Baldwin's method: Difference between revisions
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Under '''Baldwin's method''', candidates are voted for on [[Ranked voting]] as in the [[Borda count]]. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were never on the ballot.
It was systematized by Joseph M. Baldwin<ref>{{Cite journal|last=Baldwin|first=J. M.|date=1926|title=The technique of the Nanson preferential majority system of election|url=https://archive.org/details/proceedingsroyaxxxvroyaa/page/42|journal=Proceedings of the Royal Society of Victoria|volume=39|pages=42–52|via=}}</ref> in 1926, who incorporated [[Condorcet method|a more efficient matrix tabulation]],<ref>{{Cite journal|last=Hogben|first=G.|date=1913|title=Preferential Voting in Single-member Constituencies, with Special Reference to the Counting of Votes|url=http://rsnz.natlib.govt.nz/volume/rsnz_46/rsnz_46_00_005780.html|journal=Transactions and Proceedings of the Royal Society of New Zealand|series=|volume=46|issue=|pages=304–308|via=}}</ref> extending it to support incomplete ballots and equal rankings. Baldwin's method has been confused with [[Nanson's method]] in some literature.<ref name=":1">{{Cite journal|last=Niou|first=Emerson M. S.|date=1987|title=A Note on Nanson's Rule|journal=Public Choice|volume=54|issue=2|pages=191–193|issn=0048-5829|citeseerx=10.1.1.460.8191|doi=10.1007/BF00123006}}</ref> This method predates but is related to [[Nanson's method]]. Nanson noted Baldwin's method was already in use by the Trinity College at the University of Melbourne Dialectic Society when he invented his method.<ref name=":0">{{Cite journal|last=Nanson|first=E. J.|date=1882|title=Methods of election|url=https://archive.org/details/transactionsproc1719roya/page/197|journal=Transactions and Proceedings of the Royal Society of Victoria|volume=19|pages=197–240|via=}}</ref>{{Rp|217}}
This system was re-invented in 2022 under the name '''Total Vote Runoff''', by [https://en.wikipedia.org/wiki/Edward_B._Foley Edward B. Foley] and [https://en.wikipedia.org/wiki/Eric_Maskin Eric Maskin], and proposed for use in the United States as a way to fix problems with the [https://en.wikipedia.org/wiki/Instant-runoff_voting instant-runoff method] in US jurisdictions that use it, ensuring majority support of the winner and electing more broadly-acceptable candidates.<ref>{{Cite news|last=Foley|first=Edward B.|url=https://www.washingtonpost.com/opinions/2022/11/01/alaska-final-four-primary-begich-palin-peltola/|title=Alaska’s ranked-choice voting is flawed. But there’s an easy fix.|date=November 1, 2022|work=Washington Post|access-date=2022-11-09|last2=Maskin|first2=Eric S.|language=en-US|issn=0190-8286|quote=the way Alaska uses ranked-choice voting also caused the defeat of Begich, whom most Alaska voters preferred to Democrat Mary Peltola … A candidate popular only with the party’s base would be eliminated early in a Total Vote Runoff, leaving a more broadly popular Republican to compete against a Democrat.|author-link=Edward B. Foley|author-link2=Eric Maskin}}</ref><ref>{{Cite journal|last=Foley|first=Edward B.|date=2023-01-18|title=Total Vote Runoff: A Majority-Maximizing Form of Ranked Choice Voting|url=https://papers.ssrn.com/abstract=4328946|language=en|location=Rochester, NY}}</ref><ref>{{Cite web|url=https://electionlawblog.org/?p=132792|title=“Total Vote Runoff” tweak to Ranked Choice Voting|last=Foley|first=Ned|author-link=Edward B. Foley|date=November 1, 2022|website=Election Law Blog|language=en-US|access-date=2022-11-09|quote=a small but significant adjustment to the “instant runoff” method … equivalent to a candidate’s Borda score, and eliminating sequentially the candidate with the lowest total votes}}</ref><ref>{{Cite web|url=https://electionlawblog.org/?p=132963|title=An Additional Detail about “Total Vote Runoff”|last=Foley|first=Ned|author-link=Edward B. Foley|date=November 8, 2022|website=Election Law Blog|language=en-US|access-date=2022-11-09|quote=Begich and Peltola each get half a vote by being tied for second place on this ballot}}</ref>
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[[Baldwin's method]] satisfies the [[Condorcet criterion]].<ref name=":1" /> Because Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated. Furthermore it satisfies the [[majority criterion]], the [[mutual majority criterion]], the [[Condorcet loser criterion]] and the [[Smith set|Smith criterion]].
[[Baldwin's method]] does not satisfy the [[independence of irrelevant alternatives]] criterion, the [[monotonicity criterion]], the [[participation criterion]], the [[consistency criterion]] and the [[independence of clones criterion]]. [[Baldwin's method]]
[[Baldwin's method]] can be run in polynomial time to obtain a single winner, however, at each stage, there might be several candidates with the lowest Borda score. In fact, it is NP-complete to decide whether a given candidate is a potential Baldwin winner, i.e.
In practice, the computational bottleneck can be resolved easily enough by adopting some tiebreaking method (like eliminating all tied candidates simultaneously). However, the high frequency of near-ties leaves these methods open to lawsuits (similarly to [[Instant-runoff voting|plurality-with-elimination]]) and can lead to chaotic results.
==Cardinal Variant==
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v_c(u_c) = MIN + (MAX– MIN) \frac{(u_c – u_{min})}{(u_{max} – u_{min})}
\end{equation}</math>
For example, in a [0, 10] system the translation is
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It would transform [1, 3, 5] to [0, 5, 10].
===Related systems===
[[STAR voting]] is a simplified version of this where instead of eliminating each candidate one by one all but the last two candidates are removed at once. This alteration recovers the [[monotonicity criterion]].
[[Distributed Voting]] is a [[
==Notes==
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