a number of important sec-
ondary variables. Perhaps most importantly, the models control for area- and race-specific characteristics
that may influence a district’s propensity for selecting moderate candidates. First, the models include a
term, District Extremism or the absolute value of district ideology, which allows for the possibility that
some districts are so extreme that even a same-party election would not lead to the selection of a moderate
candidate. Indeed, whereas most partisan-homogenous districts possess at least some mass of voters from
the opposite party (who would choose the more moderate candidate in a same-party election), some dis-
tricts may prove so homogenous that even a same-party general election will not encourage the election
of a moderate candidate. Figure 2 illustrates this possibility through hypothetical voter density plots com-
paring this sort of extreme district to a more “typical” partisan homogenous district. I measure District
Extremism using Tausanovitch and Warshaw’s (2013) measure of district ideology, publicly available at
In addition to accounting for the ideological preferences of the district itself, I also account for an-
other important variable, Difference in Extremism, that likely influences a district’s propensity for choosing
moderate candidates. According to Ahler et al.’s (2016) field experimental findings, voters in the top-two
primary appear unable to discern small differences in candidate extremity. I posit that voters’ inabilities
may be less pronounced when there are clearer differences in candidates’ extremity and moderation. is
variable allows my models to control for this possibility, and I define it as follows:
Difference in Extremism =
|ideologyw inner |−|ideologyloser |
Given that the ideology measure is centered near 0, Difference in Extremism captures how extreme the two
candidates are relative to one another. As Difference in Extremism increases (i.e. as one candidate becomes
Figure 2: Extreme Districts, the Election of Moderates, and the
Need to Control for Area Characteristics
more extreme than the other), one should expect voters to elect the more moderate candidate at a higher
rate—perhaps even absent a same-party general election. After all, if one candidate in a race is completely
out-of-touch with the center of the political spectrum relative to the other candidate, it is not likely she will
win the race (e.g., Canes-Wrone et al. 2002). Much like Election of Moderate, the inclusion of Difference
in Extremism is not possible absent candidate ideology scores, once again rendering Bonica’s CFscores as
ideal underlying measures.
e models presented below also include a variety of other control variables. ough available from
other sources, I measure most of these variables using the DIME dataset.6First, I have created an indicator
for whether the winning candidate in the race was an incumbent (Incumbent Winner = 1) and whether
the seat in question was an open seat (Open Seat = 1). I expect incumbent winners may be more insulated
from the effects of same-party competition, as incumbents can anticipate challenges that may come from
primaries or from a same-party election. Additionally, I have coded Upper Chamber as a binary variable
indicating whether or not a race was at the state-upper-chamber level. I do not have strong hypotheses
about the directionality of the associated coefficient for this variable, but it is possible that larger, more
diverse constituencies (in states for which upper and lower chamber districts are not identical) are pre-
disposed to electing more moderate candidates. I also include a Party variable, which represents the party
of the winning candidate.7McGhee and Shor (2016) in particular find significantly different results by
party in their study of the top-two primary, so I have chosen to include this covariate in each of my tests.
Given that the outcome variable in these tests is continuous in one case (Winner Extremism) and binary
in another (Election of Moderate), I first turn to linear regression and logistic regression (both with state and
year fixed effects where appropriate), respectively, to analyze these data. However, like any other regression,
linear and logistic regression impose a functional form on the data, so I use matching as a robustness check
on my findings.8In each case I use nearest-neighbor matching implemented by GenMatch() in R(Sekhon
2011), to optimize post-match balance. I report balance statistics in each table as the smallest p-value
resulting from difference-in-means tests between pre- and post-matching Xcovariates.
6All such data is publicly available at
7Because the top-two primary allows candidates to indicate partisan preference instead of official affiliations, I code as “Re-
publican” any candidate who makes reference to common names for the Republican Party. is would include both “Prefers
Republican Party,” as well as “Prefers GOP” and variants of these two.
8An approach also adopted by McGhee and Shor (2016).
Test 1: Election of Moderates in Pre- and Post-Reform Washington and California
In the above sections, I have argued in favor of the general assertion that same-party competition in the
general election should lead to the election of more moderate candidates. In this first test, I attempt to
hold the state (and district, as much as possible) constant, and leverage policy changes over time in order
to examine my main assertion. More specifically, I test whether exposure to same-party general election
competition after top-two reform increases the probability that a race will end in the election of the more
moderate candidate. In addition, however, I use these data to test whether the presence of the top-two
primary generally is associated with a greater likelihood that the more moderate candidates win.
In this test, I report six models, which differ on combinations of outcome variables, “treatment” vari-
ables, and the presence of fixed effects. However, each model includes the same basic set of control vari-
ables. us, the most basic model (Model 1 in Table 2) takes the form
f(Candidate_Extremism)i=β0+β1(Same_P ar tyi)+β2(Incumbenti)+β3(Openi)+
β4(P artyi) + β5(State_Upperi) + β6(Dif f_Extremei) + β7(Dist_Extremei) + ϵi
Model 2 is identical to Model 1, only Model 2 includes fixed effects by state. McGhee and Shor
(2016) find systematic differences between Washington and California in their data, so including state
fixed effects may have particularly important empirical ramifications. Model 3 is similar to Model 2,
but instead of including fixed effects by state, it substitutes those fixed effects for a binary pre-/post-reform
indicator. Models 4-6 are identical to Models 1-3, only changing Winner Extremism to Election of Moderate,
respectively. Table 1 reports the results of each of these regressions.
e matching analyses, the results of which are reported in Table 2, proceed similarly. at is, analysis
numbers in Table 2 include the same variables as the corresponding models in Table 1. For models that
include fixed effects in Table 2, I include binary indicators for each state in the Xvector to ensure that
matches for treated cases are drawn from the same state. As in the regression models, I include the variables
Incumbent, Open, Party, Upper Chamber, District Extremism, and Difference in Extremism in Xas well.
Analyses 1 through 6 vary outcome variables and the inclusion of fixed effects in the same way described
above in the regression models.
