# Improved Condorcet Approval

Improved Condorcet Approval or ICA or tCA is a variant of Condorcet//Approval devised by Kevin Venzke to satisfy the Favorite Betrayal criterion. It uses the tied at the top rule.

## Definition

1. 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.
2. The voter submits a ranked ballot, with equal-ranking and truncation permitted. Let v signify the total number of voters.
3. A voter implicitly approves every candidate whom he explicitly ranks.
4. 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).
5. 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.
6. If S is empty, then let S contain all the candidates.
7. Elect the candidate in S with the greatest approval.