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Improved Condorcet Approval: Difference between revisions
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'''Improved Condorcet Approval''' or '''ICA''' or '''tCA''' is a variant of [[Condorcet//Approval]] devised by Kevin Venzke
==Definition==
#The voter submits a ranked ballot, with equal-ranking and truncation permitted.
#A voter
#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].
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#Elect the candidate in ''S'' with the greatest approval.
An equivalent definition:
#Collect ballots as above.
#Identify all of the pairwise losses.
#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.
#If any candidates do not have any pairwise loss, disqualify all the candidates who do have some pairwise loss.
#Elect the (non-disqualified) candidate with the greatest approval.
==Comments==
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The above definition defines t[a,b] to be the number of voters tying ''a'' and ''b'' in the top position. This is the most conservative change from [[Condorcet//Approval]], since it's only in this case that we can be sure the voter would like to do whatever is necessary to ensure that the winner is either ''a'' or ''b''.
However, it might be more intuitive, and preferred, if t[a,b] were defined rather as the number of voters ranking ''a'' equal to ''b'' and explicitly voting for both. This requires a simple change to step #3
For the second definition, replace step 3 with:
:Disregard any pairwise loss that can be reversed or turned into a pairwise tie if the voters approving both candidates and ranking them equal are counted in favor of the pairwise loser.
==Links==
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