Dear Abd ul-Rahman, > I am most concerned about majority *consent.* Jobst is ignoring the > fact that I'm suggesting majority *consent* for decisions;
What exactly is "majority consent"? In my understanding "consent" means *all* voters share some opinion... > what do you call it when a minority imposes its will on a majority? It is not democratic whenever some group can impose its will on the others (in the sense of making their preferred outcome certain). No matter whether that group is a majority or a minority. From this it follows that a method which is always deterministic cannot possibly be democratic. > Question: if the majority explicitly consents to this for a specific > election, does the election method satisfy the Majority Criterion? If the system would have allowed the majority to decide otherwise, the *system* is majoritarian. >> > I'm not sure at all what a "just share of power" is. >> >> Me neither. But no power at all is definitely not a just share of power. >> By posting on this topic I hope a discussion on this will eventually >> begin. > What I pointed out here was that the ratings given did not contain > sufficient information to determine justice. Yes it does. I gave a reasoning why I consider C the more just solution because everyone prefers it to the "democratic benchmark". > Again, without defining justice, but relying upon common understanding > of it, we can easily construct scenarios that fully explain the > ratings as sincere, but which have quite different implications > regarding justice. In the challenge election, to repeat, we have > > 55: A 100, B 0, C 80 > 45: A 0, B 100, C 80 > > It was assumed that the ratings were "sincere," though that was not > defined. I gave at least two interpretations of this, so it was defined. I prefer the "preferences over lotteries" interpretation. > Now, it's obvious that C is what we would ordinarily understand as the > best winner. But a majority will disagree, and thus the challenge. I > don't recall the exact wording, but is there a method which, if > adopted, would cause C to win, even if the A and B voters are selfish, > and we might assume, the A voters know that they are in the majority? > > The answer given was Borda with equal ranking prohibited. Now, when I > first read this, I did not properly understand it. I should repeat > what I did before, only correctly. > > Let me be explicit about how this could elect C. I will modify the way > Borda count from how it is usually stated to make it equivalent to a > Range 2 election (CR 3). > > Sincere votes. > > 55: A>C>B > 45: B>C>A > > Counts: A, B, C > > 55: 2 0 1 > 45: 0 2 1 > > totals: > > A 110, B 90, C 100. This does not elect C. However the B voters, if > they understand the situation, can vote > > 45: C>B>A > > or counts A, B, C: > 45: 0 1 2 > > totals: > A 110, B 45, C 145. C wins, so it appears a quite desirable strategy > for the B voters, as we would understand the sincere ratings. > > Is there a counter-strategy? What if the A voters reverse their second > and third preferences? > > 55: 2 1 0 > > With the strategic votes from the other side the totals are > > A 110, B 100, C 90; they defeat the compromise attempted by the B > voters. However, the gain is relatively small, it would seem (but > there is an assumption that a gain of 20 in rating is "small." Not > necessarily.) > > and with the original sincere Borda votes from the B voters, this > counterstrategy would give us > > totals > A 110, B 135, C 90. > > So, somewhat off the topic, but interesting nevertheless, the B > voters, being not only selfish, but clever, mount a secret campaign to > get all the B voters to vote the strategy. However, they also arrange > to leak this information to the A voters, and, *supersecretly*, they > are not going to do that, they are going to vote sincerely. If the A > voters fall for it and vote strategically, to defeat the nefarious > stratagem of the B voters, and the B voters then simply vote > sincerely, B prevails, which is a disaster for the A voters and a > total victory for the B voters. > > The A voters are *probably* better off simply voting sincerely. And > that was Jobst's point. I don't think that was my point. In order to get a stable situation, i.e. a group strategy equilibrium, all voters should order reverse to make sure the other faction cannot reverse the outcome to their advantage. So the A voters are better off voting C>A>B. For this reason, I consider Borda a possible but not a good solution to the problem. Juho's suggestion to use weights like 1.4, 1, and 0 improves this since with them C is already elected with sincere ballots. > Explicitly, Jobst stated that the ratings given were not utilities, > and that he doesn't believe in utilities as having any meaning. Again, this is not true. I only stated that I don't believe in *measurable* utilities or, most importantly, even in *commensurable * ones. That does not mean I regard the term "utility" as meaningless. When someone prefers some A to some B, I think we can interpret this as A having "more" utility for her than B. But this "more" need not be representable by real numbers. Yours, Jobst ---- Election-Methods mailing list - see http://electorama.com/em for list info