Introduzione

EnWe give a standard proof of the results of Tulipani: if $T:X \rightarrow X$ and a dicotomic family exisists on $(X,T)$ then a continuous finitely additive probability measure (charge),which is invariant for T, exisists

An inversion relation of multinomial type

AbstractRecently Huevers, Cummings, and Rao proved that if Ψ and Φ are functions satisfying the relation Ψ(ϰ1…,ϰn=∑|s|=nnsφ(ϰs11,…ϰsnn then there exist unique numbers cs such that Φ(ϰ1…,ϰn=∑|s|=ncsΨ(ϰs11,…ϰsnn In this paper, an explicit expression for cs is established

On generalized inverses of matrices over integral domains

AbstractIt is proved that a matrix A over an integral domain admits a 1-inverse if and only if a linear combination of all the r × r minors of A is equal to one, where r is the rank of A. Some results on the existence of Moore-Penrose inverses are also obtained

Introduzione

EnWe give a standard proof of the results of Tulipani: if $T:X \rightarrow X$ and a dicotomic family exisists on $(X,T)$ then a continuous finitely additive probability measure (charge),which is invariant for T, exisists

Bibliography

Abstract

Bibliography

Abstract

Bibliography

Abstract

May's theorem in an infinite setting

We generalize May's theorem to an infinite setting, preserving the elementary character of the original theorem. We define voting scenarios and generalized voting scenarios, and prove appropriate versions of May's theorem. The case of generalized voting scenarios specialized to a countably infinite set of voters and the collections of all coalitions that have asymptotic density, shows that majority rule is the only aggregation rule that satisfies neutrality, irrelevance of null coalitions, anonymity, and positive responsiveness.Voting scenario Preference profile Aggregation rule Majority rule Countably many voters