Consensus sequences based on plurality rule
type: Item
instance of: scholarly article
title: Consensus sequences based on plurality rule
zbMATH Open document ID: 0768.92007
DOI: 10.1007/BF02460666
author: W. H. E. Day
author: F. R. McMorris
published in: Bulletin of Mathematical Biology
publication date: 1993-01-16T00:00:00Z
review text: The authors consider social choice problems of the following form: there are \(k\) voters and a set \(S\) of alternatives. Each voter \(i=1,2,\dots,k\) selects an alternative \(p_ i\in S\). This gives a profile \(P=(p_ 1,\dots,p_ k)\). The problem is to find a consensus function (or social choice rule) \(f\) which associates with each possible profile a most preferred (consensus) alternative \(f(P)\in S\). More generally, \(f(P)\) need not specify a single chosen alternative, but may be a set of alternatives, or may even specify several (consensus) sets of alternatives. In the biological interpretation which the authors have in mind, the voters are molecules and the set of alternatives is \(S=\{A,C,G,T\}\), where these letters represent the nucleic acid bases adenine, cytosine, guanine, and thymine. A profile like \(P=(A,A,C,G,A,A,G,C,T)\) represents a possible \(k\)-tuple of bases appearing at an aligned position in each of \(k\) molecules. The social choice problem mentioned above is then equivalent to the biological problem of finding a consensus of such aligned molecular sequences. The authors study consensus functions \(f\) of the following special form: with each profile \(P\in S^ k\), \(f\) associates a collection \(f(P)\) of subsets of \(S\), where each of these subsets is interpreted as a possible consensus result, and a subset containing more than one element corresponds to a so-called ambiguity code in biology. In particular, they define plurality rules which are median rules, and characterize them in terms of certain axiomatic properties.
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 92B05
Mathematics Subject Classification ID: 91B14
zbMATH DE Number: 94282
zbMATH Keywords: Condorcet properties
zbMATH Keywords: consensus of aligned
zbMATH Keywords: molecular sequences
zbMATH Keywords: molecules
zbMATH Keywords: nucleic acid bases
zbMATH Keywords: adenine
zbMATH Keywords: cytosine
zbMATH Keywords: guanine
zbMATH Keywords: thymine
zbMATH Keywords: consensus functions
zbMATH Keywords: ambiguity code
zbMATH Keywords: plurality rules
zbMATH Keywords: median rules
zbMATH Keywords: axiomatic properties
Wikidata QID: Q52410344
reviewed by: Manfred Nermuth
MaRDI profile type: Publication
cites work: The median procedure for n-trees
cites work: The median procedure in cluster analysis and social choice theory
cites work: On the derivation of majority rule
cites work: A formalization of consensus index methods
cites work: Condorcet Social Choice Functions
cites work: Q4198056
cites work: The Complexity of Some Problems on Subsequences and Supersequences
cites work: Consensus n-trees
cites work: A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decision
cites work: Consensus functions defined on trees
cites work: A characterization result for the plurality rule
cites work: Characterizations of the plurality function
cites work: Pattern recognition in several sequences: Consensus and alignment
cites work: Social Choice Scoring Functions
cites work: A Consistent Extension of Condorcet’s Election Principle
full work available at URL: https://doi.org/10.1007/bf02460666
OpenAlex ID: W4205710087
description: scientific article; zbMATH DE number 94282