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

[Kevin Venzke]

Hi Chris,

--- En date de : Lun 12.1.09, Chris Benham <cbenhamau at yahoo.com.au> a écrit :
> Kevin,
> 
> You wrote (11 Jan 2009):
> 
> "There are reasons for criteria to be
> "important" other than how easy they are to
> satisfy. 
> Otherwise why would we ever bother to satisfy the difficult
> criteria?"
> 
> Well, if  as I said "none of the criteria were
> incompatible with each other" then
> presumably none of the criteria would be
> "difficult".

That's not what I meant. I meant: Why do we *currently* ever bother
to satisfy difficult criteria? What do we mean when we say we value
a criterion? Surely not just that we feel it's cheap?

> >With mono-add-top and Participation, the
> quasi-intelligent device in
> >reviewing its decision to elect X gets
> (possibly relevant) information 
> >about other candidates besides X.
> 
> "How can it be relevant? X was winning and X is the
> preferred candidate
> on the new ballots."
> 
> You know that Condorcet is incompatible with mono-add-top
> (and so of course
> Participation), 

Condorcet isn't incompatible with mono-add-top. Only top tiers probably
are.

> so if we value compliance with the
> Condorcet criterion information
> about candidates ranked below X must sometimes be relevant.

I didn't realize that whether information is "relevant" depends on 
whether a valued criterion requires the information.

If you need to identify majorities, then the fact that a ballot shows
no preference between Y and Z, is relevant information.

> But even if  the 
> quasi-intelligent device is mistaken in treating them as
> relevant, then that is a much
> more understandable  and much less serious a blunder than
> the mono-add-plump
> failure.

Ok. I still don't really see why, or what makes the difference.

> >It's absurd that ballots that plump for X should in
> any way be considered 
> > relevant to the "strength" of the
> pairwise comparison between two other candidates.
> >This absurdity only arises from the
> algorithm specifically using (and relying on) 
> > a majority threshold.
>  
> "We have Mutual Majority and beatpath GMC displaying
> the same phenomenon."
>  
> No. I don't accept that 'being tossed out of the
> favoured (not excluded from winning)
> set' is exactly "the same phenomenon" as
> 'being joined by others in the favoured set'.
> The latter is obviously far less serious.

In an actual election method it would be exactly the same phenomenon.
Removed from that context it isn't clear how any of this is serious, let
alone "obviously" far more/less serious. The logical problem is the same,
that according to you, the new ballots only contain information on one 
candidate and should only affect that one candidate. I guess you imagine
the "win" as a pie that has to be split up, and it's better for the
candidate to get a "smaller" piece than none at all. Never mind, that
the logic causing this is still just as bad, or that real elections don't
award divisible pies.

Anyway, you already said there was no way to explain why it isn't
completely absurd for Mutual Majority to behave as it does. I don't
think that whether Mutual Majority's behavior is absurd should depend
on whether you remember that Mutual Majority has this behavior.

> >"I don't feel there's an advantage to
> tending
> >to elect candidates with more approval, because 
> >in turn this should just make voters approve fewer
> >candidates when they doubt how the method 
> >will use their vote."
> >
> >And why is that a negative?  I value LNHarm as an
> absolute
> >guarantee, but in inherently- vulnerable-to-Burial 
> Condocet 
> > methods, I think it is better if they have a
> "watch who you rank
> >because you could help elect them" Approval
> flavour.
> 
> "This is a negative because it suggests that your
> positional criterion
> will be self-defeating."
>  
> How can it possibly be "self-defeating"?  What
> is there to defeat?

I thought there was some intention behind your criterion. You talk about
the "clearly strongest candidate" so I assumed this idea is important to
you. If insisting on electing the "clearly strongest candidate" creates
incentives that *change* who this candidate is, then what have you 
accomplished?

> >From your earlier post:
> >"In the three-candidate case, at least, I think
> it's a problem to elect a 
> > candidate who isn't in the CDTT."
> >
> >Why?
> 
> "Because in the three-candidate case this is likely to
> be a failure of MD or SFC, 
> or close to it."
>  
> I'm happy to have MD, and I don't care about SFC or
> "close failures" of  MD.

Regarding SFC: It's a bit strange to elect Y when a majority of the
voters prefer X to Y, but there's no majority that prefers anybody to X.
There could be a good reason for it, but that doesn't mean it wouldn't
be better if we never had to do that.

I would say that I don't think the CDTT is that much more valuable, than
the combination of MD and SFC, especially if you use pairwise definitions
of these two.

> "In the three-candidate case it's also compatible
> with LNHarm. By adding a vote for 
> your second choice, you can't inadvertently remove your
> first preference from the CDTT."
>  
> Well since Condorcet is incompatible with LNHarm, that
> doesn't explain why Condorcet
> fans should like it.

I don't agree. There are various degrees to which Condorcet methods fail
LNHarm. It's quite clear that Schulze(wv) performs better here than C//A
for example. SFC shows this more clearly than CDTT though.

>  Also I think this is mainly just
> putting a positive spin on gross unfairness
> to truncators and the related silly random-fill incentive.
>
> 25: A>B
> 26: B>C
> 23: C>A
> 26: C
> 100 ballots (majority threshold = 51)
> 
> B>C 51-27,   C>A 75-25,   A>B 48-26.
>  
> In Schulze(Winning Votes), and I think also in any method
> that meets "beatpath GMC" and mono-raise, 
> the 26C truncators can virtually guarantee
> that C be elected by using
> the "random-fill" strategy. That is silly and
> unfair.

They have to vote for A, and the B voters have to give those C 
preferences, which they shouldn't (if they have the same quality of
information as the C voters). I'd rather say this shows that the LNHarm
effect and random-fill incentive are limited, even with three 
candidates.

If you simply give the win to C, without them having to fabricate 
anything, then you not only punish the non-truncating B voters, you
also punish the C voters when instead they actually do like B 
second-best, and vote accordingly.

To my mind the idea that a method is "unfair" to certain types of
voters isn't very useful, because it's not clear what exactly a voter
is entitled to (independent of guarantees made by criteria).

> Also, by artificially denying  the clearly strongest
> candidate  any method that doesn't
> elect C must be vulnerable to Pushover, certainly much more
> than those that do elect C.
> 
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html
>  
> (not that that is a very relevant strategy problem for the
> methods like WV that have the
> much easier and safer random-fill strategy for the
> C>>(B<=>C) voters.)

1. I'm not concerned about push-over. In this scenario, to attempt
a pushover strategy again requires C voters to expect that they are
getting significant support from B voters. Without that support, C
is the *weakest* candidate, and even a few insincere A>B votes are 
likely to elect A.

2. I am not sure why you suspect that under margins it can't happen 
that by adding to A's margin over B, you can cause this margin to become
larger than B's margin over C, when this change has no effect on the
latter margin. You lessen the margin of C over A, but there's no 
guarantee that it will become weaker than B>C.

3. Push-over works under Schwartz//Approval when B would be the CW, but
when the B>A win is reversed (but not the C>A win), C has the most
approval.

Kevin Venzke