[EM] round robin tournaments

[Kevin Venzke]

Hi Robert,

--- 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.

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.

This is one of my main criticisms of margins, that it doesn't try to
gauge the importance.

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.

>    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.

Margins is probably easier to define, but is that much more desirable 
than being easy to solve?

>    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?
(And beat some other guy who had no chance of winning.) I would guess
pretty much none, as far as voters would say.

Methods getting confused by the presence of weak candidates (which is 
basically what we are talking about here) is not good. If a candidate
can't win, he shouldn't be affecting the result.

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.

Kevin Venzke