Smith//IRV

The method

1. Eliminate all candidates not in the Smith set.

2. Perform an IRV tally among remaining candidates.

Notes

Smith//IRV passes ISDA (Independence of Smith-dominated Alternatives) but fails mono-add-plump (adding in ballots that bullet vote the winner shouldn't make the winner lose), which is the opposite of several other Condorcet-IRV hybrids.

Smith//IRV's precinct-summability depends on how large the Smith Set is. In general, if the Smith Set has n candidates in it, then each precinct only has to report the top n-2 preferences each voter has over the Smith Set candidates. For example, if the Smith Set has 3 candidates, only each voter's 1st choice in the Smith Set need be known, since IRV will eliminate the candidate with the fewest 1st choices, and then there will be only 2 candidates remaining; the winner in IRV when only 2 candidates remain is guaranteed to be the winner of the pairwise matchup between the two candidates, so only the pairwise table need be consulted then to determine the winner. If there are 4 candidates in the Smith Set, each voter's 1st and 2nd choice in the Smith Set must be known, since once the candidate with the fewest 1st choices is eliminated, 3 candidates will remain, and then the 2nd choices of the voters who ranked the just-eliminated candidate 1st must be known to determine who to eliminate next; then there will be only 2 candidates remaining, etc.

One hybrid of Smith//IRV and Benham's method would be "eliminate everyone outside the Smith Set, then do IRV, but before each elimination, elect the Condorcet winner (based solely on pairwise matchups between uneliminated candidates) if there is one."

Some discussion on Smith//IRV vs. other Condorcet-IRV hybrids (names differ in the linked article):

Condorcet win if there is one". er"

See also

• Instant-runoff voting