I can sympathize that win strength should be (strength of victory)*(importance of race). But if you're going with that philosophy, then "strength of victory" should not be percentage margin (W-L)/(W+L), but rather statistical confidence (W-L)/sqrt(W+L). The sqrt(W+L) divisor is proportional to the standard deviation of the margin. Multiply that "statistical confidence" by the "importance" factor W+L, and you get
(W-L)*sqrt(W+L) = sqrt((W-L) * (W²-L²)) Since ordering is all that matters here, and the sqrt function is monotonic over this domain, you can remove the sqrt: (W-L) * (W²-L²) Or play with the formula to keep the ordering but make the units come out as votes: sqrt( (W-L) * sqrt(W²-L²) ) I understand the attractiveness of the much simpler margins formula W-L. But to argue that that formula is actually a fairly-weighted product of two factors seems like a post-facto rationalization to me. As for the [35 A>B, 25 B, 40 C] example and the (Margins, smith/max win) suggestion: that doesn't really solve the problem, because it gives the adjusted scenario [30 A>B, 25 B, 45 C] to C. 2011/6/27 robert bristow-johnson <[email protected]> > > On Jun 24, 2011, at 9:44 PM, Kevin Venzke wrote: > > Hi Robert, >> > > hi Kevin, > > > >> --- En date de : Ven 24.6.11, robert bristow-johnson < >> [email protected]> a écrit : >> >>> my spin on why Margins makes the most sense is: >>> >>> 2. the measure of importance of an >>> election is proportional the number of voters participating >>> in it. if very few people weigh in on an election, it >>> must not be very important. >>> >> >> Knowing the larger of X and Y tells you more about X+Y than knowing X-Y. >> > > but, statistically, both max(X,Y) and |X-Y| have mean pretty much > proportional to X+Y, if X and Y have identical p.d.f. form, but different > means. > > > Let's try an example. Suppose the counts are 4 and 3. If you know the >> 4, you know that the number of participants was from 4 to 8. If you know >> the difference, 1, all you know is that there was at least one >> participant. >> > > true, but razor-thin, close elections with a lot of voters doesn't indicate > a strong popular case pro or con. since (at least i believe) random lots > should be used only for absolute ties where the popular support of both > candidates is indistinguishable, then based on counting all the votes very > carefully and verifying, if the number of votes for Candidate A exceeds > those for Candidate B but only 1 vote, then a decision must be made and it > must be for Candidate A. but i still don't get how you are concluding that > the *net* electoral sentiment for Candidate A is decisive (considering the > alternative), particularly if a million votes are cast, if Candidate A gets > only one vote more than B. > > Winning Votes has *no* salience attached to how close or decisive an > election is. i just cannot get past that. a measure of how decisive an > election is, is a factor and how many voters weigh in on the election is a > factor also. Margins represents the product of those two factors in a > simple and elegant manner. > > just like in a simple binary election, decided by a "simple majority", the > reason we grant preference to the candidate with more votes is that > satisfying the greater number of voters who supported that candidate is more > important than satisfying the lessor number of voters. it's utility. or > utilitarianism. the candidate with the simple majority has the mandate. > > likewise, as in Ranked Pairs or beatpath or MinMax-margins, the pairwise > election with the greater margin has the mandate. why give preference to > the smaller set of *net* voters who prefer C over D than to the larger set > of *net* voters who prefer A over B? (the model i am using is that every > vote for B over A is equal weight and cancels a vote for A over B.) in both > cases we are trying to minimize the number of disappointed voters. > (minimizing the number of disappointed voters is also what the Plurality > guys are claiming, but they don't see the picture right). > > > This is one of my main criticisms of margins, that it doesn't try to >> gauge the importance. >> > > it *does*. but it makes it *one* factor of two, the other factor being the > *decisiveness*. > > net salience = (popular import) x (decisiveness) > > = (number of voters) x (percent defeat margin) > > the main criticism of Winning Votes is that it doesn't try to gauge the > decisiveness. > > > There's no fixing this either. If you want losing votes to count they >> need to lessen the importance, or else you have a huge monotonicity >> issue. >> > > well, losing votes *should* count. but with a negative weighting, and they > do with Margins. > > it's like all of the winning voters are saying "This is what we want! And > it's important!". The losing voters may have lost the "This is what we > want!" battle, but we don't totally remove their voice. Their votes have > the effect of reducing the importance of the "mandate" that the winners can > claim. and they *should* be able to do that, as the razor-thin example of > 50000 to 49999 states. that election doesn't really say diddley about > whether we should pick Candidate A or Candidate B. perhaps, there was a guy > and his wife, both for Candidate B, who missed the election. even with a > big turnout, that election was too damn close to indicate the sentiment of > the electorate. > > > > 4. simplicity has its attraction. >>> >> >> I find WV simpler because you don't