[EM] round robin tournaments RBJ

[Kevin Venzke]

Hi Robert,

Thanks for your response.

--- En date de : Lun 27.6.11, robert bristow-johnson <rbj at audioimagination.com> a écrit :
> > --- 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.

I suppose that is true, but it doesn't seem very reliable. I did a 
little test (math) of every situation where you know the total number 
of voters is 100 and you know either the WV strength or the margin. The
actual vote counts were in increments of 10 (i.e. 100-90, 50-30, 20-0,
etc.). Knowing the strength gives you a possible range of total 
participation in that contest. I checked how far off you are on average
if you guess participation is right in the middle of the possible range.
The result I got was that with margins your guesses averaged almost 20%
off (that is, 20% of the full count of voters), more than double WV's
inaccuracy. The maximum inaccuracy was also double (50% vs 25%). Also,
WV was closer in 61% of the scenarios vs. margins beating WV in 11%. 
(The rest were tied.) When margins was better, it was by 5%.

You may say that on balance it doesn't matter, but I just want to note
that on this point WV definitely seems more accurate.

> > 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.

I come to this conclusion because when the "most important" contest is
between A and B, candidate C most likely should be regarded as noise,
and probably isn't close to winning even if he manages to change the
result.

It could be that the participation of all the contests is actually very
close. I tend to doubt it. Assuming that's not true, we know by 
definition that fewer voters are voting in C's contests. That makes it
hard to win.

> 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.

Are there any other methods that have "salience attached to how close or
decisive an election is"? It seems important to you but where does it
come from? Most methods don't even have a pairwise matrix, so do they
just all flunk your test, and you "just cannot get past" any method
besides margins? If not, I am curious where you find that other methods
have this kind of "salience."

A nice thing about looking at support/importance/participation is that
a majority with a common preference can usually get what they want 
without having to sacrifice any sincerity. (That's a goal of mine.) If
it takes "pure votes" to win, a majority opinion is not easy to out-
maneuver (either deliberately or through chance).

> >>    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).

I think I tried to explain this above but I'll do it again here. If the
most "important" contest is A-B, then C, I deduce, is less important. C
probably has no chance of winning. So if "B" in your scenario "loses
decisively" to C it is mainly just on paper. The candidate he "loses"
to can't win the election.

So there is no complaint from the C voters when the C>B contest is 
dropped. Quite the contrary, they probably *want* that contest to be
dropped.

> > (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 you are defining "decisively" in margins terms then this beating has
nothing to do with C's general viability as a candidate. C can beat B
"decisively enough" while getting creamed (decisively... actually
decisively) by A.

If you want to complain "but B lost to C" don't you have to argue for a
C win? Doesn't it seem a little self-serving (and problematic) if it's 
the *A* voters who are making this complaint?

> > 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.

It's close (important) contests being reversed due to the presence of
weak candidates. Contests with less "participation" (even if "decisive")
usually involve candidates with less ability to actually be elected.
So when you respect a decisive but less important contest, you don't know
who is actually happy about it.

> > 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.

I would disagree that being in the Smith set means a candidate "can win."
To beat a Smith candidate pairwise you only need barely half his total
support. With that amount of support, basically no decent method is going 
to elect you. Yet there you are, in the Smith set.

> > 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? 

B wins in WV (B's loss of 35 is weakest). A wins in Margins (A's loss of
5 is weakest).

Why shouldn't B win? I think it will be seen as a joke if A wins. The
perceptible difference between A and C is that A got fewer votes and his
supporters ranked a second candidate. It is hard to understand how this
can make A a better outcome than C.

Maybe you can make the argument... But you probably have to deliver it
to people lacking a lot of time and patience.

And I don't like a C win because there is a majority for B over C. If 
C wins, then A and the A voters are being punished for their sincerity,
when this scenario has no need to make anybody regret.

> (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?

When you use margins, Schulze, Tideman, River, or Minmax all pick A.
If you use WV with these, you get B.

Kevin Venzke