[EM] Miscellaneous MMPO & MDDA comments.

[Kevin Venzke]

Mike,

--- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit :
> Premise requirements, from the voter's point of view:
> 
> SFC applies to you if you're in a majority of voters who prefer the CW to 
> someone, Y, whom you want to keep from winning, and if no one falsifies a 
> preference (or at least if the number doing so isn't great enough to change 
> the election outcome).

Something that strikes me as odd about SFC is that it guarantees that a
certain majority can do something which, if they knew that they were part of
this majority, they wouldn't need to do anyway.

It almost seems to me that SFC is a criterion designed to reduce possible
complaints about the result.

> The votes-only FBC seems to be the top-end counterpart to LNHarm and LNHelp. 
> Probably the only attainable top end counterpart to those criteria. But if 
> they have other attainable top-end counterparts, that would be an 
> interesting and important thing to find out.

Yes, I can think of one, but it's not very interesting. FBC is more similar to
LNHarm than LNHelp. FBC requires that increasing v[a,b] can't help {a,b} (that 
is, it can only help A at B's expense), and LNHarm requires that increasing v[a,b]
can only hurt B.

LNHelp says that increasing v[a,b] can only help A. The "top-end" counterpart
would say that increasing v[a,b] can't hurt {a,b} (can only hurt B by helping
A). In other words, it must *never* be optimal strategy (i.e., be best for {a,b})
to vote A=B. The problem with this is that most likely the optimal strategy will 
be to vote the more viable candidate over the less viable one.

If you insist on this latter property and FBC at the same time, then the
probability that the winner comes from {a,b} must be totally independent of
whether you vote A=B, A>B, or B>A.

The latter property is satisfied by "MinGS" ("elect the candidate whose fewest
votes for him in some contest is the greatest") and Woodall's DSC method (which
is not a pairwise count method).

> CR, MMPO, and MDDA are all equivalent to Approval in an 
> acceptable/unacceptable situation when the voter votes optimally (with power 
> truncation available in MMPO & MDDA). Is that a general fact, that all 
> FBC-complying methods are equivalent to Approval under those conditions, or 
> are there exceptions?

I'm a bit confused when you say that MMPO is "equivalent to Approval in an
acceptable/unacceptable situation." If you use MMPO on approval ballots, you
don't get the same results as under Approval. In fact, the approval loser can
win.

> Though I'd like to keep SFC, and the freedom to vote all preferences, the 
> 3-slot limitation would be acceptable if it can bring compliance with a more 
> important criterion.

I think voters will be less intimidated by a three-slot ballot. Also, it makes
the approval component more obvious.

> Kevin spoke of replacing disqualification with something more sophisticated. 
> I hope that wouldn't mean more complicated, because that would spoil it as a 
> public proposal. The beauty of Approval, CR, MMPO and MDDA is their 
> simplicity, in addition to their FBC compliance.

I'm currently out of ideas on this subject. I don't know what we might replace
SFC with.

>       In MMPO, the voter should always rank all the unacceptable 
>candidates in reverse
>       order of winnability, to maximize the votes-against of the most 
>winnable ones.

>       In MDDA, the voter should sometimes do that, but sometimes should 
>truncate
>       the unacceptables. For instance, if it's certain that the 
>acceptables can't beat the
>       unacceptables at Approval, then the only hope is to disqualify the 
>unacceptables,
>       and that goal is best helped by ranking them, in reverse order of 
>winnability.

However, in MDDA, this could have the effect of causing a "least winnable"
unacceptable candidate to win instead of an acceptable candidate. In MMPO,
that couldn't happen.

It seems to me that MDDA is less friendly to order-reversal strategies than
MMPO is. That seems like an advantage to me.

>       Also, when it isn't an acceptable/unacceptable situation, it could 
>matter that MMPO
>       meets LNH, while MDDA meets SDSC. And that matters even whether 
>power
>       truncation is available or not. So the choice between LNH and SDSC 
>would then be
>       a factor in the choice between MMPO & MDDA.

I would take SDSC over LNHarm. But additionally, I note that MDDA doesn't
fail the Plurality criterion (at least, with 3 candidates, but I haven't had
success generating a failure with more candidates), and *is* equivalent to
Approval when all voters use just the top and bottom of the ballot.

I wonder if you saw this scenario, under MMPO:

n A
1 A=C
1 B=C
n B

When n>2 then C wins decisively, no matter how large n gets.

Kevin Venzke



	

	
		
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