need to do subtraction to determine >> the defeat strengths. You find which side is higher and then you're done >> with the losing side's figure. If you draw a triangle showing the wins, >> you only have to write one number per win to say what happened. >> > > but it doesn't say enough of what happened. > > the traditional vote-for-one ballot is simpler than a ranked ballot > necessary for Condorcet (or IRV or Borda or Bucklin), but it doesn't say > enough of what the reality is. that's why i am for ranked-choice voting > over the traditional ballot or for Approval voting (not enough information > is collected from the voters). WV doesn't sufficiently say what has > happened when the election was very close. > > > Margins is probably easier to define, but is that much more desirable >> than being easy to solve? >> > > yes. we want simple rules. simple rules that make sense. simple rules > like simple majorities. simple rules like more votes count for more than > fewer votes. the margins are just that (they are *net* votes). > > more *net* voters carry more weight than fewer *net* votes. > > > 5. Winning Votes communicates >>> something regarding the number of voters participating, but >>> says nothing about how close the election was. an >>> election with a razor-thin result, even with a lot of people >>> voting, does not measure well the will of the people. >>> if it's 99,999 voters and 50,000 said Candidate A and 49,999 >>> said Candidate B, that does *not* say that Candidate A has >>> such a great mandate to lead. Margins says his/her >>> mandate to lead is 1 and Winning Votes says it's >>> 50,000. how can that make any sense? >>> >> >> Because WV is measuring "importance," per your item #2, not closeness. >> What "mandate" does a candidate have, who lost the most important race? >> > > if he (let's call him "A") lost it by only one vote, perhaps more mandate > than the candidate (let's call him "B") who beat him by just one vote, if > that candidate (B) lost decisively to a candidate that A has beaten (or lost > barely to a candidate that A has decisively beaten). > > > (And beat some other guy who had no chance of winning.) >> > > now, how is that the case, if that other guy (call him "C") beat your guy > ("B") decisively? if C didn't beat B decisively, then maybe you gotta case > for electing B. but if B beats A by one vote (in the race with more > participants), yet B is beaten by C decisively (with slightly fewer > participants) who is then decisively beaten by A (again, with slightly fewer > participants), i don't see how anyone would coronate B instead of A. > > if a vote for A>B cancels a vote for B>A (as it should for > one-person-one-vote), it's the number of *net* votes for A (that have no > canceling vote for B) that stands as the number of human beings with > franchise that cry out to not be disappointed. > > think Utilitarian. > > > I would guess pretty much none, as far as voters would say. >> > > an inescapable problem for elections that are very close, that could have > gone either way, is that the winner does not emerge with a great mandate. > he'll do what agenda he campaigned on, if he can, but he cannot claim that > the nation has clearly spoken. > > when there is a multicandidate election decided by Condorcet compliant > ranked-choice voting, if there is a cycle, it is a lot like a tie, with > nebulous results. no candidate will come out of that with a big mandate > either. the motivation now is that of decisiveness (readily deciding a > winner on election night, even under nebulous results), determinism (not > deciding by coin flip, unless it just cannot be avoided), and some coupling > to voter expression (elections with wider margins speak more loudly than > those with narrow margins). > > > Methods getting confused by the presence of weak candidates (which is >> basically what we are talking about here) is not good. >> > > no, i'm talking about weak *results* a.k.a. close elections. > > > If a candidate can't win, he shouldn't be affecting the result. >> > > but this is all what happens in a cycle. the candidate in the Smith set > *can* win, but so can the other candidates in the Smith set claim that. > > > Anyway, a margins proposal is DOA, from the moment anybody would point >> out the 35 A>B 25 B 40 C scenario. Does anybody actually disagree with >> that? One's EM postings will have to be very, very clever to persuade >> the media, public, etc., that A should win that race. >> > > > and even more clever to persuade me. lessee... > > 35 A>B > 25 B>A A>B by 10 > > 40 C>A > 35 A>C C>A by 5 > > 60 B>C > 40 C>B B>C by 20 > > looks like B wins to me. why shouldn't he? (maybe because C's great > defeat by B is not because B is so great, but that C is Sarah Palin: gets a > lot of hard-core supports but a lot more of us know that she's a total > doofus.) > > so maybe instead of Ranked Pairs or MinMax with margins (i presume Schulze > would also elect A), it should go to the candidate in the Smith Set with the > greatest winning margin over any other in the Smith Set. but it still > should be based on margins. > > but it *is* an interesting problem. Marcus, can you comment? Schulze > beatpath method would also elect A, no? can you persuade us that A should > win in this scenario? > > bestest, > > > -- > > r b-j [email protected] > > "Imagination is more important than knowledge." > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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