[EM] round robin tournaments

[robert bristow-johnson]

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 <rbj at audioimagination.com 
> > 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                  rbj at audioimagination.com

"Imagination is more important than knowledge."