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It is likely possible that the [[tied at the top rule]] can be made to work with something like Smith//Approval. Example:
4 A>B| >C
3 C| >A>B
4 C| >B>A
There is an A>B>C>A cycle, with C winning with 7 approvals. If 2 of the A-top voters swap A and B, then B becomes the CW. To avoid needing this, if these voters instead vote A=B, then they can create a pairwise tie between A and B according to the tied at the top rule. However, this still means C beats A and A ties B, so all 3 candidates are in the Smith set. To circumvent this, perhaps it's possible to ignore C's defeat against A because A is in a "special tie" with B, who beats C, which then makes A and B the only candidates in the Smith set. An alternative is to, instead of converting the matchup between A and B into a tie, completely erase or drop it. This leaves B as the Condorcet winner with a pairwise victory against C.
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