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

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 Feld et al. (1987). We find that, in m orthogonal dimensions, the feasible outcomes must lie within % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaca% qGTbaaleqaaaaa!36F8![sqrt {text{m}} ] radii of the center of the yolk