demon said:
Why can't elections be held through elimination? Keep eliminating candidates by number of votes until only one remains. That would do away with the whole matter of candidates whose chances of winning are zero taking votes that would otherwise go to a candidate with an actual chance of winning.
Actually that is incorrect. What you are proposing is an instant run off election, where if one candidate does not win, his supporters then go toward their second choice. Supoose there's a system with 3 candidates, A, B, and C.
Suppose that voter preference across the nation breaks down in this manner, from most favored to least favored.
35% prefer A,B,C
33% prefer B,C,A
32% prefer C,A,B
Now, candidate C will have the least number of first place votes, so his votes then run off to candidate A, so candidate A would win the election as the most overall preferred candidate. Now assume that for some reason candidate A becomes *more popular* the preference shifts to:
37% prefer A,B,C
31% prefer B,C,A
32% prefer C,A,B
This time, Candidate B would be eliminated and his votes would transfer to candidate C and C would beat A.
Why is this bad? Because if you notice, candidate C did not become overall more popular, but A became overall more popular thus losing him the election, because he took net votes from the wrong candidate. This example is simplified, as it does not include all possible ranking permutations, but it's not far fetched to think that all permutation would not be equally popular. In this election, if we had a runoff election, most voters who choose President Bush would probably choose Kerry over Nader, most who vote Nader would undoubtedly choose Kerry over Bush. a Nade, Bush, Kerry ticket would be quite rare, as would a Bush, Nader, Kerry. That still leaves four permutations, but it's enough to experience the same result, albeit in a more complex scenario.
Is this "better" than a plurality system? There are less instances of a paradoxical outcome, but this paradoxical outcome is quite a damning argument against a run off system if it came to be. There are no perfect voting schemes involving more than two choices, all can result in paradoxical outcomes given the right circumstances, however, if I made the decision, I'd probably choose some form of max-flow algorithm.
The main advantage of the plurality system is that it's simple to understand. A run off election is still pretty simple, but more convoluted than the plurality system. Max flow system would be even more complex still. Voting theory become even uber cooler in the case of voting for amendments and change to legislation in congress, where the order that things are voted on can substantially change the chances of whether a bill is passed or not, regardless of voter preferences.
