Electoral Thresholds as Coordination Devices

Date01 April 2017
DOIhttp://doi.org/10.1111/sjoe.12175
Published date01 April 2017
AuthorMatías Núñez,Dimitrios Xefteris
Scand. J. of Economics 119(2), 346–374, 2017
DOI: 10.1111/sjoe.12175
Electoral Thresholds as Coordination
Devices
Mat´
ıas N´
u˜
nez
University of Cergy-Pontoise, FR-95011 Cergy-Pontoise, France
matias.nunez@u-cergy.fr
Dimitrios Xefteris
University of Cyprus, CY-1678 Nicosia, Cyprus
xefteris.dimitrios@ucy.ac.cy
Abstract
In this paper, we study one-person–one-vote parliamentary elections where voters care both
about the winner of elections and about the composition of the parliament. Parties enter
the parliament if and only if their vote share exceeds some predetermined threshold. We
show that equilibria generically exist in which all parties obtain a non-degenerate vote-share
and, perhaps more importantly, we show that the size of the electoral threshold acts as a
coordination device, which crucially affects the win prospects of the Condorcet winner party.
In particular, we argue that the win prospects of the Condorcet winner party decrease with
the size of the entry threshold.
Keywords: Entry threshold; Poisson games; strategic voting
JEL classification:D7; H1
I. Introduction
Most analyses of strategic voting behavior focus on situations where voters’
interests are unidimensional – the only issue at stake is the identity of
the election winner. This assumption, even if it is an obvious choice for
certain types of elections (e.g., presidential elections), seems to poorly
describe the context of other types of elections (e.g., local or parliamentary
elections). This is because the results of local or parliamentary elections are
usually multidimensional – the most voted ticket usually gains control of an
office while any ticket that surpasses a predetermined electoral threshold
is represented in the city council/parliament.1
This research has been developed within the center of excellence MME-DII (ANR-11-
LBX-0023-01). M. N´
u˜
nez also thanks the French National Research Agency (ANR) for their
support through the program ANR-14-CE24-0007-02.
1In Europe, these thresholds vary from about 2 percent (Denmark and Cyprus) to 10 percent
(Turkey) as far as parliamentary elections are concerned. We consider only elections with a
CThe editors of The Scandinavian Journal of Economics 2015.
M. N´
u˜
nez and D. Xefteris 347
To see how these other interests on the part of a voter might dramatically
affect her voting behavior, consider the example of a voter who cares both
about the winner of parliamentary elections (the party that receives most
votes) and about her preferred party entering the parliament and an electoral
threshold of 1 percent. If the voter expects that around 11 percent of the
voters (sincerely) vote for her preferred party, that around 43 percent of
the voters will vote for large party A, and that around 46 percent of the
voters will vote for large party B, then she would most probably prefer to
abandon her most preferred party and vote for the large party she dislikes
less. However, if the electoral threshold were close to 11 percent, the voter
would most probably prefer to stick with her preferred small party because
the probability that her vote might actually help her preferred party to enter
the parliament should be much higher than the probability that her vote
will determine the election’s winner.2Note that if all voters who rank first
the small party prefer large party Ato large party B, and if all voters who
rank first large party Aprefer the small party to large party B, then:
1. the Condorcet winner party (the party that would beat any of the other
parties in a two-way race) is party Aand the Condorcet loser party is
party B;
2. when the threshold is 1 percent, the Condorcet winner party will most
probably win (which is an efficient outcome in terms of who wins the
elections);
3. when the threshold is 11 percent, the Condorcet loser party will most
probably win because voters who vote for the small party will stick
with their preferred party and the small party will end up out of
the parliament with a very high probability (which is a profoundly
inefficient electoral outcome, both in terms of elections’ winner and in
terms of representation).
In this paper, we provide a formal analysis of situations such as the
example presented above and we aim to shed some light on the effect of
electoral thresholds on the electoral outcomes. To this end, we employ a
model with strategic/instrumental voters3who have multiple goals: voters
single district. In other words, we do not consider situations in which the voters are divided
into different districts, and then each district elects one member of the parliament.
2Our model assumes that a voter’s preferences on the set of competing parties is her private
information. Among others, this implies that voters are uncertain about the distribution of
candidates’ scores in the election.
3The strategic voting literature provides invaluable insights into the effectiveness of various
electoral systems and it has explained phenomena that for a long time were unsolved riddles
for researchers in the field. For example, Palfrey (1989), and the series of papers that
followed (Feddersen, 1992; Myerson, 2002; Messner and Polborn, 2004), have explained
CThe editors of The Scandinavian Journal of Economics 2015.

To continue reading

Request your trial

VLEX uses login cookies to provide you with a better browsing experience. If you click on 'Accept' or continue browsing this site we consider that you accept our cookie policy. ACCEPT