Dear Steve! > No, my "immunity from majority complaints" criterion (IMC) is more > demanding than that. It can't be satisfied merely by extending a > "single winner only" voting method so it also constructs a social > ordering consistent with maximal strength beatpaths. The social > ordering must be more self-consistent than that sometimes is. My web > pages provide an example that shows BeatpathWinner is not immune even > when extended to construct a social ordering. (See "Scenario A10" in > appendix A of the "immunity from majority complaints" webpage linked > to the www.alumni.caltech.edu/~seppley webpage.) [...] > But the reverse isn't true. When the top candidate is immune in > Jobst's sense, it does not imply that some social ordering could be > constructed (with the winner atop the social ordering, of course) > that is immune from majority complaints in my sense. Jobst's immunity > is significantly weaker, not just weaker in the mild technical sense > of a social ordering not being required. [...] > I do not know if River satisfies I2C.
I replied to that in a separate posting a minute ago. As to my writing... >> Immunity from binary arguments means the method elects an immune >> candidate. A candidate x is immune when for each defeat y>x, there >> is a sequence of defeats x>...>y all having the same or larger >> *strength*. So, beatpath, ranked pairs, and river all are immune >> no matter how strength is defined, but the meaning of "immune" >> changes with the meaning of "strength" of course! your replied: > That's what I meant when I said I wasn't sure your (weaker) immunity > criterion would be satisfied. One must redefine it in order to claim > satisfaction, and that's not quite the same as satisfying the > original criterion. The justification for one criterion won't > necessarily hold for an amended criterion. Not immunity is redefined but "strength". It's the same as when you redefine "defeat against the status quo" as a majority of at least 2 out of three -- you then only redefine "defeat" but not notions that use "defeat". At least that is the mathematical understanding of "definition". Of course, as a result of a changed meaning of defeat or defeat strength, also the *meaning* of other notions can change, but meaning is not the same as definition. However, I find this quite unimportant, so let's switch to the real things: > But I'm thinking that since people are so familiar > with "majority rule" that the main danger is from complaints based on > a "majority rule" argument. Also, it may be that people with a mild > preference for y>x will also tend to support the argument to replace > x by y. Not just people with a strong preference. Personally, I share your opinion. But in my compromise proposal I explicitly tried to include concepts which I'm not persuaded of personally but which seemed to be important to many members of the list anyway, so I included some means to distinguish between weak and strong preferences. But when we do so, we can no longer insist that cycles of the form A>B>C>A be broken at the defeat with the least winning votes, which would be required by the "winning votes versions" of immunity. > Attempting interpersonal comparisons of preference intensities given > only expressions in ballots is too difficult for me! And I'm not > certain it's the right goal anyway. Suppose selfish evil people tend > to have preferences that are more intense than those of socially > responsible people? I do agree absolutely. That was also the main objection I had against using ratings, so I only introduced the smallest level of distinction between preference strength possible. However, even that still feels like comparing the strengths of preferences of different people, as your showed by your example. I'm really not sure if we can consistently take preference strengths into account. > (You can infer that I hope there is no need to "compromise" with > advocates of Approval or with people who want to let voters express > ratings.) see above. > The greater the number of people who say x is better than y, the more > likely it is that x is better for society than y. That's interesting since it reminds me of what Llull seems to have replied when confronted with the question of what to do when there is no candidate who beats all others: He argued that when A is socially better than B, then certainly at least half of all voters will recognize this and vote accordingly, so that the socially best candidate will necessarily win all comparisons :-) Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
