Summed-Ranks: Difference between revisions
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Add reference to Borda and Approval, as it's a version of Borda that behaves like Approval when voters only use two ranks
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'''Summed-Ranks''' (abbreviated '''SR''') is a ranked voting method based on [[Approval voting]] and the [[Borda count]].
{{definition|
Rankings may be of any length, ranking as many or as few candidates as desired. Several candidates can be ranked at
▲Rankings may be of any length, ranking as many or as few candidates as desired. Several candidates can be ranked at a same rank position.
The winner is the candidate with the fewest candidates ranked over him/her, as summed over all of the ballots.
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Each candidate bottom-ranked on a ballot is counted as having all candidates, including all of that ballot's other bottom-ranked candidates, ranked over him/her on that ballot.
}}
== Analysis ==
SR meets criteria not met by other Borda versions. These are listed
▲SR meets criteria not met by other Borda versions. These are listed and defined below:
=== The [[favorite betrayal criterion]] ===
SR passes the [[favorite betrayal criterion]]. Because of of SR's FBC compliance, SR gives no incentive or need for
SR passes [[Later-no-help]]. Because of SR's
=== Others ===
▲Because of SR's FBC compliance, SR gives no incentive or need for the "compromise strategy" described below in this article. There's never a reason to not rank one's favorite in 1st place, along with whatever compromise(s) one wishes to also rank there.
▲2. [[Later-No-Help]]:
▲Because of SR's LNHe compliance, SR never gives incentive or need to rank unacceptable candidates. If the most important goal is to keep the winner from coming from a certain set, then, for that goal, it it's never necessary to rank any member of that set.
▲3. SR's other criterion-compliances are similar to those of other Borda versions. For example, SR passes Participation and [[Consistency]], and fails Independence from Irrelevant Alternatives (IIAC) and Clone-Independence (but, as described below, SR's clone problem is greatly alleviated).
In addition to Participation, SR passes Participation's more-easily-passed variations:
==== Mono-Add-Top
{{definition|Adding, to the election, a ballot that votes X at top shouldn't cause X to lose.}}▼
▲Adding, to the election, a ballot that votes X at top shouldn't cause X to lose.
▲Mono-Add-Unique-Top:
== Comments ==
▲Adding a ballot that votes X over everyone else shoudln't cause X to lose.
SR greatly alleviates the typical Borda clone problem. In ordinary Borda, it's advantageous for a faction or party to nominate many
But SR's treatment of bottom-ranked candidates penalizes that large number of identical candidates, on ballots that bottom-rank them.
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SR's count labor is proportional only to the first power of the number of candidates. It's only necessary to make one pass through each ballot.
SR's method-chosen ratings for each rank position can be regarded as approximations to the ratings that voters would assign in
SR is for when it's desired to give voters the simple instruction to mark 1st choice(s), 2nd choice(s), etc., instead of asking them to rate the candidates or alternatives, and the number of alternatives is prohibitively large for a Condorcet
[[Category:Ranked voting methods]]
[[Category:Single-winner voting methods]]
[[Category:Monotonic electoral systems]]
[[Category:
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