Sunday, November 05, 2006

Plurality fairness and majority rule

Single winner elections where every one has one vote and the highest voter-getter wins is called Plurality.

Supporters of plurality say that that it is a good method because it is conservative, assuming that voters will spend time before the election to rally behind a single candidate, and shift their support as other similar candidates appear with more support. So by the time the actual election is held, everyone has compromised as far as they are going to. Given this condition, there's no reason to consider the highest voted candidate won't stay there even if a new vote was conducted.

Rejectors of plurality will say that voter ARE willing to compromise further because they didn't have enough information before the first vote to guage the strength of their favorite candidate. They note that when the plurality winner fails to exceed a majority of the vote (50%), a different candidate may have been able to win by further compromise. Thus the idea of a "runoff" was deviced to allow lower candidates to withdraw and endorse another candidate who stands a better chance to win.

The simplest runoff approach is to allow the top-two candidates in the plurality count to compete against each other in a new round of voting. This allows a majority of voters to decide which of the two deserves to be elected.

Example: A=40%, B=35%, C=25%
Eliminate C
Result: A=55%, B=45%
Winner A by a majority

Now "majority rule" is assured, but we may notice that a different "majority winner" might have come out if there's more than 3 candidates. Then perhaps a top-three runoff was held, having 3 rounds, keeping the top-three for a second round, and a third round top-two for a final winner.

Now it seems "harmless" to add a third round, and helpful, allowing more voters to pick the "final two", even if majority rule itself doesn't demand this step.

But once you go to 3 rounds, things get somewhat funny. Afterall the reason we want to go to 3 rounds is that we could change the final-two, and change the winner. However how can we judge which candidates deserve to make the final round?

Remember back to the plurality supporters. They believe candidates should be rewarded for having the most votes and that this "reward" encourages compromise before the election and that voters who don't choose to compromise before election day don't want to compromise.

Now we are considering a 3-round runoff where one or both of the plurality top-two may be knocked out and disallowed their chance to compete in the final round.

When we went from top-one (one round) to top-two (two rounds), the top-one candidate couldn't complain easily since he is guaranteed to make the final round and a chance to win. However when you move from top-two (two round) to top-three (three round) runoff, you're risking the "guarantee" that the plurality-second candidate will get his fair chance in the final round to win.

I consider this a "plurality fairness" principle. If we agree elections are MEANT to encourage pre-election compromise, then we want to exclusively reward this compromise with equal treatment.

Plurality treats ALL candidates fairly.
Top-two runoff treats TWO candidates fairly.
Top-three runoff treats TWO candidates fairly, BUT they may NOT be the same as the plurality top-two candidates.

For this reason, I can not support a three round runoff. If we want to treat THREE candidates fairly, then we ought to move to a Condorcet style election where all the candidates, (or all the candidates that pass some threshold requirement, like plurality top-three) are treated as equals.

With that background, I support IRV (Instant Runoff Voting) for political elections, but only as a top-two runoff. I do not support a bottom-up elimination process in a single winner election.

This means there's still a "spoiler effect" in 3-way races where a 4th candidate pulls down a candidate competing for second, but I believe it is the best we can do.

If we use bottom-up IRV and it disallows a plurality-second candidate a chance to compete in the final round, we will create an enemy of IRV, and we can not afford to make such enemies.

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