I sent also another mail that explained that the basic / simplest tree method uses bullet votes (and is therefore limited to giving opinions that influence one branch only), and that trees can be used with richer votes too. In that case tree methods become hybrids since the tree concept and the idea of explicit clones can be combined with many different vote counting rules.
As I described in that mail, trees could be used also just as preprocessing rules that force the votes to respect the agreed clone sets. After this is done, those "clone compliant" votes could be consumed by any method (e.g. some Condocet method could take the "clone compliant" ranked votes as input). One could thus indicate which candidate of the competing branch is preferred by voting e.g. A>B>C (where B and C are the clones of the competing branch, and A is the only candidate of one's own branch). This vote is "clone compliant". Juho On 7.8.2011, at 16.48, Jameson Quinn wrote: > Like IRV, tree approaches would not allow supporters of candidates from other > branches to help decide which of the "clones" on the winning branch wins. > They would also not allow a situation where A likes B but B doesn't like A. > In both cases, this leads to an IRV-like center-squeeze problem, which, > especially in one-dimensional scenarios, is quite costly in terms of Bayesian > Regret. > > Perhaps you can think of ways to fix this, but if so, you'll have to be more > specific than "tree methods". > > .... > > As to SODA; I included my proposed chicken-fix rule in the "optional rules" > section of the SODA page. And it's remarkably unsatisfying. Here is a fix for > what I think is the most significant practical problem scenario in all of > voting theory; and yet half the people would skip that section, half of the > people who read it wouldn't understand why it matters, and half the people > who did wouldn't understand why it works. So, although this is something I'd > love to be able to brag about more, I didn't even include "fixes the chicken > problem" anywhere among the top 15 advantages in the advantages section. > > Oh well. > > Jameson Quinn > > 2011/8/7 Juho Laatu <juho4...@yahoo.co.uk> > On 7.8.2011, at 2.04, Jameson Quinn wrote: > >> >> >> 2011/8/6 <fsimm...@pcc.edu> >> Jan, >> >> IRV elects C like all of the other methods if the B faction doesn't >> truncate. But IRV elects A when the B >> faction truncates. Of course, with this knowledge, the B faction isn't >> likely to truncate, and as you say C >> will be elected. >> >> The trouble with IRV is that in the other scenario when the B faction >> truncates sincerely because of >> detesting both A and C, IRV still elects A instead of B. >> >> Also, if the A faction votes A>B, then B clearly should win, but does not >> under IRV. So yes, IRV solves the chicken dilemma, but in so doing causes >> other problems. (This same argument, as it happens, works against tree-based >> methods.) >> >> I still claim that SODA is the only system I know of that can solve the >> chicken dilemma without over-solving it and making other problems. > > I wouldn't say that trees "over-solve" the problem. The tree approach to the > chicken problem could be called "explicit clones". That's quite natural. Some > candidates just announce that they are clones and that they will support each > others. That sounds like a pretty exact solution, not an over-solution. > > Do trees "cause other problems" then? They do not allow the voter to support > one of the clones without supporting the other. But this is exactly what the > intention of the explicit clone approach is. Also the need to declare a > branch in the tree could be considered to be a practical problem / increased > complexity. And the need to identify the clones is an extra task / problem. > But maybe not really. What other (more serious) problems would the trees > cause? > > Juho > > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info
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