On Sun, 2005-10-16 at 22:47 +0200, Kevin Venzke wrote: > I don't know of a way to weaken LNHarm which would still result in a guarantee > that voters could "take to the bank."
My hope would be that we can come up with a system where voters could feel comfortable ranking all but one of the viable candidates. So, if we end up in a situation like we were at one point in 1992, where Clinton, Bush and Perot were all viable candidates, voters could feel comfortable ranking two out of three of them, without worrying at all about helping anyone defeat their first choice. For such a system, we could then recommend that voters do not rank anyone below their least favorite viable candidate (which would be a very minimal amount of strategy to impose). So, the partial definition of Later-no-harm for viable candidates criterion" (LNHarmVC) could be: "Adding a /viable/ preference to a ballot must not decrease the probability of election of any candidate ranked above the new preference." The trick, of course, is to define "viable" in mathematical terms in such a way that matches the popular view of viability. A simple, but probably incorrect, definition would be "any candidate who is ranked on a majority of ballots". I would hope we could come up with a less stringent definition, because that would potentially mean that a candidate in a close, polarized three way race might not be "viable" by the definition. An alternative definition might be "any candidate who could win without violating Plurality". I think working with the MMPO example you posted a while back may help to arrive at an answer: n A m A=C m B=C n B When n>2 and m=1, then C wins decisively, no matter how large n gets. The horrifying thing about this particular example is that it seems quite feasible for a fringe write-in candidate to win under this example. It's a gross Plurality violation, which is clearly unacceptable. More to my point above, a write-in candidate would very rarely be considered "viable", so violating LNHarm for this candidate is not a big concern. However, there's probably a threshold for m which that result doesn't look so bad. Clearly, when m>n, it's hard to argue that anyone but C should be the winner. Is there a lower value for m relative to n where the result is still defensible? Is there anything mathematically interesting about that threshold, that might lead us to a good definition of "viable"? Rob ---- election-methods mailing list - see http://electorama.com/em for list info
