Total approval chain climbing: Difference between revisions

← Older edit

Total approval chain climbing (view source)

Revision as of 23:48, 7 August 2023

1,973 bytes added , 9 months ago

Replaced reference and attribution with reference to earlier EM post.

VisualWikitext

Kristomun

1,208

edits

Revision as of 04:16, 2 September 2018 (view source) Psephomancy (talk \| contribs) (Category:Condorcet method → Category:Condorcet methods) ← Older edit		Latest revision as of 23:48, 7 August 2023 (view source) Kristomun (talk \| contribs) (Replaced reference and attribution with reference to earlier EM post.)
(11 intermediate revisions by 5 users not shown)
Line 1: '''Total approval chain climbing''' ('''TACC''') is a Condorcet [[completion method]] using an [[Approval ballot\|approval]] component, invented by ~~Forest~~Jobst ~~Simmons~~Heitzig in 2005.<ref>{{cite web\|url=http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-March/080299.html\|title=Chain Climbing methods\|website=Election-methods mailing list archives\|date=2005-03-04\|last=Heitzig\|first=J.}}</ref> In the three-candidate case it is equivalent to electing the candidate in the cycle who defeats the approval loser pairwise. The motivation is to reduce [[burial]] incentive. It works as follows:<blockquote>1. Sort the candidates by increasing total approval. ~~(Full definition should be added)~~ 2. Starting with an empty "chain of candidates", consider each candidate in the above order. When the candidate defeats all candidates already in the chain, add her at the top of the chain. The last added candidate wins.</blockquote>Note that because of [[Condorcet cycle\|Condorcet cycles]], it isn't always possible for one candidate to beat all others. Because of this, the procedure may stop before all candidates can be added to the chain. [[Category:Single-winner voting methods]]▼ [[Category:Condorcet methods]]▼ == Example == * 34: A>B\|>C * 35: B\|>C>A * 31: C>A\|>B Approvals (using the [[approval threshold]] symbol "\|") are A 65, B 69, C 31. C is added first into the chain because C has the lowest approval, and then B, not A, is added into the chain, because B is the only candidate who [[pairwise beat\|pairwise beats]] C. A can't then be added in, because A can only beat B and not also C. Therefore, B is the winner. == Notes == TACC and its variants are notable for always electing from the [[Banks set]], a subset of the [[Uncovered set\|uncovered set]] and thus the [[Smith set]].. TACC is [[Smith-efficient]] because all members of the Smith set pairwise beat all candidates not in the Smith set, therefore once a Smith set member is added to the chain, a non-Smith set member can't be added to the chain, because they can't beat the Smith set member, and thus, can't beat everyone in the chain. Since this implies a Smith set member must be the last added candidate, only members of the Smith set can win. == Variants == * TSCC: see [[User:MellowMoon/Total Score chain climbing]] == References == <references/> ▲[[Category:Smith-efficient Condorcet methods]] [[Category:Condorcet-cardinal hybrid methods]] ▲[[Category:~~Single-winner voting~~Aggregate methods]]