Kevin Venzke wrote: "Try this method (an IRV variant) for example:
The voter ranks the candidates. Full ranking or truncation are allowed; equal ranking is not allowed. Say that X is the number of candidates still in the running. While X>1: If more than half of the original count of ballots rank candidate C in the Xth position (i.e. strictly last among candidates remaining), then eliminate C. Otherwise eliminate the candidate with the fewest top preferences as in IRV. End while. Elect the remaining candidate." Kevin, It seems to me that the specification of "more than half the original count of ballots" instead of "more than half the unexhausted ballots" causes this to fail Independence from Irrelevant Ballots(IIB). What compensating advantage do you get by doing that? In the 49A,24B,27C>B scenario you have long held that A shouldn't win because A has the only majority-strength pairwise loss (to B). And yet no candidate is ranked "strictly last" on more than half the ballots so nothing stops B from being eliminated and A winning just like in regular IRV. I suggest this: "Voters rank the candidates,truncation allowed, above-bottom equal ranking not allowed. Until one candidate remains, eliminate candidates one at a time according to these rules: (1)If one or more of the (remaining) candidates are not ranked (among remaining candidates)above bottom or equal-bottom on more than half the ballots that make some ranking distinction among remaining candidates, eliminate the one of these that is top-ranked (among remaining candidates) on the fewest ballots. (2)Otherwise eliminate the candidate that is top-ranked (among remaining candidates) on the fewest ballots. Elect the remaining candidate." What do you think of that? This meets Sincere Defense and keeps IRV's IIB while being much more Condorcetish than regular IRV. Chris Benham Thu Dec 20 21:43:33 PST 2007 Hi, I think an approach towards implementing this kind of logic in an election with unnumbered candidates would be to allow voters to torpedo the options they perceive as furthest from them. Try this method (an IRV variant) for example: The voter ranks the candidates. Full ranking or truncation are allowed; equal ranking is not allowed. Say that X is the number of candidates still in the running. While X>1: If more than half of the original count of ballots rank candidate C in the Xth position (i.e. strictly last among candidates remaining), then eliminate C. Otherwise eliminate the candidate with the fewest top preferences as in IRV. End while. Elect the remaining candidate. Imagine that the candidates can more or less be plotted on a one-dimensional spectrum. Considering that candidates are more likely to try to stand as near to the median as possible, and not spread throughout the space where voters lie, IRV is likely to eliminate all the median options and end with a final showdown between two strong candidates who were able to grab large quantities of "outer" voters. In this variant method, assuming these two candidates aren't the preference of the median voter, it is likely that IRV's two finishers could be the first two candidates eliminated. Their supporters' second preferences would very quickly be freed up to help support candidates closer to the median. And this process is capable of repeating indefinitely until the final two candidates are truly those that came nearest to the median. This is an "instant" generalization of my two-round method suggestion where the final round consists of the top two candidates from the first round,who didn't receive a full majority of the "against" votes of that round. Kevin Venzke Make the switch to the world's best email. Get the new Yahoo!7 Mail now. www.yahoo7.com.au/worldsbestemail ---- Election-Methods mailing list - see http://electorama.com/em for list info