Improved Condorcet Approval: Difference between revisions
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==Definition== |
==Definition== |
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#Optionally define a proportion of the votes ''q'' as the minimum necessary on the winning side of a pairwise comparison for this win to be counted. Set it to zero to do without ''q''. |
#Optionally define a proportion of the votes ''q'' as the minimum necessary on the winning side of a pairwise comparison for this win to be counted. Set it to zero to do without ''q''. |
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#The voter submits a ranked ballot, with equal-ranking and truncation permitted. |
#The voter submits a ranked ballot, with equal-ranking and truncation permitted. Let ''v'' signify the total number of voters. |
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#A voter ''approves'' every candidate whom he explicitly ranks. |
#A voter ''approves'' every candidate whom he explicitly ranks. |
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#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). |
#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). |
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#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] ''and'' v[y,x]>'' |
#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] ''and'' v[y,x]>''qv''. |
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#If ''S'' is empty, then let ''S'' contain all the candidates. |
#If ''S'' is empty, then let ''S'' contain all the candidates. |
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#Elect the candidate in ''S'' with the greatest approval. |
#Elect the candidate in ''S'' with the greatest approval. |