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The likelihood of the Borda effect in small decision‐making committees
Author(s) -
Colman Andrew M.
Publication year - 1980
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1980.tb00776.x
Subject(s) - condorcet method , voting , preference , approval voting , simple (philosophy) , mathematics , statistics , mathematical economics , majority rule , econometrics , psychology , computer science , political science , artificial intelligence , law , epistemology , philosophy , politics
Simple plurality voting allows the surprising possibility that a majority of a committee or an electorate may prefer one of the defeated alternatives to the plurality winner. Relatively little attention has been devoted to this paradox (which is distinct from Condorcet's ‘paradox of voting’) since the 18th century. With seven‐person committees choosing among three alternatives, the theoretical probability of its occurrence is shown to be 0.126 in a completely uniform culture in which all preference rankings are equally likely. The observed relative frequency was, however, found to be 0.020 when 70 university students who were randomly assigned to 10 seven‐person groups ranked 20 triplets of randomly chosen girls' names, and this was significantly lower ( P < 0.001) than the theoretical probability in a completely uniform culture.