Cooperative phenomena in crystals and the probability of tied Borda count elections
type: Item
instance of: scholarly article
title: Cooperative phenomena in crystals and the probability of tied Borda count elections
zbMATH Open document ID: 1107.91034
DOI: 10.1016/S0166-218X(01)00308-0
author: Thierry Marchant
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: The author derives an alternative formula for the number of \(n\)-step closed paths on a triangular lattice, and corrects the formula published by C. Domb [On the theory of cooperative phenomena in crystals. Adv. Phys. 9, 149--361 (1960)], where apparently a factor \(l!\) emerged from typesetting as \(1\). Modelling voter (strict) rankings of three candidates by the edges of the lattice, the author notes that a Borda tie corresponds to a closed path and so is able to use the formula to determine the probabilities that a vote of \(l\) voters results in a tie under Borda count.
Mathematics Subject Classification ID: 91B12
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 82D25
zbMATH DE Number: 1792301
zbMATH Keywords: Borda
zbMATH Keywords: probability of ties
zbMATH Keywords: random walk
zbMATH Keywords: triangular lattice
Wikidata QID: Q60692076
reviewed by: Duncan J. Melville
describes a project that uses: OEIS
MaRDI profile type: Publication
cites work: A Random Voting Graph Almost Surely has a Hamiltonian Cycle when the Number of Alternatives is Large
cites work: Condorcet's paradox
cites work: Q4834167
DBLP publication ID: journals/dam/Marchant02
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description: scientific article; zbMATH DE number 1792301