In 1960, C. Domb published a paper entitled On the theory of cooperative phenomena in crystals in which he presented an expression for the number of cycles of length l in a triangular lattice. This expression was erroneous. We present a correct expression and we show that it is linked, in social choice theory, to the probability that all candidates are tied in an election with the Borda rule.

We model Monroe’s and Chamberlin and Courant’s multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (these variants correspond to optimizing total voter ...

On personal and professional levels, the Marquis de Condorcet did like his fellow Academy member J.C. Borda. It is not clear why; maybe it was the regrettable tension that sometimes exists between abstract and applied mathematicians, or maybe Condorcet harbored jealousy over Borda beating him by over a decade in recognizing the complex and interesting mathematical issues that arise in the socia...

O avanço da radiologia digital proporcionou uma melhoria significativa à qualidade das imagens radiológicas. Essa evolução trouxe muitos benefícios para o diagnóstico por imagem como a agilidade do processo, resolução espacial, diminuição tempo necessário de exposição, entre outros. Os últimos trabalhos publicados mostraram que função transferência modulação ou MTF (Modulation Transfer Function...

The Condorcet winner in an election is the candidate that would be able to defeat each of the other candidates in a series of pairwise elections. The Condorcet efficiency of a voting rule is the conditional probability that it would elect the Condorcet winner, given that a Condorcet winner exists. A closed form representation is obtained for the Condorcet efficiency of Borda Rule in three candi...

We characterize a rule for aggregating binary evaluations – equivalently, dichotomous weak orders – similar in spirit to the Borda rule from the preference aggregation literature. The binary evaluation framework was introduced as a general approach to aggregation by Wilson (J. Econ. Theory 10 (1975) 63-77). In this setting we characterize the “mean rule,” which we derive from properties similar...