Markus wrote: > Dear Mike, > you wrote (4 Feb 2004): > > Not only does Plurality pass your "SDSC", -snip- > If you mean Steve Eppley's "minimal defense" with "your 'SDSC'" > then your example doesn't demonstrate a violation of this > criterion since this majority of the voters doesn't rank > candidate B "no higher than tied for bottom". > > Steve Eppley wrote (http://www.alumni.caltech.edu/~seppley): > > Any ordering of the alternatives must be an admissible vote, > > and if more than half of the voters rank y over x and x no > > higher than tied for bottom, then x must not be elected.
Markus has taken an excerpt out of context, and in this case it is misleading. (Perhaps I should search my election- methods-list folder to see how often my writing has been misrepresented.) Here's more of what I actually posted at the webpage Markus cited, which shows how Markus distorted my definition: minimal defense: If more than half of the voters prefer alternative y over alternative x, then that majority must have some way of voting that ensures x will not be elected and does not require any of them to rank y equal to or over any alternatives preferred over y. (Another wording is nearly equivalent: Any ordering of the alternatives must be an admissible vote, and if more than half of the voters rank y over x and x no higher than tied for bottom, then x must not be elected. This criterion, in particular the first wording, is promoted by Mike Ossipoff under the name Strong Defensive Strategy Criterion. -snip- ) The definitions in that "table of contents" webpage have been made brief and simple for the sake of laymen who might read the page. The complete definition of minimal defense is in a document two clicks away from that page. (Click on "minimal defense" then click on "Strategic Indifference".) Minimal Defense: For all subsets X of the alternatives, if there exists an alternative y that more than half the voters prefer over every alternative in X, then there must exist a set of voting strategies for that majority that ensures no alternative in X will be elected and does not require any of them to misrepresent any preferences except possibly lowering alternatives in X. I should add a clause to strengthen that: "... and without having to lower any alternative in X below a tie for bottom with their least-preferred alternative(s)." In addition to the obvious reduction of preference misrepresentation implied by this clause, I seem to recall from years ago that the clause serves to ensure a group strategy equilibrium (much more desirable than a Nash equilibrium) by preventing the creation of new strategic reversal opportunities that could arise if X is lowered below other alternatives. It may be unclear when organizing the defensive strategy how popular the other candidates will be on election day. For instance, if some supporters of y downrank x below z (rather than tied for bottom with z) to deter suporters of x from attempting a reversal strategy (x over z over y), then supporters of z who prefer z over y over x may be given an opportunity to elect z by reversing x over y. It was near-accidental that I noticed Markus' message. I haven't read the previous messages in the thread, but it's clear from the subject line that Mike was referring to some (re)definition of SDSC allegedly posted by Markus, not to a definition posted by me. ---Steve (Steve Eppley [EMAIL PROTECTED]) ---- Election-methods mailing list - see http://electorama.com/em for list info