Cycle avoiding trajectories, strategic agendas, and the duality of memory and foresight: An informal exposition

Abstract

Abstract. This paper considers the notion of cycle avoiding trajectories in majority voting tournaments and shows that they underlie and guide several apparently disparate voting processes. The set of alternatives that are maximal with respect to such trajectories constitutes a new solution set of considerable significance. It may be dubbed the Banksset, in recognition of the important paper by Banks (1985) that first made use of this set. The purpose of this paper is to informally demonstrate that the Banks set is a solution set of broad relevance for understanding group decision making in both cooperative and non-cooperative settings and under both sincere and sophisticated voting. In addition, we show how sincere and sophisticated voting processes can be viewed as mirror images of one another -embodying respectively, "memory" and "foresight." We also show how to develop the idea of a "sophisticated agenda," one in which the choice of what alternatives to propose is itself a matter of strategic calculation.

Susceptibility to coalitional strategic sponsoring

“…Fifth, in our paper, we ignore the possibility of voters adopting sophisticated behavior as defined by Farquharson (1969) and further characterized by McKelvey and Niemi (1978); we implicitly assume that sponsors are more energetic than voters, and our aim was to focus on an aspect of the influence of sponsors on the voting outcome; but as pointed out by Miller (1995: 115), in some contexts, issues are "sufficiently small and simple that the final outcome does not depend on the particular type of voting behavior," whether sophisticated or sincere. However, taking account of sophisticated voting would clearly be an important improvement to the analysis, with larger issues, and would relate our results to the numerous results of the literature on sophisticated voting (for example, Shepsle and Weingast 1984;Banks 1985;Miller et al 1990aMiller et al , 1990b.…”

Orderings based on the banks set: Some new scoring methods for multicriteria decision making

“…20 As noted on page 11, the Banks set may be defined in terms of externally stable chains, rather than maximal chains and hence a compelling alternative definition for the shortestchain score would be the length of the shortest externally stable chain, rather than the shortest maximal chain. Related, the Banks set may be constructed by growing amendable agendas using Banks trajectories [27]. I base the scores in this article on maximal chains for two reasons: (1) the original construction in [5] was in terms of maximal chains and (2) the alternative would over-count the number of chains (e.g., if the majority preference relation were transitive, any subset of alternatives containing the Condorcet winner is an externally stable chain).…”

Social choice theory, social decision scheme theory, and group decision-making

“…Afterwards the participants would rate their satisfaction with each social choice rule and the degree to which it fulfilled the desirable characteristics. Social choice theorists such as Feld and Grofman (1988); Fishburn (1973); Grofman (1981); Kameda (1996); McLean and Urken (1995);Miller, Grofman, and Feld (1990); Riker (1982Riker ( , 1986; and Taylor et al, (2006) provide a rich source of ideas for such research. Castore and Murnighan (1978) used a somewhat similar experiment to assess member support for group decisions under different social choice rules.…”