Smith//IRV

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Revision as of 17:31, 4 February 2020 by Kristomun (talk | contribs) (Show that Smith//IRV is non-summable because the size of the Smith set can't be known in advance. Improve reference.)

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. [1]

Smith//IRV's precinct-summability depends on how large the Smith Set is: while a non-summable method like IRV requires O(c!) space in the worst case, Smith//IRV only requires O(k!), where k is the number of candidates in the Smith set. However, it's not possible to decide beforehand how large the Smith set will be; any such restriction will cause the method to violate universal domain. Thus, Smith//IRV is non-summable in full generality.

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 and other Condorcet-IRV hybrids (names differ in the linked article): [2]

See also

References

  1. ↑ Green-Armytage, J. (2011). "Four Condorcet-Hare hybrid methods for single-winner elections" (PDF). Voting matters (29): 1–14.
  2. ↑ https://rangevoting.org/SmithIRV.html
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