Baldwin's method: Difference between revisions

CandidatesUnder '''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-inventedrechristened in 2022 under the nameas '''Total Vote Runoff''', by Nobel Memorial Prize laureate economists [https://en.wikipedia.org/wiki/Edward_B._Foley Edward B. Foley] and [https://en.wikipedia.org/wiki/Eric_Maskin Eric Maskin], andwho proposed for use in the United Statesit as a way to fix problems within the [https://en.wikipedia.org/wiki/Instant-runoff_voting instant-runoff method]. inMaskin USand jurisdictionsFoley note that useunlike itinstant-runoff, ensuringTVR ensures majority support offor the winner and electingtypically elects 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>

[[Baldwin's method]] satisfies the [[Condorcet criterion]].<ref name=":1" /> becauseBecause 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]] also violates [[reversal symmetry]] (unlike [[Nanson's method]]).<ref>{{Cite web|url=https://www.mail-archive.com/election-methods@lists.electorama.com/msg00625.html|title=Re: [Election-Methods] Borda-elimination, a Condorcet method for public elections?|website=www.mail-archive.com|access-date=2019-06-19}}</ref>

[[Baldwin's method]] can be run in polynomial time to obtain a single winner, however,but at each stage, there mightmay 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., whether there exists an elimination sequence that leaves a given candidate uneliminated.<ref>{{Cite journal|last=Mattei|first=Nicholas|last2=Narodytska|first2=Nina|last3=Walsh|first3=Toby|date=2014-01-01|title=How Hard is It to Control an Election by Breaking Ties?|journal=Proceedings of the Twenty-first European Conference on Artificial Intelligence|volume=263|issue=ECAI 2014|series=ECAI'14|location=Amsterdam, The Netherlands, The Netherlands|publisher=IOS Press|pages=1067–1068|doi=10.3233/978-1-61499-419-0-1067|isbn=9781614994183}}</ref>. This implies that this method is computationally more difficult to compute than Borda's method.<ref>{{Cite journal|last=Davies|first=Jessica|last2=Katsirelos|first2=George|last3=Narodytska|first3=Nina|last4=Walsh|first4=Toby|last5=Xia|first5=Lirong|date=2014-12-01|title=Complexity of and algorithms for the manipulation of Borda, Nanson's and Baldwin's voting rules|journal=Artificial Intelligence|volume=217|pages=20–42|doi=10.1016/j.artint.2014.07.005|issn=0004-3702}}</ref>

[[Distributed Voting]] is a [[Cumulativecumulative voting]] variant.