Dear Jobst and Steve, Please allow me to join your conversation. Jobst, you wrote: >As to TRUNCATION RESISTANCE, I fear the proposal might FAIL that because >of the specific definition of defeat strength. With defeat strength = >winning votes, this criterion also follows from immunity, but with >defeat strength defined otherwise, it will probably fail. It seems this >will be a general problem with cardinal weighted pairwise -like methods, >do you agree? If so, we should figure this out more clearly since it may >undermine our hopes that cardinal weighted pairwise will have better >strategy properties...
Woah there, let's not get too upset. First of all, yes, under the current definition of the cardinal pairwise method, it is possible to change the result from a sincere CW to another candidate via truncation. This is not possible in winning votes, and it is possible in margins. In some intermediate versions of my cardinal pairwise proposal, I had a majority/minority beat provision, which stated that any pairwise defeat where the winning side constitutes a majority of the valid vote was automatically stronger than a pairwise defeat where the winning side does not constitute a majority of the valid vote. If you add this provision, then cardinal pairwise meets the truncation resistance criteria. (The provision itslef was designed for this purpose.) So, if you think that the criteria are really important in itself, you can just add that provision. However, I haven't included that provision in the most recent versions of my proposal, because I currently consider it to be awkward and unnecessary. Basically, the truncation resistance criteria say that you shouldn't be able to pull off a successful burying strategy just by truncating your ballot, or insincerely ranking two candidates as being equal -- instead, if you want to bury someone, you have to actually reverse at least one preference ordering. I recognize the usefulness of these criteria, and I consider them to be a valid point in favor of winning votes against margins, but I don't think that their importance should be overstated. That is, they don't mean that strategizing voters will have less of an ability to bury a candidate, they just means that they need to use reversal rather than truncation to do so. I submit that if voters are determined to strategize, the need to use order-reversal won't be much of a barrier. I submit that in cardinal pairwise, those who are likely to truncate against a candidate will generally fall into the high-incentive, low-ability category of strategic voters which I define in my proposal (section 6b). That is, when C>A>B voters are willing to truncate to bury A in order to help C, i.e. to vote C>A=B, it is likely that the difference between candidates A and C will be large, the average C>A and A>C rating differentials will be large, and the A>C defeat, assuming one exists, will be difficult to overrule in cardinal pairwise, making the truncation strategy unlikely to be effective. To sum up, cardinal pairwise's anti-strategic properties apply to both strategic truncation and strategic order-reversal. Winning votes makes strategic truncation ineffective, but those who want to strategize can easily get around that by using order-reversal instead. my best, James ---- Election-methods mailing list - see http://electorama.com/em for list info