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...

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...

On the occasion of Robert J. Aumann's being awarded the 2005 Nobel Prize in Economics, this paper gives a personal view on some of Aumann's contributions, and primarily on his approach to foundational issues in game theory, economics, and science as a whole. It is based on numerous discussions...

The paper presents a notion of rationalizing choice functions that violate the “Independence of Irrelevant Alternatives” axiom. A collection of linear orderings is said to provide a rationalization by multiple rationales for a choice function if the choice from any choice set can be...

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...