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Journal ArticleDOI

Party Formation and Coalitional Bargaining in a Model of Proportional Representation

TL;DR: In this article, a game theoretic model of a parliamentary democracy under proportional representation where "citizen candidates" form parties, voting occurs and governments are formed is studied. And the coalition governments that emerge as functions of the parties' seat shares, the size of the rents from holding office and their ideologies.
Abstract: We study a game theoretic model of a parliamentary democracy under proportional representation where 'citizen candidates' form parties, voting occurs and governments are formed. We study the coalition governments that emerge as functions of the parties' seat shares, the size of the rents from holding office and their ideologies. We show that governments may be minimal winning, minority or surplus. Moreover, coalitions may be 'disconnected.' We then look at how the coalition formation game affects the incentives for party formation. Our model explains the diverse electoral outcomes seen under proportional representation and integrates models of political entry with models of coalitional bargaining.

Summary (2 min read)

1. Introduction

  • In democracies that use proportional representation (PR), it is unusual for a single party to control more than half the seats in parliament.
  • The recent game theoretic models of PR, notably Diermeier and Merlo (2000) and Baron and Diermeier (2001), (collectively referred to as BDM) employ the efficient bargaining approach to coalition politics to provide an explanation for the size diversity of coalitions.
  • If all the invitees agree to join the government and if the prospective government wins the backing of a majority of legislators, then the government assumes office.
  • In particular, the authors see that there is a non monotonic relation between rents from office and connected coalitions.
  • The next section discusses some more papers which are related to their work.

3. The Model

  • In this section the authors formalize the political process under PR.
  • Let ei = 1(0) indicate that group i contests (does not contest) the elections.
  • The process of government formation is comprised of three stages: formateur selection, proto-coalition formation and the vote of confidence.
  • The formateur selection process described here (variously 7Note that the authors could alternately have assumed that people care for policy and rents (or directed transfers) in the ratio α and 1 − α.
  • Each member of the legislature simultaneously votes to approve or to disapprove the proto-coalition.

4. Solving the Legislative Model

  • Thus, the authors will first solve for the coalition formation and policy making stage for a given legislature.
  • Once the coalition wins the confidence vote, policy making and division of the spoils of office is decided by the bargaining among members Let Dk denote the proto coalition most preferred by a member of party k, i.e. Dk=argmaxD∈W∩Y vk(D).
  • For simplicity, the authors assume that Dk is unique for each k (otherwise choose with equal probability).
  • Let (C, Si, {xi}) denote a parliament comprised of C(> 0) parties where Si denotes party i’s seat share and xi its ideal point.

5. A symmetric three party characterization and a ‘limiting result’

  • Each party has well defined preferences denoted by a weak ordering Âi over the set of possible coalitions.
  • If the above condition fails to hold, the next best feasible alternative for party 1 is {1, 2}.
  • The following diagram shows the various equilibrium coalitions when party 1 is the formateur.
  • On the other hand, when they are on the same side, the authors can get again get disconnected coalitions when P is very high as the far extreme party will call on the smallest partner which may be farthest from it.

6. Party formation

  • The authors are now able to define the political equilibrium.
  • Given these definitions the authors can now easily show existence.
  • Non-Duvergerian predictions for PR have been made (see the papers cited in section 2), in particular showing that only two parties can form under PR.
  • The authors wish to look at conditions under which the median group forming the party is the unique equilibrium.

8. Robustness: How critical are the assumptions?

  • Voting behavior and inability of parties to commit to positions other that their ideal points.the authors.
  • This implies a continuum of one candidate equilibria where any candidate can stand in equilibrium.
  • 11 Notice, that this contrasts with Duverger’s hypothesis that PR leads to a multiparty (more than two) system.
  • The authors now present some results which contrast with random selection.
  • Thus there exists at least one coalition which Hence, parties commanding a majority of seats will not accept the proposal of a minority government by an extreme party.

9. Empirical relevance and concluding remarks

  • Moreover, by endogenizing the political entry stage the authors have shown how their legislature is consistent with a party formation game under the assumption of sincere voting.
  • The authors can usefully compare their paper to the papers by BDM which use efficient bargaining and perfect commitment within the coalition.
  • Moreover, whether it is the case that the party selected to be the formateur has an informal pre electoral understanding with a set of parties which together can win a majority in parliament.

