jimmysnyder said:
That's my issue. The candidate is gone, but the votes aren't.
Yes, they are. When a candidate is eliminated, all of the votes for him (in any position, first, second, etc.) are also discarded.
The idea is to mimic a regular runoff election, which uses multiple rounds of voting. In a regular runoff, you start with a maximal list of candidates, and each voter casts a single vote for the candidate of their choice. Then, if no candidate gets a majority, the least popular candidate is eliminated from the list, and the process is repeated. The downside of this approach is that you have to do lots of rounds of voting, and the campaign process can become confusing and tortuous as the list changes. So, instant run-off voting attempts to mimic this process by having everyone vote only once, but also rank every candidate when doing so. Then, you use that data to conduct a "virtual" run-off, where instead of revoting at each stage, you use the listed preferences to infer what the votes would have been.
jimmysnyder said:
Yes, E is the winner with 50% of the votes. But A had 60% and lost. that is the problem.
No, you're double-counting votes (they add up to 110%). The order of elimination is important; note that, if you start counting unused votes, every candidate receives 100% of the total. There is only a problem if you can show that more people ranked A above E than vice-versa, which I guess is what you're getting at with the example that follows.
jimmysnyder said:
Suppose 20% chose A first and the remaining 80% chose A second. A would still lose to E who only had 20% first choice votes and 30% third choice votes.
So, let me see if I follow: there are 5 candidates (A, B, C, D and E), each of whom get ~20% of the first-choice votes. A is the second-choice of all of the voters who opted for B, C, D or E first. Suppose A loses round 1 and is eliminated, and that the A-voters' second choices are equally distributed among the remaining 4 candidates. Now, candidates B, C, D and E are left, each of whom has ~25% of the votes. Suppose B loses this round, and is eliminated. All of the second-choice votes for B were for A, but A is eliminated, so we use their third-choice votes. Suppose these are uniformly distributed amongst C, D and E, leaving each of them with ~33% of the vote. Now, C is eliminated, and we again throw out the second-choice votes for A. Likewise, we throw out any third-choice votes for B, and suppose that the resulting votes are split between D and E. This leaves D and E with ~50% of the vote each. Suppose D loses, and E wins. Is this what you had in mind? The question, then, is whether more voters ranked A (or B or C or D) above E than vice-versa. Looking at the assumptions, we see that all of the A, B, C and D voters ranked A above E, while only the E voters ranked E above A, which is to say that 80% of the voters would have rather seen A win than E, the ultimate winner.
So, yeah, that is a potential quirk. However, it depends on the very unlikely scenario where everyone wants to see candidate A as their first- or second-choice, and yet candidate A still loses the first round. If any other candidate loses the first round in this example, the result is that A will win. However, there is probably a way to modify the elimination/voting procedure to avoid this kind of outcome...
