An extension of Condorcet's paradox by McGarvey (1953) asserts that for every asymmetric relation R on a finite set of candidates there is a strict-preferences voter profile that has the relation R as its strict simple majority relation. We prove that McGarvey's theorem can be extended to...

In this paper we study the social preferences obtained from monotone neutral social welfare functions for random individual preferences. It turns out that there are two extreme types of behavior. On one side, there are social welfare functions, such as the majority rule, that lead to stochastic...

A review of Steven E. Landsburg's book More Sex is Safer Sex, the Unconventional Wisdom of Economics. The surprise 2005 best seller Freakonomics by Steven Levitt and Stephen Dubner launched a small genre of books by economists applying economic reasoning to everyday life and finding...

The purpose of this paper is to examine the extent to which the concepts of individual and collective choice unsed in economic theory desribe "predictable" or "learnable" behavior. Given a set X of N alternatives, a choice function c is a mapping which assigns to nonempty subsets S of X an...

Arrow's theorem asserts that under certain conditions every non-dictatorial social choice function leads to nonrational social choice for some profiles. In other words, for the case of non-dictatorial social choice if we observe that the society prefers alternative A over B and alternative B...

We propose and discuss two postulates on the nature of errors in highly correlated noisy physical stochastic systems. The first postulate asserts that errors for a pair of substantially correlated elements are themselves substantially correlated. The second postulate asserts that in a noisy...

We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise operators that are obtained as products of tiny noise...

Consider an election between two candidates in which the voters’ choices are random and independent and the probability of a voter choosing the first candidate is p 1/2. Condorcet’s Jury Theorem which he derived from the weak law of large numbers asserts that if the number of voters tends...

The Gibbard-Satterthwaite theorem states that every non-trivial voting method between at least 3 alternatives can be strategically manipulated. We prove a quantitative version of the Gibbard-Satterthwaite theorem: a random manipulation by a single random voter will succeed with non-negligible...