Voting with abstention

• Published date: 01 February 2022
• Author: Friedel Bolle
• Date: 01 February 2022
• DOI: http://doi.org/10.1111/jpet.12537

J Public Econ Theory. 2022;24:30–57.30

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wileyonlinelibrary.com/journal/jpet

Received: 5 February 2021

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Revised: 29 March 2021

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Accepted: 14 June 2021

DOI: 10.1111/jpet.12537

ORIGINAL ARTICLE

Voting with abstention

Friedel Bolle

Department of Business and Economics,

European University Viadrina Frankfurt

(Oder), Frankfurt, Germany

Correspondence

Friedel Bolle, Department of Business

and Economics, European University

Viadrina Frankfurt (Oder), Postfach

1786, D‐15207 Frankfurt (Oder),

Germany.

Email: bolle@euv-frankfurt-o.de

Funding information

German Ministry of Education and

Research, Grant/Award Number: FKZ

01LA1139A; Deutsche

Forschungsgemeinschaft,

Grant/Award Number: BO 747/14‐1

Abstract

Most voting models in the literature neglect abstention,

but is such a simplification justified? I investigate this

question in a model with outside pressure on voters.

For sequential voting (e.g., roll call votes), with and

without an abstention option, there is a unique sub-

game perfect equilibrium, which implies that true ma-

jorities always succeed. Abstention can be an

equilibrium strategy for some voters, in particular un-

der complex decision rules (e.g., weighted voting,

double majorities). Simultaneous voting often has a

unique pure strategy equilibrium but also a plethora of

mixed and pure/mixed strategy equilibria. Therefore,

only with equilibrium selection, can we evaluate the

consequences of neglecting abstention. For equal

weight voting, equilibria selected by the procedure of

Harsanyi and Selten change completely with an ab-

stention option, even if abstention itself is not or rarely

used. With small enough outside pressure, however,

the selected equilibrium honors true majorities in both

cases.

1|INTRODUCTION

I want to investigate a model which differs in two respects from most other voting models.

First, it assumes vote‐dependent costs instead of participation costs and, second, it allows

abstention.

This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits

use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or

adaptations are made.

© 2021 The Authors. Journal of Public Economic Theory published by Wiley Periodicals LLC.

On September 3, 2019, the British Conservative Party withdrew the whip from 21 of its MPs

because they voted against the party line. This means, they were practically expelled from their

own party. Only 10 of the suspended MPs had the whip restored; only four of these could run in

the December 2019 election as Tory candidates (retaining their seats); all other “rebels”lost

their seats. This is an extreme example of the outside pressure under which not only members

of parliament but also members of other voting bodies make their decisions. MPs’outside

pressure stems from party whips, lobbyists, their electorate, and public opinion (media).

Therefore, voting according to true preferences is often connected with costs and, I think, an

appropriate model of voting on a proposal should consider such costs. True preferences are

defined as the vote in cases where it is decisive.

I will use this model to investigate the question whether or not a popular simplification of

voting models is justified. The bulk of the theoretical literature about voting on a proposal

assumes binary decisions (Yes‐No voting) and binary results (accepting or rejecting a proposal).

Does the introduction of an abstention option have a considerable strategic effect? If not, the

concentration on simpler binary decisions is justified. There are voting rules where abstention

has the same effect on the voting result as voting No, for example if the acceptance of a proposal

needs a certain absolute number of Yes votes, that is, if an absolute (super‐)majority is ne-

cessary. For pluralities (= relative majorities) and many other decision rules, however, ab-

stention and No votes are not equivalent and the restriction on Yes‐No voting is a simplifying

assumption.

1.1 |Voting beyond equal weights

Under common ownership of firms, the shares of the owners are their weights whenthey vote on

proposals. Decision making in multinational organizations has to take into account considerable

asymmetry concerning the population of the countries as well as their economic, political, and

military power. This leads to veto rights, weighted voting, and the requirement of multiple

(super‐)majorities. For examples of votes with complex decision rules, see Posner and Sykes

(2014) and Bolle (2018). We will start this investigation with asymmetric voters and general

decision rules and then concentrate on almost symmetric voters and relative super‐majorities.

1.2 |Vote dependent versus participation costs

In almost all models, voting costs, if introduced at all, are participation costs. In many empirical

(e.g., Hodler et al., 2015) as well as theoretical investigations (e.g., Krishna & Morgan, 2012)

these are of central interest. Vote dependent costs may be intrinsic (party or personal loyalty,

religious requirements, conscience) or extrinsic, caused by the threats of party whips or bribes

from lobbyists or their equivalents in international organizations (Dippel, 2009) and board

meetings of firms and faculties (colleagues with special knowledge, special resources, formal or

informal power to promote people). There is a small number of nonformal articles on vote

dependent costs and their influence on voting, for example, Kilgour et al. (2006) and other

discussions of the role of party whips. Extrinsic voting costs may also stem from the effect of a

vote on public opinion and reputation. The benefits of an accepted proposal may as well stem

from different intrinsic and extrinsic sources. Costs and benefits have been discussed in detail

for voting games without an abstention option in Bolle (2018).

BOLLE

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