Majority rule outcomes and the structure of debate in one-issue-at-a-time decision-making

Abstract

In many group decision-making situations, such as faculty hiring decisions, outcomes are often arrived at by deciding one issue at a time (e.g., first rank, then subfield). It is well known that procedures limiting votes to separate orthogonal dimensions always result in a unique outcome at the generalized median, the median of each separate issue dimension. Often, however, there is conflict within groups over what ought to be the relevant (orthogonal) dimensions within which choices will be made. We show that the way in which debate is structured (i.e., the way in which the dimensions of choice are specified) can have important consequences for what outcome gets chosen, However, we also show that the range of outcomes that could arise from alternative structurings of the decision process is bounded. These bounds are expressed relative to the yolk, a sphere located centrally in the Pareto set, whose existence was first noted by Tullock (1967: 262) and whose properties have recently been developed by McKelvey (1986) and . We find that, in m orthogonal dimensions, the feasible outcomes must lie within x/m radii of the center of the yolk

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

“…The Banks set in turn contains various subsets such as Schwartz's (1986) "tournament equilibrium set," Grofman and Feld's (1986) "Schattschneider set" (see Feld and Grofman, 1988), and the "bargaining equilibrium set" , which are important in their own right. The identification of the Banks set and of its properties as a solution concept goes a long way toward demonstrating that there is an "internal structure" to majority rule top cycles which makes outcomes of majority rule processes considerably more predictable than has often previously been supposed.…”

Order Independence in Sequential, Issue-by-Issue Voting

“…Another prominent resolution of Tullock's puzzle was o¤ered by Shepsle [42] who argued that the division of a complex decision into several di¤erent jurisdictions (called germaneness), creates equilibria that would not be stable in a general, unconstrained collective decision model (See also Feld and Grofman [18] and Kramer [31], [32]). In Shepsle's approach, the focus on a lack of equilibria in spatial models of unconstrained voting is replaced by the study of particular strategic situations induced by the institutions governing proposal making, agenda formation, coalition formation and so on.…”

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.…”