While results reported in Tables 1 and 2 are somewhat mixed, a preponderance of evidence appears
Table 1: Regression Results for Test 1
Dependent variable:
Winner Extremism Election of Moderate
(1) (2) (3) (4) (5) (6)
Same Party Competition 0.129∗∗∗ 0.100∗∗∗ 0.166∗∗∗ 0.529 0.465 0.453
(0.038) (0.037) (0.038) (0.394) (0.402) (0.404)
Post-Reform = 1 0.105∗∗∗ 0.250
(0.026) (0.306)
Party 0.0004∗∗∗ 0.0005∗∗∗ 0.0005∗∗∗ 0.011∗∗∗ 0.011∗∗∗ 0.012∗∗∗
(0.0002) (0.0002) (0.0002) (0.004) (0.004) (0.004)
Incumbent Winner = 1 0.172∗∗∗ 0.157∗∗∗ 0.170∗∗∗ 2.591∗∗∗ 2.632∗∗∗ 2.587∗∗∗
(0.050) (0.048) (0.049) (0.480) (0.484) (0.478)
Open Seat = 1 0.129∗∗ 0.078 0.120∗∗ 2.167∗∗∗ 2.261∗∗∗ 2.159∗∗∗
(0.051) (0.050) (0.051) (0.492) (0.504) (0.491)
Upper Chamber 0.064∗∗ 0.065∗∗ 0.066∗∗ 0.008 0.012 0.016
(0.030) (0.029) (0.029) (0.324) (0.324) (0.325)
District Extremity 0.292∗∗∗ 0.327∗∗∗ 0.285∗∗∗ 0.074 0.036 0.050
(0.059) (0.057) (0.058) (0.643) (0.643) (0.644)
Difference in Extremism 0.336∗∗∗ 0.325∗∗∗ 0.322∗∗∗ 1.831∗∗∗ 1.838∗∗∗ 1.797∗∗∗
(0.028) (0.027) (0.027) (0.440) (0.440) (0.442)
Constant 1.173∗∗∗ 1.182∗∗∗ 1.102∗∗∗ 3.082∗∗∗ 3.043∗∗∗ 2.950∗∗∗
(0.055) (0.053) (0.057) (0.745) (0.748) (0.759)
State Fixed Effects N Y N N Y N
Observations 448 448 444 444 448 444
Log Likelihood 13.148 4.447 5.117 187.347 186.903 187.007
Akaike Inf. Crit. 42.297 9.106 28.233 390.693 391.806 392.015
Note: p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
to suggest that same-party competition in the general election is associated with the election of more
moderate candidates, but not with the election of the more moderate candidate within a given general
election. roughout the regression models and many of the matching models with Winner Extremism
as the outcome variable, same-party general election competition is a negative predictor of a winning
candidate’s extremity. Indeed, on average, winning candidates appear to be anywhere between 0.1 and
0.166 ideological units more moderate than similarly situated races that either did not face same-party
competition or did not face the top-two primary altogether.9Paradoxically, though, post-reform winners
on the whole are not more moderate than similar races pre-reform.
Figure 3 illustrates the magnitude of the association between same-party competition and Winner Ex-
tremism.10 e figure presents area plots for folded CFscores, the outcome variable Winner Extremism.
Within these plots, the grey lines represent the predicted winner extremity, absent same-party general-
election competition (holding all other variables at their means), while the black lines depict predicted
winner extremity after exposure to same-party competition. While the exact effect size, in terms of per-
centile shift, depends on where one begins within a state’s distribution of legislators, Figure 3 captures a
fairly sizeable association with the winning candidates’ ideological extremism: for an average district, expo-
sure to same-party competition would move a legislator from the 53rd to the 38th percentile in extremity
in California and the 58th to the 43rd percentile in Washington.
ese trends were not the case, however, with regard to within-election selection of the more moder-
ate candidates (Election of Moderate). Indeed, neither post-reform status nor same-party general election
competition was associated with voters’ selection of the more moderate candidate in the election. is
could perhaps be related to the strategic considerations candidates face in anticipating same-party compe-
tition. However, relative extremism of candidates within an election does not appear to matter differently
in treated and non-treated races. is is not to say that differences in winner extremism did not matter
at all. Instead (and perhaps encouragingly), Difference in Extremism is strongly associated with the proba-
bility that the more moderate candidate in an election is in fact selected by voters. is may suggest that
such differences, when large enough, are detectable to voters, and that such differences matter to them.
However, voters’ willingness to select on relative extremism does not appear to differ between same-party
and two-party general elections.
9ough not reported here, a model without a same-party competition term (and only a pre-/post-reform term) produces
a “reform” coefficient similar to the coefficient reported in Model 3.
10In this and all remaining examinations of effect size, I conservatively focus on models with state fixed effects, as these
models generally exhibit the smallest effects.
Figure 3: Same-Party Competition and Moderation, Test 1
Notes: Area plots (California, top; Washington, bottom) of winning candidates’ folded CFscores, used to measure candidates’ ideological
extremism. Leftward values indicate less extreme (more moderate) candidates. The grey dashed line represents the mean predicted
ideological extremity for two-party contests, while the black dashed line represents the mean predicted ideological extremity for same-
party contests. The gap between the two lines depicts the average decrease in extremism associated with the presence of same-party
general-election competition.
Table 2: Matching Analyses for Test 1
(1) (2) (3) (4) (5) (6)
Estimate (ATT) -0.0994 -0.0576 -0.1490 -0.0714 -0.107 -0.0357
AI Standard Error 0.0603 0.0624 0.0666 0.1037 0.0927 0.1017
p-value 0.0994 0.3558 0.0253 0.4910 0.2479 0.7254
Original Number of Treated Obs. 56 56 56 56 56 56
Matched Number of Treated Obs. 56 56 56 56 56 56
Post-Match Minimum p-value 0.0639 0.0805 0.0805 0.0639 0.0805 0.0805
Estimate (ATC) -0.1147 -0.2233 -0.0980 -0.188 -0.1108 -0.1907
AI Standard Error 0.0792 0.0868 0.0879 0.1020 0.1077 0.1098
p-value 0.1475 0.0101 0.2644 0.0651 0.3038 0.0823
Original Number of Control Obs. 388 388 388 388 388 388
Matched Number of Control Obs. 388 388 388 388 388 388
Post-Match Minimum p-value 0.000 0.000 0.000 0.000 0.000 0.000
Estimate (ATE) -0.11284 -0.2020 -0.1044 -0.1734 -0.1103 -0.0357
AI Standard Error 0.0716 0.0784 0.0799 0.0950 0.0988 0.1017
p-value 0.1151 0.0100 0.1910 0.0679 0.2641 0.7254
Original Number of Observations 444 444 444 444 444 444
Matched Number of Observations. 444 444 444 444 444 444
Post-Match Minimum p-value 0.000 0.000 0.000 0.000 0.000 0.000
As noted above, the general patterns observed in the regression results also appear in the matching
analysis, albeit with lower levels of statistical signficance on average. ese results are summarized in Table
2. In matching analyses 1, 2, and 3, treatment (same-party competition) was negatively associated with
the outcome variable of Winner Extremism. Across Models 1-3, at least one of the ATT, ATC, or ATE is
siginficantly and negatively associated with the winning candidate’s ideological extremity. Overall, when
combined with the regression results reported above, these data are largely consistent with the idea that
exposure to same-party general election competition ends with a race electing “moderate” candidates, but
not the more moderate of the two candidates in the election. Still, because units before and after the
reform are not comparable on one extremely important dimension, exposure to the top-two primary, I
turn now to post-reform data alone to hold exposure to the primary system constant.
Test 2: Election of Moderates in Post-Reform Washington and California
In this test, I compare similar districts within post-reform Washington and California to again assess
whether same-party competition and moderate election covary as expected. I estimate regression models
and conduct a series of matching analyses, using incumbency, partisanship, chamber, and difference in
extremity as control variables. In this test, however, I also include a dummy variable for the election cycle
(and match on election cycle in the matching analysis) and state.
In Model 1, I estimate the simplest specification—one with no fixed effects of any kind. In Model 2, I
introduce year fixed effects, and in Model 3, I introduce state fixed effects. Models 4, 5, and 6 are identical
but include the Election of Moderate outcome variable. One complication to these models is that California
and Washington implemented reforms at different times. us, in this dataset, data for California comes
from 2012 and 2014 while data from Washington covers the period 2008-2012. is means that the
year fixed effects function somewhat differently than usual, since only Washington has data in 2008 and
2010. Nevertheless, inclusion of fixed effects for those years does allow the models to cover unobserved
confounders specific to those years in Washington and California.
