River: Difference between revisions

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'''River''' is a cloneproof monotonic [[Condorcet method#Different ambiguity resolution methods|Condorcet ambiguity resolution method]] with similarities to both [[Ranked Pairs]] and [[Schulze method|Schulze]], but when cycles exist, can in rare cases find a different winner than either of the other two methods.
'''River''' is a cloneproof monotonic [[Condorcet method#Different ambiguity resolution methods|Condorcet ambiguity resolution method]] with similarities to both [[Ranked Pairs]] and [[Schulze method|Schulze]], but when cycles exist, can in rare cases find a different winner than either of the other two methods.


It was first proposed in 2004 by [[User:Heitzig-j|Jobst Heitzig]] on the [[Election-methods mailing list]].<ref name="River initial">{{cite web | title=Hello again -- and a new method for you! | website=lists.electorama.com Mailing Lists | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/078029.html | access-date=2020-02-17 |date=2004-04-10 |last=Heitzig|first=Jobst}}</ref><ref name="River refinement">{{cite web | title=Hello again -- and a new method for you! | website=lists.electorama.com Mailing Lists | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/110761.html | access-date=2020-02-17 |date=2004-04-11|last=Heitzig|first=Jobst}}</ref>
It was first proposed in 2004 by [[User:Heitzig-j|Jobst Heitzig]] on the [[Election-methods mailing list]].<ref name="River initial">{{cite web | title=Hello again -- and a new method for you! | website=Election-Methods mailing list | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/078029.html | access-date=2020-02-17 |date=2004-04-10 |last=Heitzig|first=Jobst}}</ref><ref name="River refinement">{{cite web | title=Hello again -- and a new method for you! | website=Election-Methods mailing list | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/110761.html | access-date=2020-02-17 |date=2004-04-11|last=Heitzig|first=Jobst}}</ref>
Jobst later refined the definition to be more similar to Ranked Pairs.<ref name="River concise">{{cite web | title=River method -- updated summary | website=lists.electorama.com Mailing Lists | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014018.html | access-date=2020-02-17 |date=2004-10-06|last=Heitzig|first=Jobst}}</ref>
Jobst later refined the definition to be more similar to Ranked Pairs.<ref name="River concise">{{cite web | title=River method -- updated summary | website=Election-Methods mailing list | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-October/014018.html | access-date=2020-02-17 |date=2004-10-06|last=Heitzig|first=Jobst}}</ref>


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The result is that only sufficient defeat information to determine the winner is included.
The result is that only sufficient defeat information to determine the winner is included.


Because not all defeats are processed, the social ordering is not linear—in general it is a tree (or river) diagram, with the victor at the base of the river.
Because not all defeats are processed, the social ordering is not linear—in general, it is a tree (or river) diagram, with the victor at the base of the river.


==Examples==
==Examples==
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==Criterion compliances==
==Criterion compliances==


River passes [[Condorcet criterion|Condorcet]], [[Smith set|Smith]], the [[monotonicity criterion]]<ref name="Votedesc"/>, independence of clones, and independence of Pareto-dominated alternatives.<ref name="IPDA">{{cite web | title=River method - a refinement, minor computational evidence, and a generalized IPDA criterion ISDA | website=lists.electorama.com Mailing Lists | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/078100.html | access-date=2020-02-17 |date=2004-04-24 |first=Jobst |last=Heitzig}}</ref> It fails mono-add-top, later-no-harm, and the [[participation criterion]].
River passes [[Condorcet criterion|Condorcet]], [[Smith set|Smith]], the [[monotonicity criterion]]<ref name="Votedesc"/>, independence of clones, and independence of Pareto-dominated alternatives.<ref name="IPDA">{{cite web | title=River method - a refinement, minor computational evidence, and a generalized IPDA criterion ISDA | website=Election-Methods mailing list | url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/078100.html | access-date=2020-02-17 |date=2004-04-24 |first=Jobst |last=Heitzig}}</ref> It fails mono-add-top, later-no-harm, and the [[participation criterion]].


In addition, River passes Heitzig's independence of strongly dominated alternatives criterion, which is weaker than independence of uncovered alternatives and stronger than independence of Pareto-dominated alternatives.
In addition, River passes Heitzig's independence of strongly dominated alternatives criterion, which is weaker than independence of uncovered alternatives and stronger than independence of Pareto-dominated alternatives.
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