Consensus sequences based on plurality rule
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.
scientific article; zbMATH DE number 94282