Table 3 summarizes the results of these regressions. As in Test 1, Test 2 also reveals a persistent as-
sociation between same-party competition and the election of less extreme candidates, particularly in the
regression models. ese results are similar in magnitude to Test 1, with effect sizes ranging from .1 to
.149 units of ideological moderation. However, the test fails to find any connection between same-party
competition and the election of the more moderate candidate within the election. Some fixed effects, al-
though not fully reported in the table, did exhibit coefficients that reached conventional levels of statistical
Table 3: Regression Results for Test 2
Dependent variable:
Winner Extremism Election of Moderate
(1) (2) (3) (4) (5) (6)
Same-Party Competition 0.149∗∗∗ 0.143∗∗∗ 0.106∗∗∗ 0.420 0.342 0.165
(0.041) (0.042) (0.041) (0.387) (0.395) (0.411)
Party 0.00030.0002 0.00030.008∗∗ 0.008∗∗ 0.007∗∗
(0.0002) (0.0002) (0.0002) (0.003) (0.003) (0.004)
Incumbent Winner 0.068 0.071 0.082 1.727∗∗∗ 1.627∗∗∗ 1.575∗∗∗
(0.054) (0.055) (0.053) (0.474) (0.481) (0.487)
Open Seat 0.019 0.029 0.022 1.290∗∗∗ 1.277∗∗ 1.302∗∗
(0.057) (0.058) (0.056) (0.492) (0.504) (0.513)
Upper Chamber 0.060 0.060 0.0640.081 0.109 0.130
(0.037) (0.037) (0.035) (0.346) (0.353) (0.355)
District Extremism 0.216∗∗∗ 0.225∗∗∗ 0.250∗∗∗ 0.368 0.572 0.584
(0.068) (0.069) (0.066) (0.708) (0.730) (0.734)
Differences in Extremism 0.356∗∗∗ 0.355∗∗∗ 0.365∗∗∗ 1.318∗∗∗ 1.279∗∗∗ 1.261∗∗∗
(0.037) (0.037) (0.036) (0.439) (0.442) (0.445)
Constant 1.114∗∗∗ 1.074∗∗∗ 1.091∗∗∗ 1.963∗∗ 1.066 0.919
(0.062) (0.069) (0.067) (0.771) (0.852) (0.860)
State Fixed Effects N N Y N N Y
Year Fixed Effects N Y Y N Y Y
Observations 324 324 324 320 320 320
Log Likelihood 24.119 21.440 8.961 158.329 154.165 152.113
Akaike Inf. Crit. 64.237 64.880 41.923 332.657 330.329 328.226
Note: p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Figure 4: Same-Party Competition and Moderation, Test 2
Notes: Area plots (California, top; Washington, bottom) of winning candidates’ folded CFscores, used to measure candidates’ ideological
extremism. Leftward values indicate less extreme (more moderate) candidates. The grey dashed line represents the mean predicted
ideological extremity for two-party contests, while the black dashed line represents the mean predicted ideological extremity for same-
party contests. The gap between the two lines depicts the average decrease in extremism associated with the presence of same-party
general-election competition.
significance. In particular, the year 2008 (Model 3) and the California state fixed effect (Models 3 and 6)
were negative predictors of Winner Extremism. is latter finding is consistent with previous findings by
McGhee and Shor (2016), who uncover ideological moderation by California Democrats.
Figure 4 again captures the magnitude of the association between same-party competition and Winner
Extremism. As in Test 1, the influence of same-party competition on winner extremism is both statistically
and substantively significant. In this test, for an average district, exposure to same-party competition
would move a legislator from the 47th to the 34th percentile in extremity in California and the 55th to
the 45th percentile in Washington.
e results of the matching results are summarized in Table 4. As in Test 1, the matching models
exhibit weaker results, though they generally provide evidence at least somewhat consistent with the re-
gression results in Table 5. Overall, the only significant results in the matching analyses involve Winner
Extremism as the outcome variable, much as in the regressions. Same-party competition does appear to be
negatively associated with Winner Extremism. However, one should exercise caution in interpreting a num-
ber of the results presented in Table 4, as covariate balance is poor for some specifications—typically those
including binary indicators for states and years. Overall, though, while the matching results are weaker
than those in the regression analysis, they are nevertheless consistent with the hypothesis that same-party
competition is negatively associated with a winning candidate’s level of extremism.
Test 3: Same-Party Competition and Election of Moderates across States
In Tests 1 and 2, I focus solely on the top-two primary states, Washington and California, in an attempt
to hold state-specific factors constant. However, doing so may fail to capture national electoral trends
influencing the election of moderate or extreme candidates. us, in my final test, I turn outside of
Washington and California for comparison districts. To assemble this comparison group, I have taken a
random sample of 100 state legislative and congressional races from outside Washington and California,
using the DIME database. e sample spans the 2008, 2010, 2012, and 2014 election cycles, and varies
considerably with regard to state (38 of 50 states represented), district ideology, partisanship (roughly
50 percent won by both Republicans and Democrats), chamber, and other characteristics of interest.11
In addition, I include a random sample of 50 districts within Washington and California that did not
experience same-party competition so that I can include state fixed effects that are not perfectly colinear
11Restricting control units to a random sample allows for more accurate and manageable collection of key dependent and
independent variables. For an extended discussion of the advantages of this approach, see Appendix C.
Table 4: Matching Analyses for Test 2
(1) (2) (3) (4) (5) (6)
Estimate (ATT) -0.1338 -0.1102 -0.0726 -0.0178 -0.0714 -0.0178
AI Standard Error 0.0596 0.0520 0.0664 0.1032 0.1048 0.1066
p-value 0.0249 0.0341 0.2740 0.8627 0.4955 0.867
Original Number of Treated Obs. 56 56 56 56 56 56
Matched Number of Treated Obs. 56 56 56 56 56 56
Post-Match Minimum p-value 0.0228 0.000 0.0805 0.0426 0.0209 0.0805
Estimate (ATC) -0.1349 -0.2056 -0.0726 -0.2045 -0.0530 -0.07197
AI Standard Error 0.0994 0.0872 0.0663 0.1403 0.1034 0.1153
p-value 0.1748 0.0184 0.2740 0.1448 0.6081 0.5324
Original Number of Control Obs. 264 264 264 264 264 264
Matched Number of Control Obs. 264 264 264 264 264 264
Post-Match Minimum p-value 0.000 0.000 0.000 0.000 0.000 0.000
Estimate (ATE) -0.0504 -0.1510 -0.241 -0.1875 -0.0500 -0.0625
AI Standard Error 0.0840 0.0560 0.0806 0.123 0.0963 0.1049
p-value 0.5479 0.0071 0.0027 0.1274 0.6035 0.5512
Original Number of Observations 320 320 320 320 320 320
Matched Number of Observations. 320 320 320 320 320 320
Post-Match Minimum p-value 0.000 0.000 0.000 0.000 0.000 0.000
with the same-party competition variable.
e models in this test differ in four ways: the inclusion of state fixed effects, year fixed effects, and
a post-reform dummy variable, as well as differences in outcome variable. Model 1 regresses Winner
Extremism on the same set of control variables present in Tests 1 and 2, and it does not include any type
of effects. Model 2 includes year fixed effects only, and Model 3 includes both state and year fixed effects.
