[EM] Generalization of Plurality, IRV, and Approval

John john.r.moser at gmail.com
Sat Aug 11 15:04:05 PDT 2018

[Note:  I am not subscribed to the list, so please copy me on replies.]

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:

11 A
15 B
17 C
22 D
20 E

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:

16 B
18 C
27 D
25 E

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.

18 C
37 D
30 E

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
now valid.
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