[EM] "Beatpath GMC" compliance a mistaken standard?

[Chris Benham]

Kevin,

You wrote (9 Jan 2009):

"Well, with "Mutual Majority," when X may win, it's possible that by
adding bullet votes for X, then every other candidate becomes able to
win."

No it isn't. (Can you give an example?) 

"Is there any way to explain, why it isn't completely absurd, that adding
bullet votes for X should cause other candidates to become eligible to 
win?"

No.

"Why is mono-add-plump important?"

Because as an election method algorithm that fails it simply can't have any
credibility as a quasi-intelligent device (which is what it is supposed to be)
and because satisfying it should be (and is) very cheap.

"Since you value Majority as a criterion, it seems to me that you
can't attack the CDTT by attacking the underlying concept."

Yes I can, because the Majority concept is only vulnerable to Irrelevant
Ballots which is much less serious than Mono-add-Plump. 

A candidate X can fall out of the set of candidates "not excluded" (that
Marcus seems to think means something significantly different from "allowed 
to win") by Majority by the removal of some irrelevant ballots (that simply 
ignore all the candidates in that set); whereas X can fall out of the CDTT by 
adding some ballots that purely bullet-vote for X.

Also I specified that by itself  this fact only makes Beatpath GMC (Marcus's
criterion that says that the winner must come from the CDTT set) appear
uniquely weird and suspect, not that it was conclusively damning.

"If we view CDTT somehow as an election method, then when it fails
mono-add-plump, the bullet votes for X are not simply "strengthening"
X, they are also *weakening* some pairwise victory of Y over Z, which X
had relied upon in order to have a majority beatpath to Z."

That just testifies to the absurdity of an algorithm specifically putting some
special significance on "majority beatpaths" versus other beatpaths.

"Of course, you can always use the mechanics of the method to explain why
something has happened. But it seems to me that the bullet voters aren't
purely "strengthening" X, they are also weakening Y and thereby also X".

This contention that "bullet voters for X aren't purely strengthening X" but are
in some way "also weakening X" is completely absurd.

"This is an oddity inherent to beatpaths, really"

I think only to beatpaths that measure "defeat strengths" in a silly way.

>But I contend that here in my "situation 2"
>election Beatpath GMC does exclude
>the clearly strongest candidate C. 
 
"You're attacking a lot more than just beatpath GMC with this scenario.
Excluding C is required by SFC (the 51 B voters are basically assured
LNHarm when voting for C, since B might be the sincere CW) and also
basically any WV method."

Yes, you catch on quick.

>In other words the CDTT set can fail to include the
>candidate that on overwhelming 
>common-sense (mostly positional) grounds is the strongest
>candidate (e.g. C in "Situation # 2").

"Having read that archive post the motivation behind the criteria 
(especially the Smith-compatible one) is unclear to me.
...The only reason you gave for adding a beatpath requirement is that 
you're "still interested" in Condorcet methods."

Sorry, do I need a better reason? One of my standards is that a single-winner
voting method should meet one of  Later-no-Harm, FBC and  Condorcet.
I value compliance with (voted) Condorcet and (voted) Smith-Schwartz.

> ...I consider the addition of compliance with "beatpath GMC" a negative if 
>without it the method can meet "Smith- Comprehensive 3-slot Ratings Winner" 
> (which should be very very easy).

"It should be very easy? What methods are there other than Schwartz//Approval?"

That will do to be going along with.

Chris Benham



Hi Chris,

If we view CDTT somehow as an election method, then when it fails
mono-add-plump, the bullet votes for X are not simply "strengthening"
X, they are also *weakening* some pairwise victory of Y over Z, which X
had relied upon in order to have a majority beatpath to Z.

Of course, you can always use the mechanics of the method to explain why
something has happened. But it seems to me that the bullet voters aren't
purely "strengthening" X, they are also weakening Y and thereby also X.
This is an oddity inherent to beatpaths, really.