Model 4 drops state fixed effects in favor of a Top-Two State indicator and also includes year fixed effects.
Models 5-8 are identical to Models 1-4, except that they are models of Election of Moderate instead of
Winner Extremism.
Table 5 summarizes the regression results. As predicted, same-party competition in the general election
is again a negative predictor of a winning candidate’s level of extremism—consistent with findings in Tests
1 and 2. However, in two of the models with year fixed effects and indicator variables for Washington
and California, same-party competition is not quite significantly associated with winner extremism. It is
not clear why these models behave differently, though it is important to note that the sample sizes are the
smallest in this test. Sample size, however, cannot explain why same-party competition appears to behave
differently in these Election of Moderate models than in previous ones. In Model 5, for example, same-party
competition was positively and significantly associated with the more moderate candidate winning.
While these results fall out when year and state effects are added, another variable, the Top-Two State
status indicator, also behaves differently in one of the models. Indeed, Model 8 displays a strong, positive
association between being in a primary state and selecting the more moderate of the two candidates in
an election. ese results stand in stark contrast to the null findings of previous models, though they are
likely not in of themselves sufficient evidence to claim that same-party competition or the top-two primary
generally have had an influence on the selection of the more moderate candidate within an election.
Much as with Tests 1 and 2, the association uncovered here between same-party competition and
winner extremism is substantively notable. Figure 5 captures the magnitude of this association. Here, for
an average district, exposure to same-party competition would move a legislator from the 56th to the 40th
percentile in extremity in California and the 55th to the 43rd percentile in Washington.
Also similar to Tests 1 and 2, the matching analyses vary in specification in exactly the same ways as the
regression analyses. Table 6 documents the findings of the matching analyses, which exhibit similar trends
to the regression models.12 While same-party competition ATT misses significance in the models, includ-
12Ideally, the Test 3 matching analysis should draw from as many potential control cases as are available, ensuring the closest
possible control matches for treated units. However, given the aforementioned practical difficulties of collecting some key
Table 5: Regression Results for Test 3
Dependent variable:
Winner Extremism Election of Moderate
(1) (2) (3) (4) (5) (6) (7) (8)
Same-Party Competition 0.181∗∗∗ 0.123 0.132 0.224∗∗∗ 0.6670.650 0.649 0.623
(0.060) (0.086) (0.086) (0.078) (0.400) (0.608) (0.617) (0.558)
Top-Two State 0.048 1.920∗∗∗
(0.070) (0.504)
Party 0.0005 0.001 0.001 0.0004 0.0060.004 0.005 0.005
(0.001) (0.001) (0.001) (0.001) (0.004) (0.004) (0.004) (0.004)
Incumbent Winner 0.192∗∗ 0.196∗∗ 0.195∗∗ 0.193∗∗ 1.234∗∗ 1.170∗∗ 1.0891.090
(0.090) (0.090) (0.092) (0.093) (0.564) (0.591) (0.614) (0.614)
Open Seat 0.047 0.043 0.042 0.054 0.745 0.541 0.556 0.560
(0.093) (0.093) (0.094) (0.095) (0.582) (0.610) (0.621) (0.620)
Upper Chamber 0.013 0.014 0.003 0.005 0.033 0.032 0.046 0.048
(0.064) (0.064) (0.065) (0.066) (0.406) (0.433) (0.449) (0.448)
District Extremity 0.194 0.214 0.188 0.184 1.014 0.575 0.629 0.627
(0.146) (0.146) (0.148) (0.150) (0.898) (0.926) (0.957) (0.957)
Difference in Extremity 0.1170.146∗∗ 0.152∗∗ 0.1101.010∗∗ 1.267∗∗∗ 1.270∗∗ 1.258∗∗∗
(0.061) (0.064) (0.064) (0.062) (0.444) (0.482) (0.494) (0.478)
Constant 1.098∗∗∗ 1.109∗∗∗ 1.037∗∗∗ 1.031∗∗∗ 0.091 0.931 0.795 0.797
(0.145) (0.149) (0.163) (0.166) (0.909) (0.994) (1.115) (1.115)
State Fixed Effects N Y Y N N Y Y N
Year Fixed Effects N N Y Y N N Y Y
Observations 180 180 180 180 176 176 176 176
Log Likelihood 63.302 61.517 59.447 62.515 106.386 98.464 96.359 96.364
Akaike Inf. Crit. 142.605 143.035 144.894 149.030 228.772 216.928 218.718 216.727
Note: p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Figure 5: Same-Party Competition and Moderation, Test 3
Notes: Area plots (California, top; Washington, bottom) of winning candidates’ folded CFscores, used to measure candidates’ ideological
extremism. Leftward values indicate less extreme (more moderate) candidates. The grey dashed line represents the mean predicted
ideological extremity for two-party contests, while the black dashed line represents the mean predicted ideological extremity for same-
party contests. The gap between the two lines depicts the average decrease in extremism associated with the presence of same-party
general-election competition.
ing dummy variables for states and years, it achieves significance for other specifications and estimands.
However, unlike the regression results, the matching data uncover no relationships between same-party
competition and within-race selection of the most moderate candidate. Along with the preponderance of
null results for this outcome variable in Tests 1 and 2, this finding also calls into question how notable
the findings in the Test 3 regression models really are with regard to within-race selection of the more
moderate candidate.
It is worth noting here that in Test 3, Difference in Extremism continues to behave as expected—much
as it has done consistently throughout each of the tests. Indeed, the larger the difference in how extreme
one candidate is relative to the other in the general election, the more likely voters are to select the most
moderate candidate presented to them. Moreover, when there is a large gap between the candidates’ levels
of extremism, winning candidates are also found to be more moderate on average. As noted earlier, this
result suggests that voters may in fact be able to detect large ideological differences between candidates
for office, even when they may lack a great deal of information about a candidate (as is often the case in
state legislative elections). While it is not clear how to explain the differences between these findings and
the experimental ones reported by Ahler et al. (2016), future research should examine whether and how
voters can discern candidate extremism.
Does Same-Party Competition Occur Deterministically?
By comparing races ending in same-party, general-election competition with pre-reform races (Test 1),
two-party general election contests in-state (Test 2), and non-top-two races (Test 3), I have shown that
same-party competition in the general election consistently covaries with how extreme or moderate win-
ning candidates are in Washington and California. Much as architects of the system claim, candidates who
prevail under this type of competition tend to be more moderate than candidates in similarly situated (but
two-party) contexts. Still, counter to proponents’ expectations, the mere threat of same-party competi-
tion does not appear sufficient to make a discernable difference on the extremity of winning candidates.
Moreover, neither same-party competition nor the threat thereof appear to render voters more likely to
pick the more moderate of the two candidates presented to them in the general election.
Given the demonstrated effectiveness of same-party competition for encouraging moderation, the re-
sults suggest that the system design has not itself failed to achieve its intended aims. Instead, although the
variables, I restrict the analysis here to the same random sample used in the regression analyses. Nevertheless, in Appendix C, I
demonstrate the robustness of these results by re-executing Test 3 using data on all available legislative races as match candidates.