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PARTY FORMATION AND COALITIONAL BARGAINING IN A
MODEL OF PROPORTIONAL REPRESENTATION
January 28, 2004
Abstract. We study a game theoretic model of a parliamentary democracy under
proportional representation where ‘citizen candidates’ form parties, voting occurs
and governments are formed. We study the coalition governments that emerge as
functions of the parties’ seat shares, the size of the rents from holding office and
their ideologies. We show that governments may be minimal winning, minority
or surplus. Moreover, coalitions may be ‘disconnected’. We then look at how the
coalition formation game affects the incentives for party formation. Our model
explains the diverse electoral outcomes seen under proportional representation and
integrates models of political entry with models of coalitional bargaining.
Siddhartha Bandyopadhyay
Dept of Economics,
University of Birmingham,
Birmingham B15 2TT, U.K.
e-mail: s.bandyopadhyay@bham.ac.uk
Mandar Oak
Department of Economics,
Williams College,
Williamstown, MA 01267
e-mail: moak@williams.edu
Key words: proportional representation, party formation, coalitions
JEL classification: C72, D72, H19
We thank Samrat Bhattacharya, Eric Bond, Stephen Coate, James Jordan, Vijay Kr-
ishna, Tamar London, Antonio Merlo, Neil Wallace, and participants at several conferences
and seminars for comments and especially Kalyan Chatterjee and Tomas Sj¨ostr¨om for end-
less discussions and suggestions. All remaining errors are ours.
1

1. Introduction
In democracies that use proportional representation (PR), it is unusual for a single
party to control more than half the seats in parliament. In a study of 313 elections in
11 democracies in Europe (see Diermeier and Merlo (2001)) from 1945-1997, it was
found that only 20 of the elections returned a single party with more than half the
seats in parliament. Hence, in such democracies minority and coalition governments
are more prevalent. Moreover, coalition governments differ in the number of partic-
ipants as well as the ideological cohesion of their members. For example, in a study
of fifteen European democracies in the post war period, Gallagher, Laver and Mair
(1995) find that about 35% of coalitions were minimal winning, 36% were minority
coalitions while the rest of the coalitions (29%) were surplus coalitions. Laver and
Schofield (1990) and Indridason (2001) report instances of ideologically disconnected
coalition governments being formed over the same time period in Europe.
The recent game theoretic mo dels of PR, notably Diermeier and Merlo (2000) and
Baron and Diermeier (2001), (collectively referred to as BDM) employ the efficient
bargaining approach to coalition politics to provide an explanation for the size diver-
sity of coalitions. According to this approach, the party in charge of putting together
a coalition (called the formateur) can buy the support of other parties by adapting
a compromise policy p osition or by making side payments in return for support. Us-
ing this they are able to generate equilibrium governments which can be minority,
minimum winning or surplus. This is a major point of departure from the previous
theoretical literature since Riker (1962) which had consistently predicted minimum
winning coalitions in equilibrium. However, these recent papers do not consider the
issue of disconnected coalitions
1
. They also do not look at whether their results are
consistent with endogenous party entry.
1
Brams et al (2001) is one of the few papers which explicitly addresses this issue.
2

In this paper we construct a game theoretic model of PR which endogenizes party
formation, voting as well as coalitional politics. Our paper shares some features with
the aforementioned literature in that we also use the formateur selection procedure
2
but precludes the possibility of efficient bargaining (in particular, of being able to
make unlimited side transfers) or the ability to be able to commit to a policy at the
government formation stage. Instead, we assume, that under a coalition government,
the implemented policy is approximated by the seat-weighted average of the ideal
policies of the coalition partners and each party in the coalition receives a share of
power (to be interpreted as rents from office or directed transfers in the paper) in
proportion to its seats. This approach allows us to formalize the issue of how party
entry and government formation are affected by the relative importance of ideology to
rents from office. In doing so, we generate a number of refutable predictions about the
role of policy motivation vis-a-vis political power in the determination of government
formation as well as political party formation.
The particular assumption about the bargaining outcome has strong empirical sup-
port. Empirical studies of power sharing among coalition partners (see Browne and
Fendreis (1980) and Laver and Schofield, (1990)) have found substantial evidence
that coalition partners share cabinet portfolios in proportion to their relative seat
shares. Since a large bulk of political power is vested in various ministerial offices,
the politician in charge of a particular ministry is entitled to that power as well as
the right to make a policy in the relevant area.
Our second point of departure from the previous literature concerns our treatment
of the status-quo in the event of the failure to form a government. We assume that
in the event that the attempts at government formation fail, a consensus government
comprised of all the parties is formed. Under such government, the implemented
policy is the seat-weighted average of the ideal points all the members of the legislature
2
Ansolabehere et al (2003) provide empirical support for the use of such models
3

