Hi folks, I've been trying to imagine how the candidate withdrawal option (CWO) might play out, if added to something like beatpath or ranked pairs in a large-scale public election. (Briefly, CWO is that any non-winning candidate can order a post-election re-tally in which they are deleted from the ballot.) One nice thing about CWO Condorcet is that it retains both Condorcet efficiency and minimal dominant set efficiency; no withdrawal should change the winner from a minimal dominant set member to a non-member. Furthermore, I suppose that the withdrawal of a non-minimal-dominant set candidate shouldn't ever change the result of an election. Although CWO may produce a kind of messy aftermath to some sincere cycles, I'm starting to think that it may help keep the burying strategy in check to some extent. Here are a few brief supporting arguments for this notion:
1. The actual candidates involved (assuming that they are humans) may be better-equipped than any deterministic voting algorithm to judge whether a burying strategy has in fact been the cause of a particular cycle. 2. Candidates are more likely to withdraw in favor of similar candidates, which means in effect that defeats among similar candidates are more likely to be dropped. This effect is somewhat similar to that of the cardinal pairwise method, and in both cases it means that the more high-incentive burying strategies are less likely to be successful. (Let's say A>>B>C voters vote A>C>B in order to cause a false C>B defeat that overrules a genuine B>A defeat. Let's say that A is very different from B, who is fairly similar to C. Thus, the A>B voters have a strong incentive, but the C>B defeat is unlikely to overrule the B>A defeat, because B and C are relatively similar candidates.) 3. If there is a median candidate involved in a false cycle with two opposing wing candidates, and the median candidate is the initial winner, then neither of the wing candidates are likely to withdraw. However, if one of the wing candidates is the initial winner, then the opposing wing candidate has a fairly clear incentive to withdraw in favor of the median candidate. If a median candidate is involved in a cycle with two candidates from the same wing (lets say left for this example), this suggests that someone from the right wing buried the median under a leftist candidate, and so if the cycle resolves in favor of a left-of-center candidate, the strategizing right-wing voters have themselves to thank. Anyway, I'm not suggesting that CWO is preferable to cardinal pairwise. What I am suggesting is that if cardinal pairwise is considered to be too complex, then CWO may be a workable substitute in some situations. Another interesting topic for me is CWO in the case of direct issue voting. Obviously a proposition can't decide to withdraw by itself, so I suppose that in order to use CWO in a multiple-issue direct issue voting scenario, each option would have to have some sort of sponsor-type person with the authority to withdraw it in the event of a cycle. Again, perhaps not an ideal solution, but perhaps workable. Any comments? my best, James ---- Election-methods mailing list - see http://electorama.com/em for list info