Table 6: Matching Analyses for Test 3
(1) (2) (3) (4) (5) (6) (7) (8)
Estimate (ATT) -0.1360 0-.1463 -0.0944 -0.1654 0.0925 0.0925 0.0926 -0.0741
AI Standard Error 0.0653 0.1085 0.1293 0.09922 0.1095 0.1748 0.1881 0.1223
p-value 0.0373 0.1775 0.4650 0.0955 0.3979 0.5962 0.6226 0.5447
Original Number of Treated Obs. 54 54 54 54 54 54 54 54
Matched Number of Treated Obs. 54 54 54 54 54 54 54 54
Post-Match Minimum p-value 0.0292 0.0042 0.004 0.0419 0.0293 0.006 0.002 0.0419
Estimate (ATC) -0.0870 -0.2543 -0.3072 -0.2533 -0.0246 0.2131 0.1639 0.0902
AI Standard Error 0.0941 0.0958 0.0981 0.0852 0.1362 0.1145 0.1311 0.1110
p-value 0.3547 0.0004 0.0017 0.0029 0.8567 0.0627 0.2112 0.4165
Original Number of Control Obs. 122 122 122 122 122 122 122 122
Matched Number of Control Obs. 122 122 122 122 122 122 122 122
Post-Match Minimum p-value 0.012 0.000 0.000 0.000 0.0004 0.000 0.000 0.000
Estimate (ATE) -0.1021 -0.2212 -0.2361 -0.2153 0.0113 0.1875 0.1420 0.0284
AI Standard Error 0.0748 0.0817 0.0876 0.0759 0.1127 0.1088 0.1185 0.0966
p-value 0.1726 0.0068 0.0071 0.0046 0.9197 0.0849 0.2309 0.7687
Original Number of Observations 176 176 176 176 176 176 176 176
Matched Number of Observations. 176 176 176 176 176 176 176 176
Post-Match Minimum p-value 0.008 0.000 0.000 0.000 0.000 0.000 0.000 0.000
top-two primary seems to be falling short of its overall goal (widespread candidate moderation), the inter-
nal mechanism designed to moderate candidates appears to be functioning as desired. Given this finding,
how might proponents of the top-two primary address the apparent failures of the system? If the internal
mechanism functions properly, why has the system not been broadly effective? As noted earlier, I suggest
the answer to this puzzle lies in the failure of many extreme districts to encourage same-party competition.
at is, same-party competition may not occur as deterministically in such districts as reformers might
have hoped.
As a first step toward addressing this second puzzle of why same-party competition may not be oc-
curring with sufficient frequency, I again turn to the post-reform data found in Test 2. One advantage of
comparing post-reform units within the same state is that all districts were, in theory, subject to the source
of the same-party “treatment” of interest, the top-two primary. However, the threat of actual same-party
competition is not as strong in some districts as others: some races exhibited tight three-way competition
in the first round that just barely exposed (and just barely failed to expose) candidates to same-party com-
petition in the general election, while others faced no such competition. Given that post-reform winners
in Test 1 were, overall, no more moderate than pre-reform winners, this raises the question: if same-party
competition holds the key to the top-two primary’s success or failure, do political actors (such as par-
ties or incumbents) exercise any control over whether a race ends in same-party competition? In other
words, do simple district characteristics (like partisan homogeneity) deteriministically govern which races
are “treated” with same-party competition, as proponents of the top-two primary have implicitly argued?
Or are local political parties, strong incumbents, or both able to avoid same-party competition?
I use data from both successful and failed in-party challenges to examine how much control political
actors may have over exposure to same-party general election competition. One way to leverage such data
is through regression discontunity (hereafter, RDD). In this case, “treatment” (same-party competition)
occurs only after election returns cross a clear cutpoint: when the nearest copartisan (in terms of electoral
support) to the top vote-getter in the primary election earns the second most (and not third or fourth
most) votes in that primary, same-party competition will occur. is generates a criterion for exposure to
same-party competition that resembles a forcing variable in an RDD. Formally, if
where cirefers to the highest-ranking copartisan to the top vote-getter in race iand oito the highest-
ranking non-copartisan candidate, then
1,if Xi>0
0if Xi<0
where τirefers to the treatment status for race i, i.e. whether or not a race exhibits same-party general-
election competition.
To make inferences in the RDD framework, races should be randomly distributed (at least locally) on
either side of the cutpoint. In other words, besides exposure to treatment, there should be no confound-
ing variables that explain why some races just missed out on same-party competition, while others were
narrowly exposed to it. However, if there is sorting around the cutpoint—that is, if actors know how to
(and are able to) influence their own exposure to treatment, RDD inference breaks down. While such a
phenomenon is normally an unfortunate result for the researcher, it offers interesting insight in this case
into the dynamics of exposure to same-party competition. Indeed, because standard statistical tests exist
for cutpoint sorting, one can examine whether someone appears to have exercised control over treatment.
Within the RDD literature, such a phenomenon has been referred to as “precise control” (see, for example,
Jacob and Zhu 2012).
To test for control around the cutpoint of the forcing variable, McCrary (2006) has developed a now
widely used test, which allows the researcher to examine whether discontinuities in density occur near
the relevant cutpoint in the forcing variable. Figure 6 displays a McCrary test for sorting. Were there no
sorting present, the confidence intervals around the curves should overlap. However, as the figure indicates,
the test cannot reject the null hypothesis of no sorting (p < 0.05). ese results suggest that some actor,
be it a political party, incumbent, or both, appears to be exercising some control over whether or not a
candidate faces same-party general election competition. Were the top-two primary associated with the
election of moderates regardless of the occurrence of same-party competition, this type of control/sorting
may not matter: simply being exposed to the possibility of same-party competition would be enough to
moderate candidates. However, as the above tests demonstrate, this latent threat alone is not enough to
moderate candidates. Instead, actual same-party competition is instrumental for moderates to be elected.
If candidates or parties can manipulate exposure to such competition, however, such a phenomenon counts
as a serious challenge to the future effectiveness of the system.
e results of the McCrary test provide evidence that political actors are able to avoid exposure to
Figure 6: McCrary Test for Sorting Around Cutpoint
Figure 7: Predictors of Same-Party Competition
same-party competition, but they do not indicate which actors control this exposure. Figure 7 displays the
results of a logistic regression, in which I explore some potential explanations for avoidance of same-party
competition. As one might expect, district extremism is positively associated with same-party competition.
Additionally, the positive coefficient on “party” indicates that Republicans are more likely to face same-
party competition than Democrats, though the practical implications of that result are not immediately
clear. e results also provide modest evidence that same-party competition has become more common
over time, given the positive coefficient on Year of Election.
One plausible explanation for this development is the fact that same-party competitions are more
common in open races. In other words, when incumbent legislators are not running, same-party general
elections are more likely to occur—an explanation consistent with the results show in Figure 7. is
may indicate that incumbents are better able to insulate themselves from co-partisan challenges than are
candidates in open seats. Consequently, if more districts experience same-party competition as incumbents
retire over time, the top-two primary may yet have a noticeable aggregate impact on legislator extremism
in Washington and California. Even still, this result does not negate the possibility that party leaders also
may exert influence over exposure to same-party competition. Indeed, party leaders are unlikely to ignore
the potential damage to party brand that prolonged same-party competition could cause, and future work
should examine whether party leaders have successfully resisted the moderating influences of the same-
party system.
