Voting systems and strategic manipulation: An experimental study
| Published date | 01 January 2015 |
| DOI | 10.1177/0951629813514300 |
| Date | 01 January 2015 |
| Author | Anna Bassi |
| Subject Matter | Articles |
Article
Voting systems and strategic
manipulation: An
experimental study
Journal of Theoretical Politics
2015, Vol. 27(1) 58–85
©The Author(s) 2014
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DOI:10.1177/0951629813514300
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Anna Bassi
University of North Carolina at Chapel Hill, USA
Abstract
This article presents experiments that analyze the strategic behavior of voters under three voting
systems: plurality rule, approval voting, and the Borda count. Applying a level-kreasoning model
approach, strategic behavior is found to be significantly different under each treatment (voting
system). Plurality rule leads voters to play in the most sophisticated (i.e. best response), but
not necessarily insincere, manner. Thus, this voting system displays at the same time the highest
incidence of best responses and of sincere votes. The opposite holds for the Borda count games,
where voters depart from their sincere strategy the most, without playing the best response
strategy. Approval voting shows intermediate levels of sophistication and sincere behavior.
Keywords
Approval voting; experiment; level - R reasoning; strategic voting
1. Introduction
Voting is one of the chief foundations on which democracy and its political institu-
tions are constructed and developed. Hence, understanding how citizens vote is key both
to understanding democratic processes and to constructing formal models of political
institutions.
An issue in voters’ behavior that has long interested political science scholars is
whether voters vote ‘sincerely,’for their most prefer red alternativeor ‘strategically,’ cast-
ing their vote for a different alternative in order to induce a better outcome. Let us suppose
a voter believes that her most preferred candidate has little chance of competing for the
lead in the election. Voting for such a candidate may be ‘wasted’. The voter may decide
to switch her vote to the expected leading candidate she most prefers in order to make
her vote ‘pivotal’ in determining a better outcome for herself. A rational voter faces
Corresponding author:
Anna Bassi, Department of Political Science, University of North Carolina at Chapel Hill, 361 Hamilton Hall,
CB 3265, Chapel Hill, NC 27599-3265, USA.
Email: anna.bassi@unc.edu
Bassi 59
this trade-off in an election. She must balance her relative preference for the different
candidates against the relative likelihood of influencing the outcome of the election.
Gibbard (1973) proved that anypreference agg regationmethod is vulnerable to strate-
gic manipulation by voters. However, it is not clear whether the strategic behavior of
the voters leads to outcomes that are less desirable than the more representative sincere
outcomes. On the one hand, a voting procedure can function as a tool to aggregate the
preferences of the society, such that the more accurately that voting represents an elec-
torate’s true preferences, the better the elected political institutions serve the society’s
objectives. On the other hand, sophisticated voting outcomes may be more efficient or
superior to sincere outcomes, electing more often the Condorcet winner alternative, the
candidate, in a multi-candidate election, who wins a simple majority against each of the
others when every pair of candidates is compared.
As Palfrey (1989) claims, when voters behave in a strategic way and expect others
to do the same, they end up voting for one of the two leading candidates, making the
Condorcet alternative more likely to be elected.
One might surmise that some voting rules are more vulnerable than others; the
degree, then, to which voters’ strategic manipulation empirically affect the rules in
elections would appear to provide a relevant criterion for evaluating alternative voting
rules.
This article explores the extent to which voters engage in such manipulation through
the use of laboratory experiments. The experiments are designed to evaluate the effect of
different voting systems and preference profiles on the emergence of strategic behaviorin
committee elections. They also analyze how strategic manipulation affects the efficiency
of the election outcomes. Strategic behavior is studied in a series of complete-information
elections in which subjects know both their own preferences and the preferences of each
member of the committee. The committee is composed of five subjects who are asked
to vote to elect one of four alternatives according to either plurality voting, approval
voting, or Borda count. Abstention is not allowed; the small size of the electorate makes
each voter highly likely to be pivotal and makes abstention, consequently, a dominated
strategy.
The experimental literature on voting in committees is wide and increasing. Lab-
oratory experiments are ideal for evaluating theories of voting and comparing the per-
formances of different voting schemes when players are not restricted to votingsincerely
(Palfrey, 2009; Woon, 2012). In order to induce preferences over outcomes, subjects are
given monetary incentives.
Experimental studies on voting behavior, beginning with the landmark articles by
Plott (1967), Fiorina and Plott (1978), McKelvey (1979), and Schofield (1983), explore
the cooperative and non-cooperative theory predictions on voting and havebeen extended
in a number of directions. For example, Williams (1994) analyzes the extent to which
voters vote retrospectively; and Palfrey (1987) and Lupia (1994) analyze the relationship
between information and voting behavior.
The findings in terms of voters’ strategic behavior are mixed. Plott and Levine(1978)
found that voters use myopic strategies; Wilson and Pearson (1987) support this ini-
tial result, finding that most of the voters are sincere myopic voters, although with
limited foresight. Wilson (1986) finds that sophisticated voting is more likely under non-
cooperative conditions, whereas Herzberg and Wilson (1988) find that only one third
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