2018-08-11 22:04:05 UTC
Instant Run-off Voting, Approval voting, and Plurality are all the same
voting rule applied to ballot sets with differing characteristics. The
rule operates in four modes: Ties allowed; Multiple Rankings Allowed;
Neither; and Both.
The voting rule is called Instant Run-off Approval Voting.
Consider a ballot with the following ranks:
1 - A
2 - B
2 - C
3 - D
4 - E
Round 1 votes:
During the first round, A is the plurality loser. We eliminate A and move
ballots to the second-ranked candidate.
Five first-rank-A ballots ranked each of D and E second (no tie). This
particular ballot ties B and C for second; thus we cast two votes:
B is the plurality loser. Ten of those go to D; five go to E; this
particular ballot ranked C tied with B, so does not move.
The various configurations:
1. Ties, Multiple Ranks: Instant Run-off Approval Voting.
2. No Ties, Multiple Ranks: Instant Run-off Voting.
3. Ties, One Rank: Approval Voting.
4. No Ties, One Rank: Plurality.
This generalization can extend Tideman's Alternative Smith and Instant
Run-off Voting to ballots with ties. Such extensions may change the
characteristics of the resulting vote rule, such as its resistance to
tactical voting and nomination. I don't know how allowing ties in
Tideman's Alternative Smith or IRV affects tactical manipulation.
IRAV has the obvious advantages of reducing ballot spoilage and increasing
voter preference expressiveness. Gaps are irrelevant: if your rankings
are 1 40 90 8000, that's just 1 2 3 4; treat it as such. All ballots are