Improved Condorcet Approval: Difference between revisions

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==Definition==

#The voter submits a ranked ballot. She is permitted to give more than one candidate the same ranking, and is not obliged to rank every candidate.

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#Identify all of the pairwise losses.

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#Disregard any pairwise loss that can be reversed or turned into a pairwise tie if the voters ranking both candidates equal in first place (possibly with other candidates) are counted in favor of the pairwise loser.

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#If any candidates do not have any pairwise loss, disqualify all the candidates who do have some pairwise loss.

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#Elect the (non-disqualified) candidate approved by the greatest number of voters.

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A more precise definition:

#The voter submits a ranked ballot, with equal-ranking and truncation permitted.

#A voter "~~approves~~" every candidate whom he explicitly ranks.

#A voter is deemed to have "approved" every candidate whom he explicitly ranks.

#Let v[a,b] signify the number of voters ranking candidate ''a'' above candidate ''b'', and let t[a,b] signify the number of voters ranking ''a'' and ''b'' equally at the top of the ranking (possibly tied with other candidates).

#Define a set ''S'' of candidates, which contains every candidate ''x'' for whom there is no other candidate ''y'' such that v[x,y]+t[x,y]<v[y,x].

#If ''S'' is empty, then let ''S'' contain all the candidates.

#Elect the candidate in ''S'' with the greatest approval.

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An ~~equivalent~~ definition:

#Collect ballots as above.

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#Identify all of the pairwise losses.

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#Disregard any pairwise loss that can be reversed or turned into a pairwise tie if the voters ranking both candidates equal in first place (possibly with other candidates) are counted in favor of the pairwise loser.

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#If any candidates do not have any pairwise loss, disqualify all the candidates who do have some pairwise loss.

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#Elect the (non-disqualified) candidate ~~with~~ the greatest ~~approval~~.

==Comments==