[EM] Strategy-free criterion

[Kevin Venzke]

Hi Chris,

> Kevin,
> 
> > I don't like the CD criterion because of the three incentives it creates, only
> > one of them is positive.
> What are they?

The disunited majority has three options to avoid the criterion's wrath:
1. The "defecting" faction can add another preference, if they have it or are
willing to lie that they have it.
2. The "defected-against" faction can compromise and try to give the other
candidate a majority of first preferences.
3. One of the candidates can simply drop out of the race, as it will be apparent
that the method poses such risks.

On an additional note, it's strange to me that CD crit allows one faction to defect
but not the other. If both factions optimistically think they are the larger one,
they will all assume CD applies to the other voters and not themselves. It seems to
me that a "real" CD criterion would take no nonsense from anyone.

> > I'm not sure I follow, that a winner barred by Plurality has more credibility than
> > a winner who won under the rules but is challenged by a second candidate who
> > regrets how his supporters filled out their ballots.
> 
> I didn't mean to make it a big competition, because I don't accept
> failure of either.  "Plumpers" for X didn't exactly "fill out" their
> ballots, they had no interest in any other candidate, so they showed up
> and plumped for X.
> 
> It would be readily apparent from the post-election ballot profile that
> if some or all of them had stayed home then X would have won.  It's the
> simplest and most egregious version of Participation failure. There is
> no excuse for any algorithm to be confused by such pure and simple
> information.

Yes but almost all proposals fail Participation, so we will be in a lot of trouble
if we insist on this kind of thinking. I understand that you see a difference in
severity, but for myself I don't see where to draw the line.

> Sometimes methods that fail Plurality meet Later-no-Harm and may have a
> (at least zero-info) random-fill incentive.  So then failures of
> Plurality would be very rare, and the occasional complaint would usually
> be answerable by the retort:
> 
> "Well suckers, you didn't make your (full) contribution to GIGO!" :)
> 
> I am intolerant of methods that fail Irrelevant Ballot Independence 
> (although I recognise that putting up with its failure might be able to
> buy something) so I'm suspicious of methods that have arbitrary
> thresholds (relating to some fraction of the "total votes") as an
> essential part of their definitions.

Well, in an environment where the concept of "median voter" is likely to be
meaningful, pairwise majorities are basically the only suggestion you can get about
what side the median voter is on. I don't think the premise of IIB is necessarily
sound, because introducing IBs can remove information we previously thought we had
about the median voter.

> > I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a
> > rule at the start:
> > 1. Disqualify all candidates with sub-majority approval if possible.
> > 2. Disqualify all candidates with a majority pairwise defeat if possible.
> > 3. Elect the most approved remaining candidate.
> 
> Given that you are using implicit approval (ranking), I struggle to see
> how rule 1 can make any difference. Can the most approved candidate
> without a "majority pairwise defeat" really have sub-majority approval
> while some other candidate doesn't?

Yes, actually Woodall showed it in 2005:

20 a>b
5 b>a
24 b>c
24 c>a
9 d>a>b
9 d>b>c
9 d>c>a

D wins in original MDDA. The new version is an A-B tie.

> >  As a Condorcet method, MinMax(margins) doesn't satisfy LNHarm.
> 
> Yes, my mistake.  I forget what name Woodall used for MMM.   I think he
> said it meets Condorcet, Mono-add-Top and "Symmetric Completion" (which
> happily means in the zero-info case there is neither truncation or
> random-fill incentive).
> 
> I know that MMM is equivalent to "elect the X who needs the fewest extra
> X-plumping ballots to become the CW."   Obviously that meets
> Mono-add-Top, which strikes me as almost implying LNHarm.

That's an interesting comparison, but note that DAC satisfies Participation
(implying Mono-add-top), and DAC is definitely not good according to Later-no-harm.

> > I wouldn't want to say a method is "good" just because no one can call it absurd.
> 
> I think it is a promising start, especially if we are aware of (and
> honest about) which criteria are  compatible with others.
> 
> I think a "votes only" definition of SFC is
> 
> * If  X has a majority strength pairwise win over Y, and it is possible
> to complete the truncated ballots in a way that makes X the CW, then Y
> can't win.*
> 
> Do you agree?

That sounds about right.

> A version that goes without the "majority" bit:
> 
> *If X pairwise beats Y, and it is possible to complete the truncated
> ballots in a way that makes X (but not Y) the CW, then Y can't win.*
> 
> I prefer the second.

They're both hard to test because they are asking us to search for ways of actually
completing the presented ballots. And it's not totally clear why it's helpful for
there to be a sort of loophole here.

This is probably clear to you, but if it's possible to complete the ballots so that
X is the CW, but it's not possible to do the same for Y, then the normal intuition
is that Y probably does have a majority loss to somebody. But it might not be to X.

An interesting idea. I'm not really sure how to look into it, or find scenarios
where we can see a contrast.

Kevin
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