Choosing the right voting rule

Why vote? In a democracy, where sovereignty belongs to the people, we organize ourselves to make decisions together. This is what voting is all about: transforming a set of individual preferences into a collective one.

Voting must therefore legitimately represent the electorate. In voting theory, the discipline of the axiomatic approach considers that for the social choice resulting from a vote to be considered legitimate, the procedure used must tick several desirable criteria or "axioms". Take, for example, the election of the next French president: the procedure must not give rise to contradictory results such as Ms. Chair is preferred to Mr. Stool, who is preferred to Ms. Armchair, who is preferred to Ms. Chair. It is also desirable that the procedure is not manipulable, and that voters express themselves sincerely without attempting to implement strategies that do not reflect their true preferences. For example, in the case where I choose to vote for Mr. Stool, who is popular and moderately reflective of my ideas, rather than for Ms. Chair, my favorite candidate but who is little known and whom I imagine has no chance of winning. Knowing that Ms. Armchair is the opposite of my political views, I'd rather vote for Mr. Stool than take the risk of favoring Ms. Armchair.

The axiomatic approach studies which voting rules best correspond to these criteria, but the perfect procedure doesn't yet seem to exist... Famous results from this discipline show that it's hard to meet all the axioms. To cite just one example, the Gibbard-Satterthwaite theorem states the difficulty of having both a non-dictatorial rule (which does not always elect the same candidate regardless of individual votes) and a non-manipulable rule. The question of sincerity is central. It concerns the way in which voters feel that their true preferences can be taken into account, and whether it is worth expressing these preferences through this or that voting procedure.

The expressive utility of voting: an intrinsic interest in voting?

If I look at myself, why do I, a human being in society, decide to vote? The motivation alone of obtaining a legitimate social outcome does not resolve the famous paradox of voting: if we were rational or selfish, given that in the case of a large election the probability of an individual vote changing the final outcome of the election is almost zero, the cost of the act of voting is greater than its expected gain. Voting is therefore a form of irrationality or altruism on our part.

An alternative explanation is that we derive intrinsic utility, independent of consequences, from expressing ourselves through the act of voting. It is this notion of expressive power that Sacha-Bourgeois Gironde and João Ferreira set out in their article. The authors test a hypothesis that has not been the subject of a comparable study to date: if it is true that individuals derive utility from the mere fact of being able to express themselves through voting, independently of the outcome of the vote, then if a particular voting rule offers them the possibility of expressing their preferences more accurately, this expressive power should be increased, and this should manifest itself, on a collective level, in greater electoral participation.

Measuring electoral participation in terms of of different voting rule’s expressive power

The authors invited around 2,000 participants in Great Britain to vote on various public health policy choices at the time of the Covid 19 crisis. Participants were randomly assigned to the following three voting procedures, in ascending order of expressive power: plurality rule (through which one distributes only one point on one's preferred candidate, as in the French presidential election), approval voting (through which one can distribute one point on one or more candidates), and a slightly modified version of the Borda rule (which consists of giving no points to one's least favorite option, one point to the penultimate, two points to the antepenultimate, etc., ). When voting online, participants had to make a cognitive effort equivalent to the act of voting in a "real" election.

Firstly, no significant differences in terms of voter turnout were observed depending on the rule assigned. On the other hand, when participants were assigned a voting rule and given the opportunity to compare this rule with another more or less expressive one, the relatively more expressive rules resulted in a significantly higher level of participation. The authors also observed that greater expressive power of the rule induces a better representation of individuals' true preferences: when given the choice to express themselves more accurately, individuals are less inclined to manipulate the voting rule.

Breaking the procedural routine to motivate people to vote?

This study shows that voters really do seem to be driven by a desire to express their preferences, in this case concerning the administration of the public good. The authors suggest that voters are subjected, in the course of their democratic existence, to a kind of procedural routinization - of repeated use of the same voting rule - that weakens their civic motivation.

The authors highlight certain conditions under which differences in opportunities to better express oneself may or may not influence participation. In particular, they suggest that awareness of alternative voting rules (and therefore the presence of explicit reference points) seems necessary to increase participation. In a context of increasing political abstention, if electoral reform were to seek to increase the expressive power of voting procedures, the authors suggest that the government could link this reform to an information campaign providing details on the nature of the old and new rules, thus highlighting more directly than in our current context, the expressive advantages of the latter.

The authors are therefore tempted to conclude that the abstentionist phenomenon is not only the result of the hypothesis regularly put forward of a disillusionment with public affairs or a disavowal of political personnel, but also simply of the electorate's loss of contact with the possibility of fully (or at least sufficiently) expressing itself through the vote.

Bourgeois-Gironde, S., Ferreira, J.V. The expressive power of voting rules. Soc Choice Welf (2023)