Date: Fri, 8 Aug 2003 12:28:48 -0700 (PDT) Subject: Re: [EM] What IRV optimizes From: "Alex Small" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]>
John B. Hodges said:IRV is the one-seat case of the Single Transferable Vote. The point of STV is to maximize "ballot effectiveness", i.e. to minimize "wasted votes". Votes are wasted in two ways: Undervotes, where you vote for someone who fails to win a seat, and Overvotes, where you vote for someone who gets more votes than they need to win a seat.
Yes, but STV accomplishes that not only by transfering votes, but also by electing multiple candidates to ensure that as many people as possible get a representative. I don't see how the variational principle you cite applies in the single-winner case.
We can talk about "total" ballot effectiveness for the method (what percentage of ballots elect a candidate), and the distribution of the ballot effectiveness through the electorate (what percentage of voters cast effective ballots). If ballots are ranked and fractional, these two figures need not be equal.
In the single-winner case, IRV (and other majoritarian methods) give a total ballot effectiveness of 50%, no more or less; total ballot effectiveness under Plurality would be the vote percentage received by the second-place candidate, which would always be less than that. More generally in the N-seat case, total ballot effectiveness is equal to the sum of the winning thresholds, expressed as percentages.
The distribution IMHO is even more important; proportional representation tries to maximize the percentage of the electorate that have effective ballots. This is in contrast to "winner take all" methods. The effectiveness of individual ballots will almost always be either zero or a fraction, since very few candidates win seats by exactly one vote.
Someone once described Approval as "Plurality done right"; It's a interesting point that in the single-seat case, Approval could give "ballot effectiveness" figures far above 50%. MCA would set a 50% floor, but the second-place candidate could rack up more than that.
Another thought I had regarding STV. STV deals with undervotes by transferring them from last-place candidates to others with more chance of winning. It measures "last place" by the votes the candidate has accumulated so far, up to that point in the process. It might be (has been) argued that this is not the best possible measure. For example, a better measure might be the candidate with the lowest Borda Count. I recall hearing of "Borda Elimination", I'm sure it has its own flaws.
--
----------------------------------
John B. Hodges, jbhodges@ @usit.net
Do Justice, Love Mercy, and Be Irreverent.
----
Election-methods mailing list - see http://electorama.com/em for list info
