Graph-Theoretical Approaches to the Theory of Voting

Abstract

In this article, language, concepts, and theorems from the theory of directed graphs are used to characterize and analyze the structure of majority preference. A number of results are then derived concerning sincere, sophisticated, and cooperative decisions under two common majority procedures. These results supplement the work of Black and Farquharson. Perhaps contrary to common-sense thinking, general strategic manipulation of processes has beneficial consequences. It is widely recognized-and not only by political scientists-that the decisions of a body may be affected not only by such obviously relevant matters as the preferences of its members and their participation in or absence from particular votes, but also by such matters as the nature of the procedure and the order in which proposals are voted on. It is also recognized that may have gamelike characteristics offering strategic opportunities both to voters as individuals and to voters in coalitions. Finally, most political scientists-though probably few politicians or citizens-are by now aware of the paradox of voting and may have some sense of its connection with these questions of decision, procedure, and strategy. Over the past decade or so a somewhat technical literature on the theory of has developed in the public choice area. The present article adds to this literature by presenting a number of new propositions concerning majority under two common procedures. These propositions pertain to the questions alluded to in the first paragraph. These new results, together with some more familiar ones, are obtained by employing language, concepts, and theorems from the mathematical theory of directed graphs. In these respects, the article will be of interest primarily to specialists in the area *This article is in part a combination and revision of two unpublished papers: