[EM] Sincere methods

[Juho Laatu]

Hello Kevin,

On Apr 2, 2005, at 21:23, Kevin Venzke wrote:

> 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. 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.

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.

> 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.

> 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.

> 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.

> 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 don't understand why, when you want to assume that voters are 
> sincere,
> you still seem to insist on Condorcet, but not on Smith. I don't see 
> the
> difference. To me, Condorcet is a half-hearted Smith.

I'm not convinced of Smith being an absolute requirement because I 
think that if the looped wins/losses within the Smith set are stronger 
than the wins/losses towards the best candidate outside the Smith set, 
I can easily sympathize with electing the best candidate outside the 
Smith set. Smith set is thus a good criterion in 99.9% or the cases but 
in some extreme cases its value can be questioned. This is linked to my 
interest to present minmax (margins) as one reasonable sincere method. 
Minmax (margins) respects Condorcet but not always Smith.

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.

> I think the scale of the election is not nearly as important as how
> straight-forward and risk-free an attempted strategy is.

I think the scale and publicity of elections has an impact on how 
straight-forward and risk-free some strategy is. Large scale makes it 
more difficult to estimate the votes. in small elections of say 5 
voters it may be possible to know or guess correctly the opinion of 
each voter's opinion (or opinion of each party who can then give 
guidance to its members on how to vote together in a synchronized 
manner). Publicity means that everyone is voting, and it is hard to 
e.g. give commands to them on how they should vote (at least more 
difficult than to party members). Publicity is also a risk to 
strategies in the sense that people might hate parties that propose 
strategies or voters that want to work against our strategy would 
notice it and could apply the same strategy or some counter strategy. 
Some strategies may also be too complex for normal voters.

>> If someone is interested, I would be happy to see examples e.g. on how
>> the "SVM: MinMax (margins), PVM: MinMax (margins)" case (this one
>> should be an easy target) can be fooled in large public elections 
>> (with
>> no more exact information than some opinion polls on how voters are
>> going to vote).
>
> Hmm, I thought James already did this with the "game of chicken" 
> scenario.

I'll respond to him in a separate mail.

>> P.S. One more comment. I have criticized also the interest to force 
>> the
>> group opinions into linear opinions
...
> I don't really understand this. When a method picks a unique winner, 
> the
> group opinions have already been made linear to some extent.
>
> And MinMax uses numeric scores. That's very linear.

It is based on linear arithmetic and the end result gives a numeric 
value to all candidates, which means that candidates can be ordered 
based on this value. But there is no tendency to maintain the 
"direction of preferences". Maybe I can best exemplify this by noting 
that minmax can elect the Condorcet loser, which is quite counter 
intuitive if one thinks that the results of a voting method should look 
like the linear preferences of some individual voter. (I also explained 
earlier in this mail why Smith set and linearization are related 
concepts.)

> It seems to me that it doesn't matter whether the election method can
> determine which votes are sincere and which are strategic. If the goal
> is to reduce vulnerability to strategy, it's sufficient for the 
> strategy
> to not work.

Yes.

> For example, let's say I criticize Condorcet methods for being 
> vulnerable
> to burial strategy. I can fix this by adding an anti-strategy device, 
> that
> the winner will be determined solely by the number of first 
> preferences.
> Now, it doesn't matter whether the method can determine who is trying 
> to
> use burial strategy: Burial strategy doesn't work.

Yes.

I think selecting an election method means balancing between methods 
that try to elect the best candidate and methods that are immune to 
strategies. If one has a favourite SVM but picks some other PVM for use 
because risk of strategic voting is considered high, then one has 
picked a voting method that doesn't always pick the candidate that is 
considered to be the best (since SVM =/= PVM in this case). People who 
thing e.g. that Condorcet and Smith are enough for sincerity have more 
freedom to pick any voting method that fulfils these two criteria, but 
people who have a complete favourite SVM have to give something up when 
they pick some other voting method for practical use.

(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.)

In addition one typically wants to give the voter possibility to 
express her opinion as completely as possible. Ratings are expressive 
but very vulnerable to some trivial strategies, rankings are quite 
expressive and quite strategy resistant, first preferences are less 
expressive but immune to many strategies (but vulnerable to some like 
need to vote a compromise candidate instead of ones favourite). Balance 
has to be sought here too. Condorcet / ranking based methods are one 
nice local optimum I think (also Approval can be defended using quite 
similar reasoning).


Best Regards,
Juho