View source for Total approval chain climbing

'''Total approval chain climbing''' ('''TACC''') is a Condorcet [[completion method]] using an [[Approval ballot|approval]] component, invented by Forest Simmons. 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.

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. 

Thread here: http://lists.electorama.com/pipermail/election-methods-electorama.com/2014-April/097912.html

(Full definition should be added)

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.

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Total Score chain climbing

'''Total Score chain climbing''' ('''TSCC''') is a Condorcet completion method using an score-component. The motivation is to reduce [[burial]] incentive.

It works as follows:<blockquote>1. Sort the candidates by increasing total score. 

2. Starting with an empty "chain of candidates", consider each candidate in the above order and do a pairwise comparison: for each ballot:

-  determine the maximum score in the "chain of candidates" for this individual ballot

-  if the candidate has a higher score then this maximum score count this as a win, 

-  if the candidate has the same or a lower score then this maximum score count this as a loss        

3. If there are more wins then losses add the candidate to the top of the chain. 

4. The last added candidate wins.</blockquote>


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[[Category:Smith-efficient Condorcet methods]]
[[Category:Condorcet-cardinal hybrid methods]]
[[Category:Aggregate methods]]