Hi, I've been reading the list for a couple weeks. I got into voting theory a couple years ago after reading a Science News article. It described IRV and I thought "Gee that's convoluted. I could do better with a simpler procedure."
I wrote a simulator and ran a few million elections. The results are at http://bolson.org/voting/ If your favorite system isn't in there, tell me about it and maybe I'll add it to the next round. I'm writing today to tell about my new favorite system: Instant Runoff Normalized Ratings (IRNR) Every voter casts a rating of each choice on a scale of -1.0 to 1.0 or some equivalent scale. Each voter's voting power is normalized, each rating is divided by the sum of the absolute values of the ratings so that each voter has a voting power of 1.0 . All of the normalized ratings are summed. The choice with the lowest rating sum is disqualified. On successive iterations votes are re-normalized without disqualified choices, redistributing a voter's voting power to the still-active choices in proportion to the original vote. The handiest checklist of qualities I could find is: http://electionmethods.org/evaluation.htm Monotonic: yes. At all stages a change in a vote directly and proportionally changes the outcome. Condorcet: yes-ish. I believe that IRNR is more powerful than Condorcet because it also addresses the degree of preference and not just the order. Otherwise, IRNR and Condorcet both address the whole votes of the whole electorate at once, and if the ratings contain no more information than rankings, IRNR should find the same winner as Condorcet. Generalized Condorcet: "yes". I wave my hand and say, yes, of course it will do the right thing. "Strategy Free": maybe not. A 51% majority could rate candidate A at 0.02 and B at 0.01, 49% could vote B 1.0 and A -1.0 . B would win. Does this violate SFC? Is it a just system anyway? If IRNR were modified to expand votes out to a 1.0 to -1.0 scale before normalizing them the 51% vote would translate to A=1.0 and B=-1.0; A would win. GSFC: no comment at this time. See Strategy Free. Strong Defense Strategy: Yes. A majority casting votes can win without mis-ordering any votes. Rating their favorite at 1.0 would achieve this. BUT, there might be a compromise choice that the majority and some of the minority rate at 0.8 which could win. Perhaps this is an imprecision in the wording of SDS. The compromise choice is backed by a super-majority. Does SDS actually mean that the winner should be picked by the largest majority? Weak Defense Strategy: Yes. A majority casting ratings of -1.0 for their least favorite choice would prevent the election of that choice. On the first round of disqualification this choice would have the lowest summary rating and be disqualified. UNLESS, there was a more widely but less vociferously disliked choice, comparable to the positive case in SDS. Are we talking largest majorities here? Favorite Betrayal Criterion: Yes. This is the most important criterion to me. I believe IRNR provides no incentive to vote other than honestly. The decision made by IRNR is always in proportion to the ratings cast by a voter, so the voter is best served by ratings which are in line with their true desires. Because of the proportional nature of IRNR, there are not the singularities that IRV suffers. Participation: Yes. There's no way for a ballot with a higher X rating than Y rating to contribute more to Y's sum than X's. Thus an additional X > Y ballot cannot elect Y over X. Summability: No. Because this is an instant runoff method, all votes must be centrally collected and run together. Computationally inconvenient, I know. It is not even representable as a candidates-factorial size array as IRV could be. Brian Olson http://bolson.org/ ---- Election-methods mailing list - see http://electorama.com/em for list info
