Poisson voting games under proportional rule

Francesco De Sinopoli,Claudia Meroni

doi:10.1007/s00355-021-01367-2

Francesco De Sinopoli, Claudia Meroni

Open Access

https://doi.org/10.1007/s00355-021-01367-2

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Abstract

We analyze strategic voting under proportional rule and two parties, embedding the basic spatial model into the Poisson framework of population uncertainty. We prove that there exists a unique Nash equilibrium. We show that it is characterized by a cutpoint in the policy space that is always located between the average of the two parties’ positions and the median of the distribution of voters’ types. We also show that, as the expected number of voters goes to infinity, the equilibrium converges to that of the case with deterministic population size.

Highlights

Citizens often act strategically as voters. Their expected behavior influences the competing parties’ positioning choices, and their actions determine the electoral outcome and, the policy that is implemented according to the electoral rule in force
We study the behavior of the equilibrium cutpoint as the expected number of voters increases and show that it converges to the equilibrium cutpoint of the deterministic model with a continuum of voters
We are going to prove the existence of a unique Nash equilibrium exploiting this fact, which allows to consider the restriction of the best response correspondence to cutpoint strategies

Summary

Introduction

The policy outcome is precisely the “cutpoint outcome”, that is, the outcome that is implemented when all the voters whose bliss points are on its left vote for the leftmost party and all the voters whose bliss points are on its right vote for the rightmost one This result has been applied to other electoral systems exhibiting positive degrees of power sharing in Meroni (2017), where the limit equilibrium outcome is characterized for the two-party case. If the expected number of voters is sufficiently large, parties choose extreme positions in equilibrium, in line with the results of the model with a continuum of strategic voters (Meroni 2017) This does not hold for every population size, depending on the distribution of voters’ types.

The model

Equilibrium analysis

Large electorate

Parties’ political competition: an example