Strategic Voting and Coordination Problems in Proportional Systems
| Published date | 01 June 2014 |
| Author | Ludovic Rheault,André Blais,Cengiz Erisen |
| DOI | 10.1177/1065912913520573 |
| Date | 01 June 2014 |
| Subject Matter | Articles |
research-article2014
Article
Political Research Quarterly
2014, Vol. 67(2) 386 –397
Strategic Voting and Coordination
© 2014 University of Utah
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Problems in Proportional Systems: An
DOI: 10.1177/1065912913520573
prq.sagepub.com
Experimental Study
André Blais1, Cengiz Erisen2, and Ludovic Rheault3
Abstract
We investigate strategic voting in proportional representation (PR) systems where parties are organized in pre-
electoral coalitions and subject to a vote threshold. We show that such political systems are likely to generate
coordination problems among the supporters of a coalition, and we examine voter behavior in this setting using a
laboratory experiment with repeated rounds of elections. Our findings suggest that in absence of electoral history,
voters cannot coordinate their efforts successfully and are more likely to vote sincerely. However, as history becomes
available, the vote threshold induces strategic coordination on parties that performed best in previous elections.
Keywords
strategic voting, coordination games, experimental method, proportional systems, thresholds
The once discounted idea that proportional representation
2009), justifying our decision to focus on this specific
(PR) triggers strategic voting has now become widely
structure of preferences. We show below that in this con-
accepted in the discipline (see, for instance, Abramson et
text, the presence of a vote threshold leads to a coordina-
al. 2010; Bowler, Karp, and Donovan 2010; Hobolt and
tion game between the supporters of a coalition—that is,
Karp 2010; Lago 2012; Viñuela and Artés 2012). voters from a specific camp have incentives to coordinate
Nonetheless, we argue that the mechanisms driving stra-
their vote on viable parties to increase the chances that
tegic voting under PR are not completely understood.
their preferred coalition forms the government. In fact,
This article focuses on one specific form of tactical vot-
the problem becomes analogous to a familiar “Bach or
ing—the strategic desertion of non-viable parties in the
Stravinsky” game.1
presence of a threshold—that we believe is fundamental
We should point out that our experimental design rules
in many PR systems. Our experimental design reproduces
out other forms of strategic voting sometimes associated
repeated rounds of PR elections with pre-electoral coali-
with PR systems. First, we impose the existence of prede-
tions and a varying vote threshold, which allows us to
termined coalitions, which means that our setup excludes
examine the evolution of strategic behavior over time.
the possibility of tactical coalition voting, that is, strate-
Our findings help to understand the mechanism behind
gic voting aimed at influencing the formation of post-
the occurrence and evolution of tactical voting in PR sys-
electoral government coalitions (Austen-Smith and
tems, which in turn leads to a rich set of implications for
Banks 1988; McCuen and Morton 2010). Second, our
the study of party systems.
design is not suited to explore threshold insurance voting
Specifically, we are interested in PR systems where
(or coalition insurance strategy), that is, voting strategi-
party coalitions are formed before elections and where a
cally for a smaller member of a pre-electoral coalition at
vote threshold is required for a party to obtain seats. We
consider instances in which voters have strict preferences
over coalitions but disagree about which party should
1University of Montreal
lead a given coalition (assuming that the party with the
2TOBB University of Economics and Technology
most votes within a winning coalition will lead the gov-
3University of California, Riverside
ernment). The idea that voters form preferences over
coalitions has found strong support in recent empirical
Corresponding Author:
studies (see, for example, ; Blais et al. 2006; Bowler,
Ludovic Rheault, Department of Political Science, University of
California, Riverside, 900 University Avenue, College Building South,
Karp, and Donovan 2010; Duch, May, and Armstrong
Riverside, CA 92521, USA.
2010; Gschwend 2007; Shikano, Herrmann, and Thurner
Email: ludovic.rheault@ucr.edu
Blais et al.
387
risk of not reaching the threshold (Cox 1997, 197–98;
Table 1. Voter Preferences without Threshold.
Fredén, forthcoming; Meffert and Gschwend , 2010).
