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

[Chris Benham]

Kevin,

You wrote (12 Jan 2009):

"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?"

When simultaneously a criterion's satisfaction's cost falls below a certain 
level and  its failure reaches a certain level of  absurdity/silliness  I start to
lose sight of  the distinction between "important for its own sake" and "very
silly not to have because it's so cheap". Mono-add-plump (like mono-append)
is way inside that territory.  

"Condorcet isn't incompatible with mono-add-top."

Oops, sorry I forgot that, but it is incompatible with Participation. MinMax(Margins)
meets mono-add-top.

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

In my view a voting method *doesn't* need to specifically "identify majorities", so it
isn't. (The voting method can and should meet majority-related criteria 'naturally'
and obliquely.)

>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."

Imagine the quasi-intelligent device is the captain of  a "democracy bus" that takes
on passengers and then decides on its course/destination after polling the passengers.

Imagine that as in "situation 1" it provisionally decides to go to C, and then as in 
"situation 2" a group of new passengers get on (swelling the total by about 28%) and 
they are openly polled and they all say "we want to go to C, and have nothing else to say"
and then the captain announces "in that case I'll take the bus to B".

Would you have confidence that that captain made rational decisions on the most
"democratic" (best representing the passengers' expressed wishes) decisions?
I and I think many others would not, and would conclude that  the final "B" decision
can only be right if the original "C" decision was completely ridiculous. Or would you
be impressed by the captain's wisdom in being properly swayed by the new passengers'
indecision between A and B?

"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 mistakenly thought the question was redundant and answered too hastily. I withdraw
my statement and instead just say that for the time being I can't think of one.

"Never mind ....that real elections don't award divisible pies."

Can I take it then that you no longer like  "CDTT,Random Ballot", which does award
a probability "pie"?

>"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."

Yes, by "strongest" I mean  "voted strongest on presumably sincere ballots".

"If insisting on electing the "clearly strongest candidate" creates incentives that *change* 
who this candidate is, then what have you accomplished?"

The criterion/standard is an end in itself.  Not everything is about the strategy game.
Higer SU with sincere voting and sparing the method common-sense  (at least) difficult 
-to-counter complaints from the positional-minded are worthwhile accomplisments.

"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."

Doesn't SFC also bar C from winning in my "situation 2" election?

>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."

I think that like FBC, LNHarm's value is greatly reduced if it isn't an absolute
guarantee. To me more valuable than either LNH by itself is that they both be
in balance. If they can't be in balance I prefer the LNHarm problem to be 
worse than the LNHelp problem.  In other words I dislike random-fill incentive
much more than truncation 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,.."

With no change to the other ballots, only 4 of the 26C ballots have to change 
to C>A for Schulze(wv) to elect C (even if  the other 22C change to C>B).

"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)."

The only "quality of information" these C voters need is that the method has
a 0-info random-fill incentive.

Chris Benham 


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