日　時：6月8日 17:00〜18:30
会　場：2号館11階　経済学部会議室B
報告者：Walter Bossert (University of Montreal and CIREQ)
タイトル：A general definition of positionalist voting rules (coauthor: Kotaro Suzumura)

Extended Abstract. In an election, a population of individuals (the voters) express their
preferences over the list of available alternatives (the candidates), and a voting rule is a
mechanism that assigns chosen candidates to these preference profiles. A prominent example
is the plurality rule which proceeds by counting, for each candidate, the number of voters
who place her or him in the top position of their respective ordering. The candidates with
the highest number of first-place positions are then elected.
The formal analysis of voting rules can be traced back at least two centuries. Among the
most fundamental early contributions are those of Bentham (1776) and Borda (1781). We
examine some proposals that appear in these classics, hoping to be able to shed further light
on the proposed election methods and their properties.
There are various possibilities of defining a voting rule. One consists of assigning a
set of chosen alternatives (that is, elected candidates) to each profile of individual voters’
preferences. A second option is to establish a social ordering of the candidates based on the
preference orderings expressed by the voters. Either of these methods can be employed for
the purposes of our project; we choose the latter for ease of exposition. That is, in Arrow’s
(1951/1963/2012) terms, we examine voting rules in the form of social welfare functions.
The plurality rule and the Borda (1781) rule are special cases of the class of positionalist
voting rules. These are election procedures that can be defined solely on the basis of the
positions in which each candidate appears in each voter’s preference ordering. We propose a
general definition of positionalist rules that encompasses those that are currently available
in the literature, and we illustrate how our definition distinguishes itself from these earlier
approaches. See Bossert and Suzumura (2018; in preparation) for details.
As argued in Bossert and Suzumura (2016/2017a, 2017b), Bentham’s (1776) principle
of the greatest happiness of the greatest number can be given an ordinal interpretation, in
which case it is equivalent to the plurality rule. We also examine a natural counterpart, the
principle of the greatest unhappiness of the least number, a proposal that focuses on the
voters whose bottom-ranked candidates are chosen. This alternative principle is tantamount
to the inverse plurality rule. Both of these principles allow for lexicographic extensions. We
discuss these extensions in the context of our definition of positionalist rules.