Thanks, the referred paper contains a clear explanation of the links between minmax and Schulze. Use of the "minmax criterion" (max interest to change to another candidate) for groups too differs from the basic minmax method in that also other pairwise preferences than those that involve candidate X directly may influence the evaluation of candidate X.
My understanding is that the main driver behind the beatpath based methods has been the interest to guarantee independence of clones (well, maybe some aesthetic values too). Unfortunately all the criteria are not compatible with each others, and doing this takes one step away from the "minmax criterion" for individual candidates (that can be used as one possible sincere social utility criterion - at least the margins based version). Using beatpaths to identify clones is also not an exact definition of which candidates are clones, but at least it covers all clones (when defined as "candidates next to each others in every ballot"). In that sense beatpaths may be seen a slight overkill, but maybe a necessary one (?) if one wants independence of clones and the decisions to be based on the pairwise comparison matrix only. Juho --- On Fri, 28/11/08, Markus Schulze <[EMAIL PROTECTED]> wrote: > From: Markus Schulze <[EMAIL PROTECTED]> > Subject: Re: [EM] Why I Prefer IRV to Condorcet > To: [EMAIL PROTECTED] > Date: Friday, 28 November, 2008, 2:41 AM > Hallo, > > Juho Laatu wrote (28 Nov 2008): > > > I didn't quite get this. When evaluating > > candidate X minmax just checks if voters > > would be interested in changing X to some > > other candidate (in one step), while > > methods like Schulze and Ranked Pairs may > > base their evaluation on chains of victories > > leading to X. > > Suppose the MinMax score of a set Y of candidates > is the strength of the strongest win of > a candidate A outside the set Y against > a candidate B inside the set Y. Then the > Schulze method (but not the Ranked Pairs > method) guarantees that the winner is > always chosen from the set with minimum > MinMax score. See section 9 of my paper: > > http://m-schulze.webhop.net/schulze1.pdf > > Because of this reason, the worst pairwise > defeat of the Schulze winner is usually very > weak. And, in most cases, the Schulze winner > is identical to the MinMax winner. This has > been confirmed by Norman Petry and Jobst > Heitzig (with different models): > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2000-November/004540.html > http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-May/012801.html > > Markus Schulze > > > ---- > Election-Methods mailing list - see > http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