and the political power is shared in proportion to the seats. Baron and Diermeier, on
the other hand, assume an exogenously given status quo while Diermeier and Merlo
assume it to be equal to the ideal point of one of the parties.
The basic structure of our model can be described as follows: there is a polity
comprised of groups of citizens who share policy preferences. Each group decides
whether or not to form a political party in order to gain representation in the legisla-
ture. Election takes place between the contesting parties and each party gets seats in
the parliament equal to its vote share. This is followed by the process of government
formation. If there exists a party that receives absolute majority, then it is selected
as the formateur, otherwise each party is probabilistically chosen to be the formateur
with the recognition probability equal to its seat share. The formateur invites any
subset of parties in the legislature to form the government.
3
If all the invitees agree to
join the government and if the prospective government wins the backing of a majority
of legislators, then the government assumes office. Otherwise a caretaker government
is instituted. The policy choice and the power sharing arrangement between the mem-
ber parties of a government is as described in the earlier paragraph. To sum up, we
model the system of PR by integrating the ‘citizen-candidate’ approach a la Besley
and Coate (1997) and Osborne and Slivinski (1996) with a variant of the coalition
formation literature.
We now summarize our main results. At the coalition formation stage, we show
how the equilibrium nature of coalitions varies both with the choice of formateur as
well as with changes in the value of ideology to rents from office. For a symmetric
three party case, we completely characterize the equilibrium coalitions. In particular,
we see that there is a non monotonic relation between rents from office and connected
coalitions. The other cases of interest we discuss is where there is a large centrally
located party with two smaller parties on either side and another where the two
3
We do not preclude the possibility that the formateur may invite a subset of parties that does
not include itself.
4

smaller parties are close to each other. We show how this can lead to disconnected
coalitions, the two small parties by leaving the large party out can appropriate more
rents for themselves. A general result that we get is that when the rents from office
are large enough, equilibrium governments are minimal winning though not minimum
size. At intermediate ranges (of the value of rents from office) we get the various kinds
of coalitions seen in democracies under PR. We then do a two dimensional analogue
with BDM and find that for their symmetric three party case we get minimum winning
coalitions under the assumptions in our model. The difference stems from the fact that
their results (on equilibrium coalition choice) are driven only by the position of the
(exogenously given) status quo and choice of formateur while our results also depend
on the ideological closeness of the parties as well as the trade-off between rents and
ideology. We then examine what incentives the coalition formation procedure gives
ideological group to form parties. We find that there exists an equilibrium of the
political game which has the median group (when it is unique) being the only group
to stand for elections and under some configurations, we show that this could in fact
be the unique equilibrium. Hence, this is contrary to the Duvergerian prediction
(see Duverger (1964))
4
that PR promotes more party formation than does Plurality
voting. We further show how political competition can increase with increases in the
value placed to rents from office. In particular, beyond a certain value of the rents,
we get a (non unique) political equilibrium where all the ideological groups contest
for elections.
The next section discusses some more papers which are related to our work. This
is followed by presenting the model, solving the legislative game and then solving
the entire political game. A comparison is done with the BDM papers using a two
dimensional policy space, followed by a robustness analysis by looking at how sensitive
4
See Feddersen (1992), Fey (1997) and Palfrey (1989) for formalizations of the Duvergerian hy-
pothesis that Plurality Rule leads to two party rule.
5

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Frequently Asked Questions (2)
Q1. What are the contributions mentioned in the paper "Party formation and coalitional bargaining in a model of proportional" ?

The authors study a game theoretic model of a parliamentary democracy under proportional representation where ‘ citizen candidates ’ form parties, voting occurs and governments are formed. The authors study the coalition governments that emerge as functions of the parties ’ seat shares, the size of the rents from holding office and their ideologies. The authors show that governments may be minimal winning, minority or surplus. 

Their model makes a set of predictions which are more precise and can provide a useful basis for further case studies along these lines. However, some things are worth further investigation-when the party elected to be the formateur is not the largest it is worth looking at whether they have informally waived the right to form the government. These issues together with a more specific procedure incorporating institutional details of bargaining among parties inside a coalition will lead the way to a more complete understanding of formateur selection considerations as well as why delays in bargaining over government formation occur.