Political polarization is among the most critical challenges to modern American democracy today. Scholars
and pundits alike worry that polarization will lead to a litany of governmental and societal ills, including
legislative gridlock and increasing personal resentment of political opponents. While primary election
reform has a mixed record in addressing polarization, reformers in California and Washington remain
optimistic about the top-two primary’s ability to drive candidates—and winners, in particular—closer to
the center of the political spectrum. To date, research has called into question the effectiveness of these
reforms: most studies have neglected to find any effect at all of top-two primaries on legislator moderation.
Nevertheless, by departing in key ways from these studies, I do find evidence that the key mechanism of
the top-two primary—same-party, general-election competition—has functioned as intentioned. More
specifically, when top-two primaries lead members of the same party to compete against one another in
the general election, winners in such districts are more moderate than similar situated districts facing
traditional two-party competition.
Still, the failure of the top-two to appreciably alter overall ideological polarization underscores the
importance of understanding how political parties and incumbents will react to institutional reforms,
particularly when those reforms are not likely to benefit them. Indeed, while reformers appear to have
hoped same-party competition would occur at high rates in partisan-homogenous districts, the “sorting”
analysis presented here suggests that political elites are able to avoid such competition in some cases.
Taken together, these findings suggest that political scientists’ claims that the top-two primary has had
“no effect” are premature and that the key to the systems effectiveness lies in reformers’ ability to find
ways to encourage more same-party competition in the general election. An important first step toward
realizing this goal will be to determine what or who, exactly, prevents races from experiencing same-
party competition. Are parties actively discouraging same-party challenges in post-reform Washington
and California? Or are incumbents ramping up their efforts to scare off primary challengers? Future
research should explore these and other sources of sorting.
Political polarization has become a phenomenon that has swept across the nation, far from a phe-
nomenon tied only to Congress or the federal government (e.g., Shor and McCarty 2011). Moreover,
whether through partisan gerrymandering or organic geographic polarization of voters, legislative districts
have become increasingly partisan-homogenous. Given these challenges, and given the promise of the top-
two primary when introduced in Washington and California, more research is needed to understand how,
when, and why the system can address legislator extremism. I argue that same-party competition provides
a useful tool for combatting such extremism, but that additional work must be done to understand why
and when such competition occurs.
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Representation? An Experimental Test of California's 2012 Top‐Two
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version 1.0 [Computer file]. Stanford, CA: Stanford University Libraries.
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Effects: A General Multivariate Matching Method for Achieving Balance in
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A: Robustness Checks Addressing Potential Strategic Donation
As noted in the main text, a potential concern about CFscores is that they are sensitive to the volume of
receipts attracted by legislators, or by other irregulaties in donation behavior. For example, while some
important legislators may attract donations from both ideological and access-seeking givers, others may
enjoy donations from only one of these types. If a legislator receives donations only from access-seekers
while another receives donations from ideological and access-seeking interests, CFscores may erroneously
measure the former legislator as more moderate than the latter legislator, for example. is concern is
particularly salient when examining state legislatures, where the volume of donations is typically lower
than in Congress.
To address this concern, I introduce a variable, Total Receipts, into the regression models from Test
2. is variable represents the total dollar amount of donations received by the winning candidate. Its
inclusion controls for the possibility that the total number of campaign funds received by the winner
explains the observed correlation between winner moderation and exposure to same-party general-election
competition. Table A1 depicts the results of regression models including this variable.
As Table A1 depicts, the inclusion of Total Receipts does not alter the substantive results presented in
the main text. at is, even after controlling for the volume of campaign funds received by the winning
candidate, exposure to same-party general-election competition remains negatively associated with ideo-
logical extremism among the winning candidates. Total Receipts is itself moderately associated with the
ideological extremism of candidates, displaying a positive, statistically significant association with Winner
Extremism. is relationship is only significant, however, when state-level fixed effects are included. is
is perhaps not surprising, given differences in fundraising between California and Washington.
Table A1: Same-Party Competition, Campaign Receipts, and Winner Extremism
Dependent variable:
Winner Extremism
(1) (2) (3) (4)
Same-Party Competition 0.144∗∗∗
(0.043) (0.043) (0.043) (0.043)
Total Receipts 0.000 0.000 0.00000∗∗ 0.00000
(0.00000) (0.00000) (0.00000) (0.00000)
Congressional Race 0.028 0.046 0.014 0.016
(0.071) (0.082) (0.069) (0.079)
Party 0.0003
0.0002 0.0003 0.0003
(0.0002) (0.0002) (0.0002) (0.0002)
Incumbent Winner 0.067 0.077 0.103
(0.055) (0.056) (0.053) (0.053)
Open Seat 0.020 0.033 0.034 0.040
(0.058) (0.059) (0.056) (0.056)
Upper Chamber 0.062 0.058 0.071
(0.038) (0.037) (0.036) (0.036)
District Extremism 0.213∗∗∗ 0.236∗∗∗ 0.285∗∗∗ 0.270∗∗∗
(0.068) (0.071) (0.067) (0.068)
Difference in Extremism 0.357∗∗∗
(0.038) (0.038) (0.036) (0.036)
Constant 1.115∗∗∗ 1.071∗∗∗ 1.143∗∗∗ 1.083∗∗∗
(0.063) (0.070) (0.061) (0.067)
State FEs? N N Y Y
Year FEs? N Y N Y
Observations 324 324 324 324
Log Likelihood 24.028 21.190 11.248 6.433
Akaike Inf. Crit. 68.056 68.379 44.495 40.867
Note: p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
Beyond concerns associated with the volume of donations, one may still reasonably worry that the
unusual electoral environment established by the top-two primary may encourage differential contribution
patterns accross same-party and two-party general-election contests. More specifically, the removal of inter-
partisan competition disallows donors both inside and outside the state/district from simply donating to
their copartisans.1us, one may argue that tests of the paper’s main results should be re-examined, using
roll-call or position-taking based measures alone.
Although concerns about differential donation patterns are important to consider, the main text focuses
specifically on CFscores for several key reasons. First and foremost, the focus of the theory underlying the
paper’s hypotheses lies in the electoral arena: to what extent do candidates exposed to same-party, general-
election competition present themselves as the more moderate of the two general-election candidate? To be
sure, revealed ideology within the legislature is ultimately a central concern for top-two primary proponents
(and opponents); but, given that such revealed preferences are themselves potentially influenced by agenda-
setting behavior, it is useful to first consider whether members present themselves more or less ideologically
to donors and the public during the campaign. Indeed, inasmuch as the goal of partisan agenda-setting
within the legislature is to present as unified a front as possible, examining electoral behavior provides
an opportunity to examine whether candidates appear to present themselves as a more or less moderate
candidate for office.
In addition to theoretical reasons for using electoral-focused rather than legislature-focused measures,
CFscores provide a variety of practical advantages over scores such as Shor and McCarty’s (2011) NPAT
scores, given the study’s race-level (and not legislator-level) level of analysis. Perhaps most crucially, CFs-
cores exist for both winning and losing candidates, while measures based on roll calls alone do not. is
fact enables the measurement of two variables featured in the main text—one dependent variable and one
1I thank an anonymous reviewer for articulated this point especially well.
independent variable. First, by allowing one to compare the ideological extremity of general election op-
ponents, CFscores enable tests involving the outcome variable, Election of Moderate. Without a measure
of the losing candidate’s preference, this entire set of tests would be rendered impossible. Second, CF-
scores enable the measurement of the variable Difference in Extremism, which captures how much more
ideologically extreme general-election candidates are from one another. Inclusion of this independent
variable is especially crucial, as it is a substantively and statistically predictor of the election of moderate
candidates throughout all three sets of tests in the paper—demonstrating that, if the gap between two
candidates is sufficiently wide, voters may possess the ability to discern which is more or less moderate.
