CPO-STV: Difference between revisions
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CPO-STV (Comparison of Pairs of Outcomes by Single Transferable Vote) is a [[preference voting|preference]] [[voting system]] designed to provide [[proportional representation]] in multi-seat elections while electing the [[Condorcet winner]] in single-winner elections. It is based on [[STV]] and [[Pairwise counting|pairwise counting]] between every possible combination of candidates that could win ("[[Winner set|winner sets]]") to determine the winner.
== Voting ==
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=== Setting the Quota ===
When all the votes have been cast, a winning quota is set. Possible formulas for the quota include the [[Droop quota|Droop Quota]], the [[Hare quota|Hare Quota]], and the [[Imperiali Quota]].
=== Comparison of Pairs of Outcomes ===
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Finally, add up the votes in each outcome.
* Escher
* Escher
Thus, {Escher, Andre, Gore} pairwise beats {Escher, Nader, Gore}, 282 to 190.
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* 8: D
The Droop Quota is floor(22/3)
Andrea has 22 first-choice votes, and is declared elected. Her 11 excess votes are reallocated to their second preferences. If this is done by fractional transfer, the resulting ballots are:
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At this point, we know that {A, C} is the Condorcet winner. Therefore, CPO-STV elects Andrea and Carter.
=== Notes ===
CPO-STV can be highly computationally complex and thus difficult to calculate when there are many candidates, as if there are, say, 5 seats to be filled and 60 candidates, then there are 60 choose 5 = 5,461,512 possible outcomes.
It has not been proven whether CPO-STV is [[Droop proportionality criterion|proportional for Droop solid coalitions]]. However, if it can be, then its cycle resolution method likely must choose from the [[Smith set|Smith Set]] of winner sets in order to do so, as Smith-efficiency guarantees Droop proportionality (the [[Mutual majority criterion|mutual majority]] criterion) in the single-winner case. One type of procedure that requires among the fewest pairwise comparisons to find one of the Smith Set winner sets is [[:Category:Sequential comparison Condorcet methods|Sequential comparison Condorcet methods]]. Since a winner set in the Smith Set can only be eliminated by another Smith winner set by this procedure, the final remaining winner set will guaranteeably be in the Smith Set. If desired, it is then possible to discover the rest of the Smith Set by checking which winner sets beat or tie the final remaining winner set, which beat or tie these winner sets, etc. One well-known procedure that works along these lines is [[BTR-IRV]].
One suggestion to modify CPO-STV to be guaranteeably proportional for Droop solid coalitions is to first eliminate all outcomes from consideration that fail Droop proportionality. In the above example, if there are 4 solid coalitions of 5 candidates each, then the upper bound of outcomes to consider is ((5^4) * 60) = 37500 outcomes, which is a reduction of outcomes to consider by a factor of about 145.
Several other such modifications are possible to reduce the number of outcomes to consider, some of which can potentially elect some outcome other than what CPO-STV would. Some are:
- As a first guess, calculate the [[STV]] outcome and see if it can win against all other outcomes (that are in consideration). (It is estimated that the STV winner set is almost always the same as the CPO-STV winner set.)
- If a set of candidates X is ranked above or equal to a set of candidates Y on all ballots, ignore all outcomes featuring candidates from Y but not X. (Based on [[Unanimity criterion|unanimity criterion]]).
== See also ==
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* [[Proportional Ordering]]
== External Resources ==
* [http://www.econ.vt.edu/tideman/rmt.pdf Better voting methods through technology: The refinement-manageability trade-off in the single transferable vote] by Nicolaus Tideman and Daniel Richardson (Public Choice, vol. 103, pp. 13--34, 2000)
* [http://fc.antioch.edu/~james_green-armytage/vm/survey.htm#cpostv Explanation and example for CPO-STV] by James Green-Armytage
[[Category:Multi-winner voting
[[Category:Proportional voting methods]]
[[Category:Condorcet-reducible PR methods]]
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