SIMPLICITY: IMPOSSIBILITY THEOREMS

If a collective choice rule satisfies (1) the standard domain restriction; (2) the weak pairwise Pareto condition; (3) independence of irrelevant alternatives; and (4) base quasitransitivity, then, if a set S is weakly, locally pairwise decisive for some alternative against another, it is weakly, globally pairwise decisive between any two alternatives. The chapter presents impossibility theorems including Arrow's first impossibility theorem. Immediately after Arrow presented his first theorem, there arose critiques of the conditions used. In response to those critiques, several series of impossibility theorems have developed, each seeking to remove the use of a condition not found compelling. The chapter discusses one of these series, dealing with the condition of transitive rationality.