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<div>
<br></div><div>(W-L)*sqrt(W+L) = sqrt((W-L) * (W²-L²))</div><div><br></div><div>Since ordering is all that matters here, and the sqrt function is monotonic over this domain, you can remove the sqrt:</div><div><br></div><div>
<meta http-equiv="content-type" content="text/html; charset=utf-8">(W-L) * (W²-L²)</div><div><br></div><div>Or play with the formula to keep the ordering but make the units come out as votes:</div><div><br></div><div>sqrt( (W-L) * sqrt(<meta http-equiv="content-type" content="text/html; charset=utf-8">W²-L²) )</div>
<div><br></div><div>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.</div>
<div><br></div><div>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.</div>
<div><div><br><div class="gmail_quote">2011/6/27 robert bristow-johnson <span dir="ltr"><<a href="mailto:rbj@audioimagination.com">rbj@audioimagination.com</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<br>
On Jun 24, 2011, at 9:44 PM, Kevin Venzke wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Hi Robert,<br>
</blockquote>
<br>
hi Kevin,<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
--- En date de : Ven 24.6.11, robert bristow-johnson <<a href="mailto:rbj@audioimagination.com" target="_blank">rbj@audioimagination.com</a>> a écrit :<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
my spin on why Margins makes the most sense is:<br>
<br>
2. the measure of importance of an<br>
election is proportional the number of voters participating<br>
in it. if very few people weigh in on an election, it<br>
must not be very important.<br>
</blockquote>
<br>
Knowing the larger of X and Y tells you more about X+Y than knowing X-Y.<br>
</blockquote>
<br></div>
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.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Let's try an example. Suppose the counts are 4 and 3. If you know the<br>
4, you know that the number of participants was from 4 to 8. If you know<br>
the difference, 1, all you know is that there was at least one<br>
participant.<br>
</blockquote>
<br></div>
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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
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).<div class="im">
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
This is one of my main criticisms of margins, that it doesn't try to<br>
gauge the importance.<br>
</blockquote>
<br></div>
it *does*. but it makes it *one* factor of two, the other factor being the *decisiveness*.<br>
<br>
net salience = (popular import) x (decisiveness)<br>
<br>
= (number of voters) x (percent defeat margin)<br>
<br>
the main criticism of Winning Votes is that it doesn't try to gauge the decisiveness.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
There's no fixing this either. If you want losing votes to count they<br>
need to lessen the importance, or else you have a huge monotonicity<br>
issue.<br>
</blockquote>
<br></div>
well, losing votes *should* count. but with a negative weighting, and they do with Margins.<br>
<br>
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.<div class="im">
<br>
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
4. simplicity has its attraction.<br>
</blockquote>
<br>
I find WV simpler because you don't need to do subtraction to determine<br>
the defeat strengths. You find which side is higher and then you're done<br>
with the losing side's figure. If you draw a triangle showing the wins,<br>
you only have to write one number per win to say what happened.<br>
</blockquote>
<br></div>
but it doesn't say enough of what happened.<br>
<br>
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.<div class="im">
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Margins is probably easier to define, but is that much more desirable<br>
than being easy to solve?<br>
</blockquote>
<br></div>
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).<br>
<br>
more *net* voters carry more weight than fewer *net* votes.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
5. Winning Votes communicates<br>
something regarding the number of voters participating, but<br>
says nothing about how close the election was. an<br>
election with a razor-thin result, even with a lot of people<br>
voting, does not measure well the will of the people.<br>
if it's 99,999 voters and 50,000 said Candidate A and 49,999<br>
said Candidate B, that does *not* say that Candidate A has<br>
such a great mandate to lead. Margins says his/her<br>
mandate to lead is 1 and Winning Votes says it's<br>
50,000. how can that make any sense?<br>
</blockquote>
<br>
Because WV is measuring "importance," per your item #2, not closeness.<br>
What "mandate" does a candidate have, who lost the most important race?<br>
</blockquote>
<br></div>
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).<div class="im">
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
(And beat some other guy who had no chance of winning.)<br>
</blockquote>
<br></div>
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.<br>
<br>
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.<br>
<br>
think Utilitarian.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
I would guess pretty much none, as far as voters would say.<br>
</blockquote>
<br></div>
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.<br>
<br>
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).<div class="im">
<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Methods getting confused by the presence of weak candidates (which is<br>
basically what we are talking about here) is not good.<br>
</blockquote>
<br></div>
no, i'm talking about weak *results* a.k.a. close elections.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
If a candidate can't win, he shouldn't be affecting the result.<br>
</blockquote>
<br></div>
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.<div class="im"><br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Anyway, a margins proposal is DOA, from the moment anybody would point<br>
out the 35 A>B 25 B 40 C scenario. Does anybody actually disagree with<br>
that? One's EM postings will have to be very, very clever to persuade<br>
the media, public, etc., that A should win that race.<br>
</blockquote>
<br>
<br></div>
and even more clever to persuade me. lessee...<br>
<br>
35 A>B<br>
25 B>A A>B by 10<br>
<br>
40 C>A<br>
35 A>C C>A by 5<br>
<br>
60 B>C<br>
40 C>B B>C by 20<br>
<br>
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.)<br>
<br>
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.<br>
<br>
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?<br>
<br>
bestest,<div class="im"><br>
<br>
--<br>
<br>
r b-j <a href="mailto:rbj@audioimagination.com" target="_blank">rbj@audioimagination.com</a><br>
<br>
"Imagination is more important than knowledge."<br>
<br>
<br>
<br>
<br>
----<br></div><div><div></div><div class="h5">
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</div></div></blockquote></div><br></div></div>