A geometric examination of Kemeny's rule

By using geometry, a fairly complete analysis of Kemeny's rule (KR) is obtained. It is shown that the Borda Count (BC) always ranks the KR winner above the KR loser, and, conversely, KR always ranks the BC winner above the BC loser. Such KR relationships fail to hold for other positional method...

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Bibliographic Details
Published inSocial choice and welfare Vol. 17; no. 3; pp. 403 - 438
Main Authors Saari, Donald G., Merlin, Vincent R.
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Science + Business Media 2000
Springer Nature B.V
Subjects
Ambivalence
Cubes
Electoral behaviour
Geometric planes
Geometry
Mathematical theorems
Mathematical transitivity
Political candidates
Preferences
Public choice
Public opinion
Rationality
Social economics
Vertices
Voters
Voting
Voting behaviour
Voting paradox
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Summary:By using geometry, a fairly complete analysis of Kemeny's rule (KR) is obtained. It is shown that the Borda Count (BC) always ranks the KR winner above the KR loser, and, conversely, KR always ranks the BC winner above the BC loser. Such KR relationships fail to hold for other positional methods. The geometric reasons why KR enjoys remarkably consistent election rankings as candidates are added or dropped are explained. The power of this KR consistency is demonstrated by comparing KR and BC outcomes. But KR's consistency carries a heavy cost; it requires KR to partially dismiss the crucial "individual rationality of voters" assumption.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0176-1714
1432-217X
DOI:10.1007/s003550050171