Weighted positional method: Difference between revisions
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(Added paper showing properties of weighted positional systems, in particular consistency. (It could use a more thorough treatment, e.g. mentioning the Archimedean property. Maybe do that later)) |
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==Criterion compliances== |
==Criterion compliances== |
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Every weighted positional method passes the [[ |
Every weighted positional method passes the [[consistency criterion]],<ref name="Smith 1973 pp. 1027–1041">{{cite journal | last=Smith | first=John H. | title=Aggregation of Preferences with Variable Electorate | journal=Econometrica | publisher=[Wiley, Econometric Society] | volume=41 | issue=6 | year=1973 | issn=00129682 | jstor=1914033 | pages=1027–1041 | url=http://www.jstor.org/stable/1914033 | access-date=2024-05-05}}</ref> the [[participation criterion]], and mono-add-top; and is [[summability criterion|summable]] with order k=1.<ref name="Votedesc">{{cite web |url=http://www.9mail.de/m-schulze/votedesc.pdf |access-date=2023-10-09 |date=2007-06-12|last=Smith|first=Warren D.|page=28|title=Descriptions of single-winner voting systems}}</ref> <!-- Cite sources directly instead of through votedesc? --> |
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Every weighted positional method except for [[First Past the Post electoral system|First past the post]] fails the [[later-no-harm criterion]]<ref name="Votedesc"/> and the [[majority criterion]]. Since [[First Past the Post electoral system|First past the post]] fails the [[Condorcet criterion]], and Condorcet implies majority, every weighted positional method fails Condorcet. |
Every weighted positional method except for [[First Past the Post electoral system|First past the post]] fails the [[later-no-harm criterion]]<ref name="Votedesc"/> and the [[majority criterion]]. Since [[First Past the Post electoral system|First past the post]] fails the [[Condorcet criterion]], and Condorcet implies majority, every weighted positional method fails Condorcet. |
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