[EM] Sincere methods

[Kevin Venzke]

Juho,

 --- Juho Laatu <juho4880 at yahoo.co.uk> a écrit : 
> > Why do you feel that WV methods aren't sensible when voters are 
> > sincere?
> 
> I don't think sincere votes would be problematic to WV methods. If I 
> have understood the history of WV methods correctly, they have been 
> introduced primarily in order to fight against certain strategic 
> threats.

I doubt this can be true without margins being very much more intuitive 
than WV.

Anyway, consider the nature of the "strategic threats" of margins. They
have to do with majority decisions (as in, more than half of the voters'
decisions) being discarded. So if WV is a kind of "revision" to margins,
it seems to me to be one which aims to preserve majority rule.

Maybe you have in an earlier post argued that majority rule (in this sense)
is not as necessary in a "sincere method." But I doubt I can be convinced
of that.

What do you think of approval voting as a sincere method? WV is more likely
to give an approval-ish result than margins is. I'm pretty sure simulations
could prove this easily.

 They were thus not introduced as sincere methods (sincere 
> method = method that provides the intended results with (e.g. ranking 
> style) sincere votes (i.e. without any strategy considerations)). 
> Methods that have been modified in order to defend against strategies 
> are thus usually not a sincere methods.
> 
> But although I see WV methods to be developed in order to defend 
> against strategies, I think they are close to being sincere (if someone 
> wants to claim so). Counting the number of voters that have 
> successfully voted for certain candidate over another is a quite 
> natural measure. Some features like the fact that 51-49 is seen as a 
> strong victory (51 winning votes) although the 49-51 defeat is so close 
> (only two voters need to change their mind), and the fact that 51-0 and 
> 51-49 are seen as wins of same strength don't look very natural to me. 
> Here margins can be claimed to be more natural.

Does it matter which measure is "more natural"? Does that affect whether a
method can be a "sincere" one?

> The claim that WV methods would maybe not be sincere methods thus means 
> that to my knowledge nobody as so far claimed them to be _THE_ method 
> that provides the ideal result in a strategy free environment.

To my knowledge, nobody makes such a strange claim about any method except
"average rating." But I suppose you define "ideal result" so that Condorcet
is satisfied.

Do you have a favorite example in which, when all abstention in pairwise
contests is informed and deliberate, margins produces a "more ideal" result
than WV?

> > Personally I don't see why it is intuitive to measure defeat strength 
> > as
> > the absolute difference between vote totals.
> 
> You mean margins. I don't want to say they are the only measure but at 
> least there are natural explanations to the margins. In some earlier 
> mails I wanted to point out that margins can be seen both as accurately 
> representing the ability to defend against changing candidate X to some 
> other candidate Y, and as the number of votes that would be needed to 
> make candidate X a Condorcet winner. There are thus at least some 
> naturalness in margins. I think those criteria can be said to describe 
> one sincere voting method. I proposed the name "Least Additional Votes" 
> for minmax (margins) to point out that the technically oriented name 
> could be replaced with something that shows that margins are natural 
> and not just one random technical algorithm.

Is the "ability to defend against changing candidate X to some other
candidate Y" really a consideration in a strategy-free setting?

> > Why do you say "sincere" criteria? Are you excluding some criteria?
> 
> Yes, most notably term "sincere criteria" excludes all criteria whose 
> target is to fight against strategies. Sincere criteria aim at electing 
> the best candidate and nothing more.

I'm not sure this is well-defined. I can imagine interpreting Condorcet,
or the Majority criterion for solid coalitions, as anti-strategy criteria.

> > This is why my favorite MinMax method is (Pairwise Opposition): The X
> > vote can create an obstacle for Y, but doesn't remove any of X's 
> > obstacles.
> > When there are only 3 candidates, I feel this method is "perfect" 
> > except
> > for its rate of indecision.
> 
> You included strategical concerns in your justifying text. In the terms 
> I used this must man that Pairwise Opposition is your favourite 
> _practical_method_. I didn't hear you saying that you would consider it 
> also to be a _sincere_method_. Maybe your favourite sincere method 
> would not be Pairwise Opposition but some other (not very different) 
> method.

Sure. If Later-no-harm is not a problem, we don't need to use MinMax(opp).

> > SVM: Schulze (wv), PVM: MinMax (pairwise opposition) and CDTT methods
> 
> Schulze (wv) is to me a good PVM but I haven't considered it to be a 
> SVM (since I believe many of its features are related to fighting 
> against strategies, not to electing the ideal winner (with sincere 
> votes)).

I still haven't understood what you mean by "ideal winner."

I consider Schulze(wv) to be a good SVM. If you show me these ballots:

49 A
24 B
27 C>B

I say the most intuitive winner is B. It's true that I have some strategy
concerns in mind. But I don't see what other reasoning is available to me:
I want to minimize voter regret, and get candidates an accurate number of
votes. If neither voters nor candidates care about their incentives, I could
just elect someone by Random Candidate. I don't know what "ideal" means.

For a practical method, I suggest that C be elected with 53% probability, and
that B be elected with 47% probability. That's also due to strategic concerns.

> Condorcet is a half-hearted Smith as you say. But one could also say 
> that Smith is a too full-hearted Condorcet. My theory on why Smith 
> looks better than it actually is, is that it tries to make the votes 
> linear too strongly. If the "god" that elects the best winner would be 
> one individual, then we could expect him to give a linear order to the 
> candidates. And in this case it looks natural that candidates outside 
> the Smith set must be lower than candidates in the Smith set. And it 
> looks natural that after this decision all that there is left is to 
> break the loops in the Smith set and make also their order linear. But 
> as we know, group opinions may contain natural cycles and one can not 
> say that they are wrong and should be corrected. For this reason I find 
> methods that try to e.g. evaluate each candidate separately more 
> natural than ones that try to force the group preferences into some 
> linearly ordered preferences.

Unfortunately these MinMax methods aren't clone-independent. Surely the
"ideal method for sincere voters" would be clone-independent?

> (Note that reason why I fear that sometimes strategy defence examples 
> could be misused is that one can claim that some method gives correct 
> result despite of certain strategic votes, but in this case the same 
> votes could be as well a result of sincere opinions, in which case they 
> should of course not be corrected.)

If they're the result of sincere opinions, then there's no problem in
"correcting" them. Suppose B voters intend to steal the election from A by 
voting C (a weak candidate) above A. Suppose the A voters defend against this 
by not giving B a ranking over C.

Then suppose that C wins instead of B due to this "strategy defense" mechanism.
If the B>C>A votes were insincere, then we're happy because B's burial
strategy backfired. If the B>C>A votes were sincere, then they're happy
because they got their compromise choice.

> In addition one typically wants to give the voter possibility to 
> express her opinion as completely as possible.

Yes, that's why I argue that LNHarm is important despite being incompatible
with Condorcet and Smith.

Kevin Venzke



	

	
		
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