Finally, unlike Shor-McCarty scores, CFscores place both state legislators and members of Congress onto
a single ideological scale. Given that the top-two primary applies to both state- and federal-level elections
in California and Washington, relying primarly on roll-call scores like Shor-McCarty would necessitate
removing federal races from the data. Given that federal cases represent some of the most high-profile
instances of same-party competition to date, removing these races would render the paper’s tests only a
partial examination of the hypotheses of interest.
Still, in spite of these reasons for focusing primarily on electoral behavior, one would still hope that
the main findings presented in the paper stand up to robustness checks that relate more directly to the
legislative process. As I demonstrate in Table A2 below, the these text do in fact persist when measuring
extremism using preference measures other than CFscores.
In the table, I retest models of the Winner Extremism outcome variable, using an alternative measure
of preferences, DW-DIME (Bonica 2018), more closely tied to the legislative process. To place candidates
into a single ideological space, DW-DIME uses information from both campaign donations and roll-call
behavior. To do so, the scores’ estimation procedure uses a sophisticated supervised machine learning
technique to map donation patterns to a target measure of legislative voting behavior. In the case of
members of Congress, the target measure of voting behavior is DW-NOMINATE; for state legislatures,
it is Shor-McCarty. Impressively, Bonicas tests show that this approach correctly classifies actual roll call
votes at a rate nearly identical to DW-NOMINATE for all members of Congress, and at a better rate
than DW-NOMINATE for first-time members. us, the scores are both firmly tied methodologically
to actual legislative behavior and predict future legislative behavior at high rate, as they derive their latent
ideological structure not solely donation patterns but from the roll call measures from which the model
learns. Additionally, the method generates ideology estimates for losing candidates, should one wish to
replicate analysis of the Election of Moderate outcome variable.
Using this measure, I find similarly strong support for the notion that winners of same-party general-
election are more moderate than simiarly situated winners exposed to traditional two-party competition.
ese results are summarized in Table A2. As the table summarizes, exposure to same-party general election
competition is consistent associated with the election of a more moderate candidate overall, regardless if
one introduces fixed effects at the state- or year- level. Taken together, then, this analysis and the donation
volume analysis indicate that the paper’s main results are not merely artifacts of unusual or overly strategic
donation patterns.
Table A2: Re-Testing Winner Extremity Hypotheses with Roll-Call-Focused Measure
Dependent variable:
(1) (2) (3) (4) (5) (6)
Same-Party Competition 0.033∗∗∗
(0.012) (0.013) (0.013) (0.013) (0.030) (0.030)
Post Reform 0.006
Democrat 0.0004∗∗∗
0.0005∗∗∗ 0.00000 0.00002
(0.0001) (0.0001) (0.0001) (0.0001) (0.0002) (0.0002)
Incumbent 0.017 0.017 0.002 0.004 0.003 0.005
(0.017) (0.017) (0.018) (0.019) (0.039) (0.040)
Open Seat 0.021 0.022 0.021 0.019 0.018 0.018
(0.018) (0.018) (0.019) (0.020) (0.041) (0.041)
State Upper Chamber 0.013 0.013 0.004 0.004 0.019 0.015
(0.009) (0.009) (0.011) (0.011) (0.025) (0.025)
District Extremity 0.0390.0370.0410.0400.1090.109
(0.020) (0.021) (0.023) (0.024) (0.055) (0.056)
Difference in Extremity 0.038∗∗∗
(0.009) (0.009) (0.012) (0.012) (0.024) (0.024)
California 0.085∗∗∗ 0.087∗∗∗ 0.082∗∗∗ 0.072∗∗∗ 0.0800.073
(0.008) (0.009) (0.011) (0.014) (0.041) (0.041)
Washington 0.045
(0.026) (0.028)
Constant 0.410∗∗∗ 0.406∗∗∗ 0.416∗∗∗ 0.399∗∗∗ 0.403∗∗∗ 0.392∗∗∗
(0.021) (0.022) (0.026) (0.028) (0.059) (0.063)
State-Level Effects Y Y Y Y Y Y
Year-Level Effects N Y N Y N Y
Observations 402 402 281 281 129 129
Log Likelihood 483.562 483.806 334.861 337.132 101.866 103.915
Akaike Inf. Crit. 949.124 947.613 651.722 650.265 183.731 181.830
Note: p<0.1; ∗∗p<0.05; ∗∗∗p<0.01
B: Facsimile of Sam Reed Meeting Notes
In August 2016, the author visited the Washington State Archive in Olympia, WA to study the records and
writings of the architects of the top-two system. e primary architect of the top-two primary system—
and primary defender in front of the Supreme Court—was then-Secretary of State Sam Reed. Given
transparency laws in place in Washington, most or all of Secretary Reed’s e-mails, meeting notes, and
other office contents from his time in office have been preserved at the Archive and are available for public
viewing. us, as part of the trip, the author photocopied many of these documents, along with columns,
new stories, and ballots from the nearly decade-long battle over the top-two. ese included the clip found
in Figure 1 of the main text.
Below, I display the full photocopy of the document from which Figure 1 was created. It should be
noted that the sentiments captured in the notes were independently reiterated in a later phone interview
with Secretary Reed directly.
C: Generating Matched Control Units Using the Population of Elections Available in DIME
In the main text, I present a matching analysis in Test 3 that compares same-party general-election contests
in Washington and California to a random same of contests from non-top-two states across the U.S. As I
indicate there, my primary reason for focusing on a relatively small random sample is practical: organizing a
dataset that matches a large number of both winning candidates and their main general-election challenger
is challenging. is is especially true when dealing with occasional missing data in Bonica’s DIME dataset.
Nevertheless, matching winning and losing candidates is important, because it allows the tests to match
on key covariates like Difference in Extremism.
Nevertheless, particularly given the asymptotic properties of matching methods, there are methodolog-
ical advantages to choosing the matched control set from the population of races available in the DIME
dataset. First, doing so ensures excellent ballance between Xcovariates, since the matches are selected from
a wide array of races. Second, particularly when calculating the ATC, drawing from the population of races
generates a larger matched sample than in the random-sample case. Given these advantages, I execute a
robustness check of my Test 3 results by generating my matches from the population of legislative races
available in Bonicas DIME dataset. While doing so precludes me from matching on variables such as
Difference in Extremism, I am able to match on whether the races winner was an incumbent, whether the
races was over an open seat, the chamber of the contest, the extremity of the district in question (folded
Tausonovitch-Warshaw scores), party of the winner, and year of the contest.
e results of these matching analyses are summarized in Table A3 and are overall quite consistent
with those presented in the main text. Indeed, races exposed to same-party general-election competition
tend to elect more moderate candidates overall than do highly similar districts that were not exposed to
such competition.
