Expressive Voting: Modeling a Voter’s Decision to Vote

The “paradox of voting” was identified by Anthony Downs in his seminal book An Economic Theory of Democracy [4]. In a large election, there is almost no chance that an individual vote will have any effect on the outcome of the election. Thus, faced with the decision of whether or not to vote, if there is any cost associated with the act of voting, then the only rational choice for a voter is not to participate. Much of the voting theory literature bypasses this problem by assuming that there is no cost to voting or that “strategic” considerations do not play a role in the voters’ decision to vote. See [5] for a discussion of the different approaches to this problem. However there is a second approach, prominently presented by Brennan and Lomasky, [2] whose line of argumentation roughly runs like this: A priori, utility could be associated with the outcome on an action or the performing of the act itsself. For modelling many cases of human choice behaviour these two choices do not make any observable behavioral difference (e.g. in ordering wine A rather than wine B vs. drinking wine A rather than wine B). Consequently, revealed preference analysis has developed a general preference for outcome based utilites. In voting situations however there turns out to be a crucial difference between the two kinds of utility attachments precisely because casting a certain ballot does not guarantee that one gets the desired outcome, nor is it any probable that the outcome changes at all. Obviously, attaching utilities to sole voting acts avoids the ”paradox of voting”, since one is guaranteed to receive the output utility associated with the voting statement made. To introduce some terminology: We call the voting behaviour induced by utilites on the outcome instrumental voting, since it takes the ballot as an instrument to bring about a certain political state. On the other hand, the voting behaviour induced by utility attachments on acts is called expressive voting, since it reflects the voter’s original preferences over parties. Brennan and Lomasky [2] argue that expressive reasoning about voting actually occurs and plays a major role in voting behaviour. Arguably, almost any realistic reasoning about whom to vote involves a superposition of the two principles, where the relative weights between these two depend upon certain aspects of the situation. Thus, in evaluating different voting procedures, one needs to analyze on how these compare from an instrumental as well as an expressive standpoint. While the instrumental approach of voting is widely studied in decision theory, the import of expressive voting in comparing voting systems is not very well understood. (see [2] for some analysis). In this paper, we explore an interesting new approach to this problem found in a recent paper by Enriqueta Aragones, Itzhak Gilboa and Andrew Weiss [1], henceforth called the AGW-approach. The basic idea of their model is that there are certain factual topics on the agenda and the agents’ utilites for the individual parties are derived by their positions on these topics. The structure of the paper is the following: In paragraph 2 we present the general model introduced by Aragnoes, Gilboa and Weiss and their semantics of