Baldwin's method: Difference between revisions
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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
== Satisfied and failed criteria ==
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[[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]] 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,
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.
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==Cardinal variant==
Assuming the scores are all scaled to fall in the range [0, 1], ballots are rescaled as follows:
<math>v_c(u_c) =
For example,
===Related systems===
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Borda scores are A 185, B 205, C 210. A beats B beats C beats A, so there is no Condorcet winner, and so A, the Borda loser, is eliminated. Since B beats C, B wins. Note that this is a different result than [[Black's method]], which would elect C. They are both related to [[Nanson's method]].
== Example ==
{{Tenn voting example}}This gives the following points table:
{| class="wikitable" style="border:none"
! {{diagonal split header|Candidate|Voters}}
!Memphis
!Nashville
!Knoxville
!Chattanooga
| rowspan="5" style="border: none; background: white;" |
!Score
|-
!Memphis
|42×3=126
|0
|0
|0
|126
|-
!Nashville
|42×2 = 84
|26×3 = 78
|17×1 = 17
|15×1 = 15
|194
|-
!Knoxville
|0
|26×1 = 26
|17×3 = 51
|15×2 = 30
|107
|-
!Chattanooga
|42×1 = 42
|26×2 = 52
|17×2 = 34
|15×3 = 45
|173
|}
Knoxville has the least amount of points, so it is eliminated.
We now have this table:
{| class="wikitable" style="border:none"
! {{diagonal split header|Candidate|Voters}}
!Memphis
!Nashville
!Knoxville
!Chattanooga
| rowspan="4" style="border: none; background: white;" |
!Score
|-
!Memphis
|42×2 = 84
|0
|0
|0
|84
|-
!Nashville
|42×1 = 42
|26×2 = 52
|17×1 = 17
|15×1 = 15
|126
|-
!Chattanooga
|0
|26×1 = 26
|17×2 = 34
|15×2 = 30
|90
|}
Now Memphis is eliminated.
This leaves us with Nashville and Chattanooga. Nashville has 42+26 points, giving it 68 points, while Chattanooga has 17+15 points giving it 32. This makes Nashville the winner.
== See also ==
|