As far as I can tell you are calling this failure "absurd" for no reason
except mono-add-plump. Why is mono-add-plump important? If it were more
difficult to satisfy, like Participation, I doubt it would ever come up.
This failure doesn't create a huge strategy problem: If you guess that you
might be better off staying home than bullet voting, then probably you can
also guess which beatpaths your vote needs to reinforce in order to 
protect the candidate you want.

--- En date de : Ven 9.1.09, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
>No,  I only wrote that the beatpath GMC *concept* is
>"vulnerable to 
>Mono-add-Plump."

I find it difficult to nail down what this means. It seems clear from
Markus' mails that he isn't going to discuss a criterion as though it
were a method. Woodall also had to define criteria differently in order
to apply them to sets. But to apply criteria to a concept?

>I think that all methods that fail Independence from
>Irrelevant Ballots are silly and
>that methods should meet the Majority criterion.  The
>Majority *concept* is 
>"vulnerable to Irrelevant Ballots" because
>candidate A can be the only candidate
>allowed to win by the Majority criterion and then we add a
>handful of ballots that
>all plump for nobody and candidate A no longer has a
>majority.

This is problematic. The same concept underlies both Majority and the
CDTT. Since you value Majority as a criterion, it seems to me that you
can't attack the CDTT by attacking the underlying concept.

>The point of my  Dec.29 demonstration was to refute any
>notion or assumption
>that all candidates in the CDTT (i.e. those not excluded by
>Beatpath GMC) must
>be "stronger" (i.e. more representative of the
>voters and so more deserving of victory)
>than any of the candidates outside the CDTT. 

Well, you would have to define "representative." In the three-candidate
case, at least, I think it's a problem to elect a candidate who isn't
in the CDTT.

>This was only the first part of my argument that  Beatpath
>GMC [compliance] is a
>"mistaken standard". What other
>criterion/standard says that the winner must come
>from set S, with S being a set that a candidate X can be
>kicked out of by an influx
>of new ballots that all plump (bullet-vote) for X?

Well, with "Mutual Majority," when X may win, it's possible that by
adding bullet votes for X, then every other candidate becomes able to
win.

You're talking specifically about mono-add-plump, but in a real single-
winner election method this would be exactly the same phenomenon:
Additional bullet votes for X cause X to lose to someone else.

Is there any way to explain, why it isn't completely absurd, that adding
bullet votes for X should cause other candidates to become eligible to 
win?

> By itself that isn't conclusively
>damning because it doesn't prove
>that Beatpath GMC can exclude the strongest candidate. 
>
>25: A>B
>26: B>C
>23: C>A
>26: C
>
>But I contend that here in my "situation 2"
>election Beatpath GMC does exclude
>the clearly strongest candidate C.  You ignored the last
>few paragraphs of my last post:

You're attacking a lot more than just beatpath GMC with this scenario.
Excluding C is required by SFC (the 51 B voters are basically assured
LNHarm when voting for C, since B might be the sincere CW) and also
basically any WV method.

If you want to use approval-based or positional arguments, I guess you
won't find much to support in the Condorcet world.

>.. I don't accept your suggestion that compliance with
>beatpath GMC is acceptably cheap 
>(let alone free), because it isn't compatible with
>my recently suggested "Smith- Comprehensive 
>3-slot Ratings Winner" criterion, which I value much
>more.
>
>http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html
>
>In other words the CDTT set can fail to include the
>candidate that on overwhelming 
>common-sense (mostly positional) grounds is the strongest
>candidate (e.g. C in "Situation # 2").

Having read that archive post the motivation behind the criteria 
(especially the Smith-compatible one) is unclear to me. For an example,
why couldn't you propose instead "CDTT-C3RW"? The only reason you gave 
for adding a beatpath requirement is that you're "still interested" in
Condorcet methods.

>So given a method that meets what I've been recently
>calling "Strong Minimal Defense"  
>(and so Minimal Defense and Plurality) and Schwartz (and so
>fails LNHarm and meets Majority 
>for Solid Coalitions), I consider the addition of
>compliance with "beatpath GMC" a negative if 
>without it the method can meet "Smith- Comprehensive
>3-slot Ratings Winner" (which
>should be very very easy).

It should be very easy? What methods are there other than Schwartz//Approval?

Kevin Venzke


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