Weighted positional method: Difference between revisions
Content added Content deleted
(Added some more examples) |
(Add clone independence failure.) |
||
| Line 17: | Line 17: | ||
The [[Borda count]] is the only weighted positional method that never ranks the Condorcet winner last.<ref>{{Cite journal|last=Smith|first=John H.|date=1973|title=Aggregation of Preferences with Variable Electorate|url=http://www.jstor.org/stable/1914033|journal=Econometrica|volume=41|issue=6|pages=1027–1041|doi=10.2307/1914033|issn=0012-9682}}</ref> It follows that the only Condorcet-compliant runoff method that eliminates one loser at a time and is based on a weighted positional method is [[w:Nanson's_method#Baldwin_method|Baldwin]] (Borda-elimination). |
The [[Borda count]] is the only weighted positional method that never ranks the Condorcet winner last.<ref>{{Cite journal|last=Smith|first=John H.|date=1973|title=Aggregation of Preferences with Variable Electorate|url=http://www.jstor.org/stable/1914033|journal=Econometrica|volume=41|issue=6|pages=1027–1041|doi=10.2307/1914033|issn=0012-9682}}</ref> It follows that the only Condorcet-compliant runoff method that eliminates one loser at a time and is based on a weighted positional method is [[w:Nanson's_method#Baldwin_method|Baldwin]] (Borda-elimination). |
||
Every [[resolvability criterion|resolvable]] weighted positional method fails [[clone independence]]: Plurality fails to vote-splitting, and every other method can be made to fail the majority criterion even for clones, hence turning a majority loser into a winner.<ref>{{cite web|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-December/001642.html|title=Resolvable weighted positional systems all fail independence of clones|website=Election-methods mailing list archives|date=2017-12-03|last=Munsterhjelm|first=K.}}</ref> |
|||
===Majority criterion=== |
===Majority criterion=== |
||
| Line 54: | Line 56: | ||
==Notes== |
==Notes== |
||
All weighted positional methods can be understood in a [[pairwise counting]] context. For example, in Borda, if a voter gives every candidate the same number of points in a matchup as they give them overall, then the winner of all matchups is the Borda winner. The connection can be further understood by dividing the total number of points a voter gave a candidate by the maximum number of points they could have given any candidate i.e. a voter who gave one candidate 7 points out of a max of 7 and another 6 out of 7 contributed a pairwise margin of 1 point, or 1/7th of a vote, to the former candidate in the matchup between the two). |
All weighted positional methods can be understood in a [[pairwise counting]] context. For example, in Borda, if a voter gives every candidate the same number of points in a matchup as they give them overall, then the winner of all matchups is the Borda winner. The connection can be further understood by dividing the total number of points a voter gave a candidate by the maximum number of points they could have given any candidate i.e. a voter who gave one candidate 7 points out of a max of 7 and another 6 out of 7 contributed a pairwise margin of 1 point, or 1/7th of a vote, to the former candidate in the matchup between the two). |
||
{{stub}} |
|||
==References== |
==References== |
||