[EM] Eric Maskin promotes the Black method

[robert bristow-johnson]

On Jun 21, 2011, at 7:56 AM, Markus Schulze wrote:

> Hallo,
>
> Eric Maskin, a Nobel laureate, is currently very
> active in promoting the Black method.

i have to confess, even though i had heard of ranked-choice voting  
before and had myself thought that what would later to be learned is  
called "Condorcet compliant" was the only logical and consistent (with  
a simple majority binary vote in all binary cases) manner to decide  
it.  and i thought of the possible problem that there was no single  
candidate who wins every pair they're in, didn't know what to call it,  
and didn't even know if there were any theorems that spoke to it, and  
decided not to worry about it.

anyway, because i'm a real neophyte to this, it wasn't until sometime  
last decade that i read anything about it until i read a Scientific  
American article of his titled "The fairest vote of all" that promoted  
Condorcet, but didn't really call it that.  Maskin labeled the method  
"true majority rule" and only obliquely raised the issue that a cycle  
could happen and mentioned Condorcet in that context.  soon after i  
learned the terms from the Wikipedia articles and at about the same  
time, we voted in IRV by about 65% (which was repealed in 2010 in a  
dramatic but really stupid slugfest between the one true faith "One  
person, one vote" crowd and those who denied anything went wrong in  
the 2009 election).

anyway, especially after reviewing his bio again, i can't help by  
admire the guy and it was an article of his that first got me thinking  
analytically about the voting systems issue.  but i wonder if he was  
using terminology that was more neology, even pre-neology.  i think he  
was trying to coin a term that would end up getting attached to his  
name.

and we've all been groping for a name for this primary voting criteria  
that is not this non-American, Frenchie, probably sorta pinko- 
socialist secular humanist "intellectual" (did i mention *not*  
American?) whose heresy is leading us away from the One True Faith of  
the Single Affirmative Vote.  we have sects in the One True Faith,  
some of us believe in the sanctity of the Two Party System: "if yer  
ain't fer us, you agin' us.  and pass da ammunition, Ma."

i don't have a better idea than "true majority rule".  but there must  
be a better one than that.  Warren, i remember you like "beats-all  
winner" for the CW.  i wonder if the "beats-all method" is a good label.


> The Black
> method says: If there is a Condorcet winner, then
> the Condorcet winner should win; if there is no
> Condorcet winner, then the Borda winner should win.
>

i hadn't heard of the Black method before, but just reading this shows  
pretty superficially a problem.  above is one way to say something...

> See e.g.:
>
> 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268
> 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww
>
> Maskin argues as follows:
>
>   If election method X is the best possible
>   election method in domain X and if election
>   method Y is the best possible election method
>   in domain Y and if domain X and domain Y are
>   disjoint and if domain X and domain Y together
>   cover all possible situations, then the best
>   possible election method is to use election
>   method X in domain X and election method Y in
>   domain Y.
>
> Maskin argues: "domain X" = "situations with a
> Condorcet winner"; "election method X" = "any
> Condorcet method"; "domain Y" = "situations
> without a Condorcet winner"; "election method Y"
> = "Borda method".
>

... and this is another way to say the same thing.  so, right away,  
Maskin is just restating an assertion as some sort of argument  
supportive of the assertion, but it is nothing new.  just a re- 
assertion.  (is that what is "begging the question" is?)

at the core, let's assume that we are already disciples of Condorcet,  
we all agree that method X is best for domain X, he doesn't say squat  
about why method Y is preferred in domain Y.  if we're nowhere near to  
a conclusion that Borda is good for anything (he might have been a  
good general, i dunno), then how do we conclude that it is preferable  
to everything else when there is no CW?  sorry, i haven't even got  
past this block.


> Maskin's argumentation doesn't work because
> of the following reason: Whether an election
> method is good or bad depends on which criteria
> it satisfies. Most criteria say how the result
> should change when the profile changes. Now it
> can happen that the original profile and the
> new profile are in different domains. This
> means that, to satisfy some criterion, election
> method X for domain X and election method Y for
> domain Y must not be chosen independent from
> each other.
>

but, this is the fundamental argument of those who claim that it is  
natural for an election to be spoiled, to be dependent upon irrelevant  
alternatives.  isn't that what the fundamental issue is about for why  
Condorcet (assuming a CW exists) is consistent with any simple- 
majority, two-candidate election where every vote carries equal  
weight?  that's what's fundamental about it, it is consistent to the  
concept that if Candidate A is preferred to Candidate B, Candidate B  
is not a winner, and being consistent with the result when the profile  
changes in that manner is both tangible and operational (we can get a  
handle on it and doing it differently, like using IRV instead, makes a  
difference).

> Example:
>
> The participation criterion says that adding
> some ballots, that rank candidate A above
> candidate B, must not change the winner from
> candidate A to candidate B.
>

does Black do this?

> Election method X satisfies the participation
> criterion in domain X. Reason: If candidate A
> was the winner in the original profile and if
> the original profile was in domain X, then this
> means that candidate A was the Condorcet winner
> and, therefore, that candidate A pairwise beat
> candidate B. If candidate B is the winner in
> the new profile and if the new profile is in
> domain X, then this means that candidate B
> is the Condorcet winner and, therefore, that
> candidate B pairwise beats candidate A. If
> candidate A pairwise beat candidate B in the
> original profile and if candidate B pairwise
> beats candidate A in the new profile, then
> this means that the added ballots rank
> candidate B above candidate A.

okay, since adding a positive number to the margin increases the size  
of the margin,  and since, if there is no cycle (domain X), the  
Condorcet winner is decided *solely* by the margins (even the signum  
function of the margins), that sufficiently satisfies the  
participation criterion, no?

> Election method Y satisfies the participation
> criterion in domain Y, because the Borda method
> satisfies the participation criterion in general.
>
> However, election method Z doesn't satisfy the
> participation criterion since the Condorcet
> criterion and the participation criterion are
> incompatible.

whoa.  the Condorcet criterion is not assumed for Z unless domain Y is  
empty.  and isn't participation and Condorcet with no cycle  
compatible?   of course it's not guaranteed to satisfy participation  
for all possible situations in domain Y.  that's not even the point is  
it?  Maskin isn't saying that the participation criterion makes Borda  
the *best* alternative method from the POV of disciples of Condorcet,  
is he?

> In short: Even if election method X satisfies
> criterion A in domain X and election method Y
> satisfies criterion A in domain Y, it doesn't
> mean that election method Z satisfies
> criterion A. Therefore, Maskin's argumentation
> doesn't work.

but is Masking saying that?  i'm groping for a definition of what he  
means by "best possible election method".  i can't tell that he means  
"participation criterion" when he says that in his construction that  
you apparently quoted.


>
> ***********************************
>
> I also question the claim that the Borda
> method is the best possible election method
> in situations without a Condorcet winner.

Bingo!

to mix metaphors, that's where the argument never really gets off the  
ground at square 1.  and restating it over and over does not provide  
evidence nor proof.

not that i can't accept some principles as axiomatic.  like  
fundamentally the "one person, one vote" value for all persons of  
franchise.  all i can say is "why shouldn't that be the case?" for  
that one.

interesting, Markus, to bring Maskin back to our attention.

thank you.

--

r b-j                  rbj at audioimagination.com

"Imagination is more important than knowledge."