FBPPAR

The following system is called FBPPAR voting, for "Favorite-Betrayal-Proof Prefer Accept Reject". It is a version of PAR voting, with an extra "stand aside" option in order to pass the favorite betrayal criterion (FBC).

1. Voters can Prefer, Accept, or Reject each candidate. Default is "Reject" for voters who do not explicitly reject any candidates, and "Accept" otherwise.
   1. For any preferred candidate, voters may also check "stand aside". (This is rarely useful; it is only worthwhile if they think that the candidate might become the leader in step 3 and stand in the way of a stronger compromise leader.)
2. Candidates get 1 point for every ballot that prefers them.
3. Candidates with over 25% Prefer, and less than 50% Reject, are called viable. If there are any such candidates who would still be viable if all "prefer/stand aside" votes were counted as "reject", the one with the most preferences is designated the leader.
4. Viable candidates get 1 point for every ballot that accepts them and does not prefer the leader.
5. Winner is the highest score.

This is largely a theoretical proposal. In real-world elections, the "compromise" option would probably never be useful.

For instance, consider the voting scenarios which meet the following restrictions:

1. Each candidate either comes from one of no more than 3 "ideological categories", or is "nonviable".
2. No "nonviable" candidate is preferred by more than 25%.
3. Each voter rejects at least one of the 3 "ideological categories" (that is, rejects all candidates in that category), and accepts or prefers all candidates in some other category.
4. No honest Condorcet cycles.

If the above restrictions hold, then the "compromise" option would never be strategically favored, and so simple PAR voting would meet FBC. It is arguably likely that real-world voting scenarios will meet the above restrictions, except for a negligible fraction of "ideologically atypical" voters. Thus, as a real-world proposal, PAR voting's greater simplicity makes it better than FBPPAR.