Voter 2
This form of strategic voting has been examined particu-
larly in Germany where supporters of the major parties
A
B
(the Christian Democratic Union (CDU) or the Social
Voter 1
Democratic Party (SPD)) sometimes cast a list vote for
A
3, 1
2, 2
the smaller coalition partner (the Free Democratic Party
B
2, 2
1, 3
(FDP) or the Greens) to help that party reach the 5 per-
cent vote threshold and, in the process, ensure that their
preferred coalition obtain a majority of the seats and form
the government (Gschwend 2004, 33). The type of strate-
gic voting that we are studying here is sometimes called
Table 2. Voter Preferences with Threshold of Two Votes.
coalition-targeted Duvergerian voting (Bargsted and
Voter 2
Kedar 2009; Hobolt and Karp 2010, 304), which simply
means the strategic desertion of non-viable parties. This
A
B
concept is close to familiar forms of strategic voting in
Voter 1
plurality systems and should be the most intuitive to
A
3, 1
0, 0
political scientists.2
B
0, 0
1, 3
Put simply, our argument is that supporters of party
coalitions face a problem similar to that depicted in other
games of coordination. Namely, many vote choices are
least preferred party lead the coalition than to see their
strategically sound, although voters lack a reference point
favorite coalition receiving no seat at all. This structure
(or “focal point”) to coordinate their efforts successfully.
corresponds to a simple Bach or Stravinsky game with
This sort of problem has been the object of extensive
two coordination equilibria: the two action profiles in
research, in particular within the field of experimental
which both voters choose the same party represent opti-
game theory (see, for example, Blume and Gneezy 2000;
mal strategies.
Crawford and Haller 1990; Duffy and Hopkins 2005;
Empirical implementations of the problem depicted in
Kim 1996; Mehta, Starmer, and Sugden 1994; Meyer et
Table 2 are challenging, because it is hardly possible to
al. 1992; Van Huyck, Battalio, and Rankin 1997). To
interpret and make sense of the choices made by voters.
understand the strategic behavior of voters, we need to
Failed or successful coordination is not informative of the
formulate hypotheses regarding the focal points that they
motivations of voters, as both A and B are strategically
will likely use to coordinate their actions.
sound choices for the two voters. Likewise, the voters’
To illustrate the problem in question, consider first the
preferences are not informative of the observed outcome.
preference ordering of two supporters of a pre-electoral
Although it is possible to tell whether a voter casts a stra-
coalition composed of Parties A and B, as depicted in
tegic vote (in the sense of a vote for the party that is not
Table 1. This setup represents the case where there is no
the first preference), without additional information we
vote threshold.3 The numbers in the cells of Table 1 cor-
cannot understand the mechanism behind strategic
respond to payoffs—the first numbers are the payoffs of
voting.
Voter 1 given her own choice (row headers) and the cor-
For this reason, we devise laboratory experiments in
responding choices of Voter 2 (column headers); the sec-
which participants are asked to play the role of voters in
ond numbers represent the payoffs of Voter 2. Those
repeated rounds of PR elections with a similar structure
payoffs are useful to represent the ordering of prefer-
of incentives. By introducing a dynamic component,
ences. Voter 1 prefers Party A within the A–B coalition,
we are able to tell whether voters make use of the his-
whereas Voter 2 prefers Party B. When their choices dif-
tory of play—information about previous elections—to
fer, both voters have an equal chance of seeing their pre-
coordinate their efforts meaningfully. Moreover, an
ferred party lead the coalition, which they prefer to the
experimental setting allows us to manipulate and assign
outcome where their least preferred party ends up as the
preferences randomly, hence avoiding endogeneity
leader. This game has a single Nash equilibrium in which
issues that could otherwise plague an analysis based on
both voters choose their favorite party, which is the
observational data. We also modify the size of the
expectation of standard proximity models of voting.
threshold to reduce the number of vote configurations
In contrast, Table 2 depicts the situation in which vot-
that can lead to successful coordination. This research
ers have the same preference ordering, but where a legal
design leads to a rich set of results allowing us to shed
threshold imposes that a party must obtain two votes to
light on the mechanisms behind strategic voting in PR
receive seats. In this case, both voters prefer to see their
systems.
388
Political Research Quarterly 67(2)
Our specific objective is to test three predictions
academic divisions to play the role of voters. Our goal...
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