Thom Bezembinder

Preference reversals : Violations of unidimensional procedure invariance

textabstractPreference reversals have usually been explained by weighted additive models, in which different tasks give rise to different importance weights for the stimulus attributes, resulting in contradictory trade-offs. This article presents a preference reversal of a more extreme nature. Let (10, 5 Migr) denote living 10 years with a migraine for 5 days per week. Many participants preferred (10, 5 Migr) to (20, 5 Migr). However, when asked to equate these two options with a shorter period of good health, they usually demanded more healthy life years for (20, 5 Migr) than for (10, 5 Migr). This preference reversal within a single dimension cannot be explained by different importance weights and suggests irrationalities at a more fundamental level. Most participants did not change their responses after being confronted with their inconsistencies.

Social Choice Theory and Practice

The area of social choice (SC) as traditionally conceived deals with a community making a decision starting from and taking into account the preferences of its members. The preferences of the individuals being diverse and the decision sought by the community being unique, SC constitutes a conflict of kind (b). The decision of the community should be based on and in some sense reflect the preferences of the individuals. How to realize this maxim is the concern of SC theory. Coombs and A vrunin proposed the above distinctions only for those kinds of conflict in which the alternatives the conflict is about are clearly distinguished and given a priori. So, the parties in the conflict do agree about what the alternatives are and they know that eventually the conflict is being resolved in one of the pre-given alternatives. Considering a set of cars ordered from low to high quality and, jointly, from low to high price - so that higher quality can only be obtained at higher price - a prospective buyer is torn between low price and high quality (conflict of kind (a)) but eventually decides on one of the pre-given cars in which (s)he deems the trade-off between price and quality optimal. In deciding where to store nuclear waste first a set of feasible sites is determined and, then, one of those sites is eventually chosen although parts of the community may have various and strong opinions on what site is best 15

On Solving Intransitivities in Repeated Pairwise Choices

An operational method is presented for deriving a linear ranking of alternatives from repeated paired comparisons of the alternatives. Intransitivities in the observed preferences are cleared away by the introduction of decision errors of varying importance. An observed preference between two alternatives that causes an intransitivity in the course of the procedure will be reversed if it is of lesser importance. The method is applicable in case one wants to take account of intensities of preference and assume these to be monotone with the probability that an observed choice coincides with a fixed underlying true choice.

Generating random weak orders and the probability of a Condorcet winner

Abstract. We present an algorithm for generating a random weak order of m objects in which all possible weak orders are equally likely. The form of the algorithm suggests analytic expressions for the probability of a Condorcet winner both for linear and for weak preference orders.

The circumplex : a slightly stronger than ordinal approach

For some proximity matrices, multidimensional scaling yields a roughly circular configuration of the stimuli. Being not symmetric, a row-conditional matrix is not fit for such an analysis. However, suppose its proximities are all different within rows. Calling {{x,y}, {x,z}} a conjoint pair of unordered pairs of stimuli, let {x,y} --> {x, z} mean that row x shows a stronger proximity for {x,y} than for {x,z}. We have a cyclic permutation pi of the set of stimuli characterize a subset of the conjoint pairs. If the arcs {x,y} --> {x,z} between the pairs thus characterized are in a specific sense monotone with pi, the matrix determines pi uniquely, and is, in that sense, a circumplex with pi as underlying cycle. In the strongest of the 3 circumplexes thus obtained, --> has circular paths. We give examples of analyses of, in particular, conditional proximities by these concepts, and implications for the analysis of presumably circumplical proximities. Circumplexes whose underlying permutation is multi-cyclic are touched