Table A3: Matching Analyses for Test 3,
Using Population of Races
Estimate (ATT) -0.173
AI Standard Error 0.070
p-value 0.013
Original Number of Treated Obs. 54
Matched Number of Treated Obs. 54
Estimate (ATC) -0.163
AI Standard Error 0.122
p-value 0.181
Original Number of Control Obs. 12741
Matched Number of Control Obs. 12741
... Other analyses suggest a few modest influences of primary rules on polarization. McGhee and Shor (2017), for example, suggested that California's and Washington's relatively recent experiences with the top-two primary slowed-if not reversed-polarization in those states due in large part to the existence of same-party runoffs (Crosson 2017). For the majority of states, however, no relationship can be found, and switching to a more open primary system appears unlikely to depolarize a legislature. ...
What Is, and Isn’t, Causing Polarization in Modern State Legislatures - Seth Masket
We examine the mechanical effect of a multiple-vote, proportional representation electoral system on party vote share in n dimensions. In one dimension, Cox (1990) has proven that such a system is centripetal: it drives parties to the center of the political spectrum. However, as populism has swept across Western Europe and the United States, the importance of multiple policy dimensions has grown considerably. We use simulations to examine how a multiple-vote PR system could alter electoral outcomes in four different European democracies: Germany, Romania, Belgium, and the Netherlands. Using this approach, we find that the system acts centripetally only when a centrist party actually exists. If a political system is sorted into ideological clusters at opposite corners of the ideological space, such a system rewards centrality among extremist clusters, not centrality more broadly. These findings suggest that the existing configuration of parties in a country can alter or even subvert the aims of electoral reforms.
Party polarization is perhaps the most significant political trend of the past several decades of American politics. Many observers have pinned hopes on institutional reforms to reinvigorate the political center. The Top Two primary is one of the most interesting and closely-watched of these reforms: a radically open primary system that removes much of the formal role for parties in the primary election and even allows for two candidates of the same party to face each other in the fall. Here we leverage the adoption of the Top Two in California and Washington to explore the reform’s effects on legislator behavior. We find an inconsistent effect since the reform was adopted in these two states. The evidence for post-reform moderation is stronger in California than in Washington, but some of this stronger effect appears to stem from a contemporaneous policy change—district lines drawn by an independent redistricting commission—while still more might have emerged from a change in term limits that was also adopted at the same time. The results validate some claims made by reformers, but question others, and their magnitude casts some doubt on the potential for institutions to reverse the polarization trend.
This paper develops a generalized supervised learning methodology for inferring roll call scores for incumbent and non-incumbent candidates from campaign contribution data. Rather than use unsupervised methods to recover the latent dimension that best explains patterns in giving, donation patterns are instead mapped onto a target measure of legislative voting behavior. Supervised learning methods applied to contribution data are shown to significantly outperform alternative measures of ideology in predicting legislative voting behavior. Fundraising prior to entering office provides a highly informative signal about future voting behavior. Impressively, contribution-based forecasts based on fundraising as a non-incumbent predict future voting behavior with the same accuracy as that achieved by in-sample forecasts based on votes casts during a legislator's first two years in Congress. The combined results demonstrate campaign contributions to be powerful predictors of roll-call measures of ideology and resolve an ongoing debate as to whether contribution records can be used to make accurate within-party comparisons.
Can electoral reforms such as an independent redistricting commission and the top-two primary create conditions that lead to better legislative representation? We explore this question by presenting a new method for measuring a key indicator of representation—the congruence between a legislator’s ideological position and the average position of her district’s voters. Our novel approach combines two methods: the joint classification of voters and political candidates on the same ideological scale, along with multilevel regression and post-stratification to estimate the position of the average voter across many districts in multiple elections. After validating our approach, we use it to study the recent impact of reforms in California, showing that they did not bring their hoped-for effects.
To improve representation and alleviate polarization among US lawmakers, many have promoted open primaries - allowing voters to choose candidates from any party - but the evidence that this reform works is mixed. To determine whether open primaries lead voters to choose ideologically proximate candidates, we conducted a statewide experiment just before California's 2012 primaries, the first conducted under a new top-two format. We find that voters failed to distinguish moderate and extreme candidates. As a consequence, voters actually chose more ideologically distant candidates on the new ballot, and the reform failed to improve the fortunes of moderate congressional and state senate candidates.
In 2012, California first used a nonpartisan “top-two” primary. Early academic studies of the effects statewide have produced mixed results on the key question: does the new law make it possible for more moderate candidates to win? This study focuses on one particular California State Assembly race, District 5, from 2012 to assess the operation of the new law in detail in one same-party runoff. Republicans Frank Bigelow and Rico Oller competed against each other in both rounds; Bigelow, the more moderate Republican, won the general election. This study uses the internal Bigelow campaign polling data (three surveys of 400 voters each) to assess the dynamics of the race, revealing not just voter attitudes towards the candidates but the reasons for Bigelow campaign choices. The results suggest that although little strategic behavior took place in the first round, voters, including Democrats, tended to support the spatially logical candidate in the general election – with the advantage to Bigelow, the candidate closer to the median voter of the district.
Little is known about the American public’s policy preferences at the level of Congressional districts, state legislative districts, and local municipalities. In this article, we overcome the limited sample sizes that have hindered previous research by jointly scaling the policy preferences of 275,000 Americans based on their responses to policy questions. We combine this large dataset of Americans’ policy preferences with recent advances in opinion estimation to estimate the preferences of every state, congressional district, state legislative district, and large city. We show that our estimates outperform previous measures of citizens’ policy preferences. These new estimates enable scholars to examine representation at a variety of geographic levels. We demonstrate the utility of these estimates through applications of our measures to examine representation in state legislatures and city governments.
I develop a method to measure the ideology of candidates and contributors using campaign finance data. Combined with a dataset of over 87 million contribution records from state and federal elections, the method estimates ideal points for an expansive range of political actors. The common pool of contributors that give across institutions and levels of politics makes it possible to recover a unified set of ideological measures for members of Congress, the President and Executive Branch, state legislators, governors and other state officials, as well as the interest groups and individuals that make political donations. Since candidates fundraise regardless of incumbency status, the method estimates ideal points for both incumbents and non-incumbents. After establishing measure validity and addressing issues concerning strategic behavior, I present results for a variety of political actors and discuss several promising avenues of research made possible by the new measures.
Does a typical House member need to worry about the electoral ramifications of his roll-call decisions? We investigate the relationship between incumbents’ electoral performance and roll-call support for their party—controlling for district ideology, challenger quality, and campaign spending, among other factors—through a series of tests of the 1956–1996 elections. The tests produce three key findings indicating that members are indeed accountable for their legislative voting. First, in each election, an incumbent receives a lower vote share the more he supports his party. Second, this effect is comparable in size to that of other widely recognized electoral determinants. Third, a member’s probability of retaining office decreases as he offers increased support for his party, and this relationship holds for not only marginal, but also safe members.
This paper presents Genetic Matching, a method of multivariate matching, that uses an evolutionary search algorithm to determine the weight each covariate is given. Both propensity score matching and matching based on Mahalanobis distance are limiting cases of this method. The algorithm makes transparent certain issues that all matching methods must confront. We present simulation studies that show that the algorithm improves covariate balance, and that it may reduce bias if the selection on observables assumption holds. We then present a reanalysis of a number of datasets in the LaLonde (1986) controversy.JEL classification: C13, C14, H31