[EM] ATLO, defection, MD, method/criterion model

[Kevin Venzke]

Mike,

 --- MIKE OSSIPOFF <nkklrp at hotmail.com> a écrit : 
> You say:
> 
> That's an interesting approach. I wonder if it's monotonic?
> 
> I reply:
> 
> So, it's easy to say "Is that monotonic?", but it's more useful, though not 
> always as easy, to post a nonmonotonicity example.

Of course that isn't news to me. Perhaps you had an easy demonstration that
it is monotonic, and so by my question I had hoped to solicit it.

> You continue:
> 
> Also interesting, this is a case where a method can satisfy SDSC while
> failing votes-only Minimal Defense, according to which A mustn't be elected
> on the above ballots.
> 
> I reply:
> 
> Yes, and that says something about votes-only Minimal Defense, doesn't it.
> 
> Would it be better for B to win with those ballots, including the ATLO line? 
> If B could win with those ballots, there'd be the co-operation/defection 
> dilemma--you know, the one that I said that ATLO gets rid of. You doubed 
> that ATLO gets rid of it, I told how it does, and now you seem to want to 
> not get rid of it, because that's what it means if B can win with those 
> ballots.

No, it would not be better for B to win.

I have a doubt about ATLO. Assuming that the C voters use ATLO, then on
these (same) ballots:

49 A
24 B (withheld C preference)
27 C|B

A is elected. But in IRV, it's always the case that A is elected here, since
there is no ATLO. So it seems to me that in this scenario, IRV is more
effective than WV+ATLO in encouraging B voters to give C a preference.

Of course WV+ATLO is better in that the C voters don't have to consider
whether to order-reverse. But it seems to me that this should also make it
easier for the B voters to persuade the C voters to vote as the B voters
wish, compared to the same situation in IRV: B voters don't need to convince
C voters to abandon C; only to not use ATLO.

What do you think: Given the sincere preferences in this scenario, does
IRV misbehave when the B voters truncate?

> Apparently votes-only Minimal Defense is a good criterion to fail.
> 
> When, to meet a criterion, it's necessary to keep something undesirable, 
> like the co-operation/defection dilemma, that suggests that maybe your 
> criteria isn't as valuable as you think it is.

The approach I prefer towards the defection problem does not require failing
votes-only Minimal Defense.

> Would you mind telling me again in what situations you believe that your 
> votes-only Minimal Defense works better or gives a fairer or more acceptably 
> right answer than SDSC does? Do you say that votes-only Minimal Defense 
> doesn't apply to Plurality, or do you apply it to all methods and say that 
> Plurality passes?

I'm not convinced that it's a good idea to elect A on the above ballots. I'm
not convinced it would help the defection problem much; actually, I suspect it
could occasionally create a very bizarre result, due to but not intended by
the voters using ATLO.

My interpretation of election methods is that all of them have a ranked
ballot component (allowing full, partial, and equal ranking). When a criterion
says "if some voter votes in X manner," this refers to this component. (This
component isn't necessarily completed sincerely.) When the ballot format of
the method restricts the input of the ranked component, or has additional
components (such as an approval cutoff), it has to behave properly (according
to a given criterion) no matter how the unrestricted ranking may be changed
to be accepted as a valid ballot.

This is why I don't feel compelled to include Steve Eppley's requirement in
votes-only Minimal Defense that all preference orders must be accepted: That
is already inherent in my model.

> But, in general, of course strategy often requires some knd of information, 
> and the best use of that information. That isn't only true of wv with AERLO 
> & ATLO, or wv without those things. It's been shown that all 
> nonprobabilistic methods will sometimes give incentives for strategy. What's 
> your best method proposal? Does it ever require any "cleverness" or strategy 
> decisions? How does it do in that co-operation/defection dilemma? How minor 
> do you claim that it's worst strategy problem is?

Since you advocate PC, which fails clone independence and SDSC, I don't mind 
selecting MinMax(pairwise opposition), which also fails those: Elect the candidate
for whom the greatest number of votes against him in a contest is the lowest
such number among all candidates.

I think the worst strategy problem is either the clear incentive to equal-rank 
at the top, or the offensive order-reversal problem that WV methods also have.

In this scenario:
49 A
24 B(>C)
27 C(>B)

The result is a B-C tie, unless both B and C factions truncate, in which case A wins.
Break the tie by Random Ballot.

For a more sophisticated method, which satisfies clone independence and SDSC,
I suggest to declare a tie among all candidates who are not barred from winning
according to Markus' majority beatpath criterion. (I refer to this method as
"CDTT,RB.")

Kevin Venzke



	

	
		
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