Discrete Optimization and Social Decision Methods

Abstract

Optimizational methods have been commonly used in societal resource allocation-distribution problems in the last few decades. A particular social decision problem is of aggregating individual preferences into a social preference. Such an aggregation of preferences over a set of alternatives gives rise to two basic problems: (i) the ranking problem (or the agenda stipulation problem) where the society has to produce a ranking of alternatives, and (ii) the choice problem (or the candidate selection problem) where the society is interested in selecting one or more of the alternatives. Axiomatic approaches to the aggregation problems have been researched since the fifties, and there are varied possibility and impossibility results which specify environments restricted to differing degrees as they relate to aggregation procedures. Most of the research along such lines may be referenced in Arrow [1], Black [2], Riker and Ordeshook [18] and Sen [21].