Smith set: Difference between revisions
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{{Wikipedia}} |
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| ⚫ | There are two definitions of the '''Smith set'''. One is general and holds for any voting method; the other can be used only when the votes permit a comparison of any pair of candidates. Thus, the Robert's Rules single elimination pairwise voting method (which is used for voting on motions and amendments) requires the more general definition because it doesn't elicit enough information to allow all pairs of alternatives to be compared. Most voting methods that use a single round of voting—even methods like Plurality Rule and |
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| ⚫ | There are two definitions of the '''Smith set'''. One is general and holds for any voting method; the other can be used only when the votes permit a comparison of any pair of candidates. Thus, the [[Robert's Rules of Order|Robert's Rules]] single elimination pairwise voting method (which is used for voting on motions and amendments) requires the more general definition because it doesn't elicit enough information to allow all pairs of alternatives to be compared. Most voting methods that use a single round of voting—even methods like [[First Past the Post electoral system|Plurality Rule]] and [[Approval voting|Approval]]—are compatible with both definitions. |
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[Actually, Plurality and Approval always choose from the Smith set, when the definition referred to here as the simple definition is used. In that way, Plurality and Approval pass the Smith Criterion as it is often defined. But not when the Smith Criterion is defined as I define it two paragraphs below on this page] |
[Actually, Plurality and Approval always choose from the Smith set, when the definition referred to here as the simple definition is used. In that way, Plurality and Approval pass the Smith Criterion as it is often defined. But not when the Smith Criterion is defined as I define it two paragraphs below on this page] |
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The Smith set can be calculated using versions of either [http://en.wikipedia.org/wiki/Kosaraju%27s_algorithm Kosaraju's algorithm] or the [http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm Floyd-Warshall algorithm]. Examples of both algorithms applied to calculating the Smith set and the Schwartz set are available [[maximal elements algorithms|here]]. |
The Smith set can be calculated using versions of either [http://en.wikipedia.org/wiki/Kosaraju%27s_algorithm Kosaraju's algorithm] or the [http://en.wikipedia.org/wiki/Floyd-Warshall_algorithm Floyd-Warshall algorithm]. Examples of both algorithms applied to calculating the Smith set and the Schwartz set are available [[maximal elements algorithms|here]]. |
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==References== |
==References== |
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* Smith, J. H.(1973). "Aggregation of preferences with variable electorate". ''Econometrica'' 41: 1027-1041. |
* Smith, J. H.(1973). "Aggregation of preferences with variable electorate". ''Econometrica'' 41: 1027-1041. |
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* [[Beatpath example 12|Example 12 candidates]] |
* [[Beatpath example 12|Example 12 candidates]] |
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* [[maximal elements algorithms|Algorithms to calculate the Smith set]] |
* [[maximal elements algorithms|Algorithms to calculate the Smith set]] |
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{{fromwikipedia}} |
{{fromwikipedia}} |
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[[Category:Voting theory]] |
[[Category:Voting theory]] |
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