It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. (...) This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated. (shrink)

Sen's classic social choice result supposedly demonstrates a conflict between Pareto and even minimal forms of liberalism. By providing the first direct mathematical proof of this seminal result, we underscore a significantly different interpretation: rather than conflicts among rights, Sen's result occurs because the liberalism assumption negates the assumption that voters have transitive preferences. This explanation enriches interpretations of Sen's conclusion by including radically new kinds of societal conflicts, it suggests ways to sidestep these difficulties, and it explains earlier approaches (...) to avoid the difficulties. (shrink)

It is well known that decision methods based on pairwise rankings can suffer from a wide range of difficulties. These problems are addressed here by treating the methods as systems, where each pair is looked upon as a subsystem with an assigned task. In this manner, the source of several difficulties is equated with the standard concern that the “whole need not be the sum of its parts.” These problems arise because the objectives assigned to subsystems need not be compatible (...) with that of the system. Knowing what causes the difficulties leads to resolutions. (shrink)