Cooperative phenomena in crystals and the probability of tied Borda count elections

Abstract

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.