Multiple vote electoral systems: a remedy for political polarization

ABSTRACT

We examine the mechanical effect of a multiple vote, proportional representation electoral system on party vote share in n dimensions. In one dimension, Cox (1990) has proven that such a system is centripetal: it drives parties to the center of the political spectrum. However, as populism has swept across Western Europe and the United States, the importance of multiple policy dimensions has grown considerably. We use simulations to examine how a multiple vote system could alter electoral outcomes in all possible parliamentary systems. We find that multiple vote systems act centripetally in multiple dimensions too, though weakly in extreme cases where parties are sorted into ideological clusters at opposite corners of the ideological space. Even in these cases, though, we find that a slight disturbance of the conditions (by introducing an additional party- even if it is very small) strengthens the centripetal properties of the multiple vote system.

KEYWORDS:

• Electoral systems
• polarization
• populism
• approval voting
• rank-choice voting
• parties

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The technical term for this system is that it is non-cumulative. In cumulative systems voters can use their votes to support candidates of the same party. For example, in Bremen and Hamburg voters are endowed with five votes each and they can use them to support the same party. We thank an anonymous reviewer for providing this information to us.

2 See Tsebelis and Ha (2014) for the theoretical argument and Tsebelis and Crosson (2020) for the application in the case of the Netherlands.

3 Another important reform at the U.S. state level is the ‘top two’ candidate primaries. Here, voters participate in a common ‘primary’ and then select between the prevailing top two candidates in the general elections. Crucially, these general-election candidates may belong to the same party. When they do, the more moderate of the two candidates tends to prevail. Since the adoption of this system in the states of Washington and California, several studies have found evidence of moderation (see Crosson, 2020; Grose, 2014, Grose, 2020). Both these reforms and their "blanket primary" predecessors were supported by bipartisan interests, as a means for combatting ideologues (see Shea, 1984).

4 The election of Doges of Venice was also done through approval voting but in multiple rounds, though a deliberately complicated system so that the influence of organized clan interests would be minimized.

5 The total number of available choice sets decreases after 5 votes, since the voters now face the decision of who to exclude in their ballot, rather than who to include.

6 The very fact that this system is the ‘acclamation vote’ of ancient Sparta indicates that the logic is simple and straightforward! Nevertheless, we do not mean to suggest that, in practice, voters would not take some time to acclimate to the system. Certainly, voters would learn how to use their new choice set to express their preferences. However, we aim primarily to underscore the potential effects of the system after these transitional factors have run their course.

7 Practically speaking, this means that the voter stops casting votes entirely (rationally or randomly) once the a threshold is reached. For precision, one may define v_j as the set of parties that lie within voter j’s range of acceptability a. By definition, $i^{-}$ for voter j must be in the set v_j in order for the voter to actually cast their vote.

8 Interested readers may use our appendix to apply our model to analyze any system or particular country they want.

9 We selected this size so that with a single vote this party would not have been represented in the Budestag, and it would not have altered the results of a single vote system.

Additional information

Notes on contributors

Jesse M. Crosson

Jesse M. Crosson is Assistant Professor of Political Science and Faculty Affiliate for the Program on Urban Studies, Trinity University.

George Tsebelis

George Tsebelis is Anatol Rapoport Collegiate Professor of Political Science at the University of Michigan, Ann Arbor.