Hello. This is James G-A, responding to the following post by Chris Benham: http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-November/026954.html
Chris and I have had a good discussion about this since his post, which has enabled me to get back up to speed on some of the things he mentioned.
So, to summarize, there are at least two distinct approaches to creating Smith/Hare hybrid single winner election methods.
One approach is to first eliminate the candidates outside the Smith set, and then to hold an IRV tally among remaining candidates. Nic Tideman's 'alternative Smith' method is a variation on this, which provides for further elimination of extra-Smith candidates in between IRV counting rounds.
Another approach is to successively eliminate the plurality loser until there is a Condorcet winner among remaining candidates. An equivalent method to this is to do an IRV tally, give each candidate a score according to the number of candidates eliminated before them, and then choose the Smith set candidate with the highest score. Douglas Woodall seems to have proposed this in 2003 or earlier, though I'm not sure if he has done so in any published forum.
In our discussion, Chris Benham and I resolved that the former approach has the advantage of satisfying the 'local IIA' criterion (which states that adding a candidate outside the Smith set should not affect an election result), while Woodall's approach has the advantage of satisfying the 'mono-add-plump' and 'mono-append' criteria (which are defined, for example, in Woodall's "Properties of Preferential Election Rules", Voting Matters December 1994).
Chris feels that the monotonicity criteria are more important, but I remain undecided about that. My conclusion at this point is that neither approach entirely dominates the other. One thing that I will say in favor of Woodall's approach is that it has the simplest definition, which suggests a certain elegance, and which means that it would probably be easier to sell to a skeptical public.
I've run a few of my election strategy simulations on Woodall's method, and so far I've found no difference between its performance and that of the other approach. So, both approaches seem to share these three highly desirable properties: (1) Smith efficiency, (2) minimal vulnerability to strategic voting, and (3) minimal voting to strategic nomination.
In my opinion, this combination is a really big deal, and I look forward to further discussion of these methods.
Sincerely, James ---- Election-Methods mailing list - see http://electorama.com/em for list info
