Voting example - PBS - different methods - different winners

masiarek

Ranks
G,B,P,R,O
18:1,5,4,2,3
12:5,1,4,3,2
10:5,2,1,4,3
9: 5,4,2,1,3
4: 5,2,4,3,1
2: 5,4,2,3,1

Ranks converted into Scores
G,B,P,R,O
18:5,1,2,4,3
12:1,5,2,3,4
10:1,4,5,2,3
9: 1,2,4,5,3
4: 1,4,2,3,5
2: 1,2,4,3,5

Voting Method and Winner
Plurality - Green
Two-Round Runoff- Blue
RCV IRV - Purple
Borda - Red
Range - Red
Approval - Red
Condorcet - Orange
STAR Voting - Orange

Here are my calculations: https://docs.google.com/document/d/1icQZ1efJV4XX7fD0_OTjNnW7uhfFV4lxbz5afTmqcyg/edit

Toby Pereira

@masiarek That's quite interesting, but converting ranks into scores like that rests on some dubious assumptions. So I don't think the score and STAR results are valid.

multi_system_fan

@masiarek I really like a new method that takes some time to understand. It's called a dodgson-hare synthesis
see http://jamesgreenarmytage.com/dodgson.pdf
Abstract: In 1876, Charles Dodgson (better known as Lewis Carroll) proposed a committee election procedure that chooses the Condorcet winner when one exists, and otherwise eliminates candidates outside the Smith set, then allows for re-votes until a Condorcet winner emerges. The present paper discusses Dodgson’s work in the context of strategic election behavior and suggests a “Dodgson-Hare” method: a variation on Dodgson’s procedure for use in public elections, which allows for candidate withdrawal and employs Hare’s plurality-loser-elimination method to resolve the most persistent cycles. Given plausible (but not unassailable) assumptions about how candidates decide to withdraw in the case of a cycle, Dodgson-Hare outperforms Hare, Condorcet-Hare, and 12 other voting rules in a series of spatial-model simulations which count how often each rule is vulnerable to coalitional manipulation. In the special case of a one-dimensional spatial model, all coalitional voting strategies that are possible under Condorcet-Hare can be undone in Dodgson-Hare, by the withdrawal of candidates who have incentive to withdraw.