November 12, 2002
Irrelevant Alternatives
A supplementary realization on the "Indepences of Irrelevant Alternatives Criteria" (IIAC) example below.Condorcet only "flunks" this criteria IF the vote ends up in a cycle. Meaning, if:
- The majority prefers A over B
- The majority prefers B over C
- The majority prefers C over A
The other voting methods can flunk IIAC, however, even if there isn't a cycle.
In the example below, I make the argument that it's fair for that scenario.
However, the Gore/Bush/Nader election did not have a cycle. The majority in Florida probably preferred Gore over Bush, and also Gore over Nader.
Plurality voting flunked there. Condorcet would not have.
Soon, I will be finished looking into and understanding all the different voting methods, and will begin implementing them into a voting application I am writing.
I am rapidly understanding that finding the correct vote-counting procedure will only take you so far. Because using a vote-counting system to find the perfect social choice depends on one thing - each participant of that vote feeling they have a perfect candidate to vote on. Or at least, each voter being equally satisfied that their candidate reflects their choice. And that's far from the truth.
And so with that, here is my summary of the different voting systems I have researched:
- Plurality: Most first-place votes wins.
- Approval: Vote for as many candidates as you want. Candidate with most votes wins. This is widely recognized as a solid counting system. I personally feel it can give too much false power to a compromise candidate, though.
- IRV: If no first-ranked candidate gets a majority (>50%), delete worst first-rank, bump up second rank for those ballots, refigure. Repeat as necessary. There are many, many flaws for IRV.
- Borda: For a five-candidate election, rank all five. 1st place gets 5 points, 2nd place gets 4 points, etc. Most points win. Technically solid, but high chance of voters voting insincerely for strategic reasons.
- Condorcet: Head-to-head cage matches. Winner beats all other candidates. If there's a cycle, it gets complicated.
- Ranked Pairs: Similar to Condorcet. I don't understand it yet.