It is known that, in Condorcet’s classical model of jury decisions, the proportion of jurors supporting a decision is not a significant indicator of that decision’s reliability: the probability that a particular majority decision is correct given the size of the majority depends only on the...

Consider the hypothesis H that a defendant is guilty (a patient has condition C), and the evidence E that a majority of h out of n independent jurors (diagnostic tests) have voted for H and a minority of k:=n-h against H. How likely is the majority verdict to be correct? By a formula of...

Arrow’s and the Gibbard-Satterthwaite theorems are proved using a common proof strategy based on a dictatorship result for choice functions. One of the instrumental results obtained shows the inconsistency between the basic assumption in each of these theorems and a mild majority principle.

In the very general setting of Armstrong (1980) for Arrow's Theorem, I show two results. First, in an infinite society, Anonymity is inconsistent with Unanimity and Independence if and only if a domain for social welfare functions satisfies a modest condition of richness. While Arrow's axioms...

Allocation rules map preference profiles into allocations, whereas trading rules map preference profiles and allocations into allocations. It is shown that no allocation rule can derive from a trading rule based on voluntary trade and satisfying a weak efficiency condition. If the trading rule...

Applying Weglorz' models of set theory without the axiom of choice, we investigate Arrow-type social welfare functions for infinite societies with restricted coalition algebras. We show that there is a reasonable, nondictatorial social welfare function satisfying "finite discrimination", if and...

This paper gives a concrete example of a nondictatorial, coalitionally strategyproof social choice function for countably infinite societies. The function is defined for those profiles such that for each alternative, the coalition that prefers it the most is gdescribable.h The gdescribableh...

We study the properties of decisions made by committees who select alternatives by constructing shortlists. We find that even when committees are themselves rational, such procedures may not give rise to rational choices. A necessary condition for this to occur is disagreement between...

A social welfare function for a denumerable society satisfies {Pairwise Computability} if for each pair (x, y) of alternatives, there exists an algorithm that can decide from any description of each profile on {x,y} whether the society prefers x to y. I prove that if a social welfare function...

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy gtops only.h That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third, . . . , or...