[EM] Sincere methods

[Juho Laatu]

On Mar 30, 2005, at 02:53, Gervase Lam wrote:

>
>> Should I thus read your comment so that you see MinMax (margins) as a
>> sincere method (the best one, or just one good sincere method) whose
>> weaknesses with strategic voting can best be patched by using Raynaud
>> (Margins)?
>
> Roughly speaking yes, but not exactly.  If you think Margins is an
> important way to measure closeness to being a Condorcet Winner, then
> Raynaud(Margins) might be the next best thing.  I cannot think of any
> other reasonable Margins method.
>
> Of course, if you are willing to move away from Margins, there are 
> other
> more simple pairwise methods around that are reasonably 'strategic
> resistant'.

I think margins is one natural sincere voting method. For practical 
purposes I accept also methods that do not make sense as sincere 
methods. They may be needed in order to fight against strategic voting.

In general think it would be very informative to always mention which 
sincere method each proposed practical voting method is based on. Or if 
there is no such complete sincere method in the background, then one 
should at least mention what (sincere) criteria have been taken as the 
basis. It seems that often the default value is simply to assume that 
the (ranking based) methods are Condorcet compatible. Many take also 
Smith set as granted I guess (I don't). For my taste using only these 
basic criteria is a bit lean. The main goal of a voting method is 
anyway to elect the best possible candidate, and defending against 
strategies is just something that may be needed in order not to let the 
voting method fail because of the strategic votes.

Examples may help to clarify what I mean. (SVM = SIncere Voting Method, 
PVM = Practical Voting Method, SC = Sincere Criteria)

SVM: MinMax (margins), PVM: Raynaud (margins)
- the case that we discussed

SVM: MinMax (margins), PVM: MinMax (wv)
- winning votes used to defend against strategies
- I think both margins and winning votes based PVMs (as well as any 
others) are ok as long as there are god reasons to use them
- someone might claim that also winning votes based methods could be 
used as SVMs (?)

SVM: MinMax (margins), PVM: MinMax (margins)
- it would be nice if the SVM could be used also as the PVM
- I think this case could be feasible in many situations; it all 
depends on if strategy threats are considered marginal or serious

SC: Condorcet, PVM: MinMax (wv)
- when Condorcet is used as the SC any defensive means are ok as long 
as they don't violate Condorcet
- if there is a top cycle, any candidate could be elected

SC: Condorcet + Smith set, PVM: ...
- now the winner (in case of a top cycle) could be anyone within the 
Smith set

SVM: Condorcet + Approval for cycle resolution, PVM: Condorcet + 
Approval for cycle resolution
- this case just demonstrates that there could be also other SVMs than 
MinMax (margins)
- The "sincere target" is thus to elect the most approved candidate if 
there is no Condorcet winner

Selecting a PVM is of course a problem of finding a balance between 
SVMs and methods that are good in eliminating strategies (= balance 
between threat of not electing the best candidate because of deviation 
from the target SVM and threat of not electing the best candidate 
because of strategic voting). In cases where strategy problems are 
considered big we end up selecting some strategy eliminating focused 
PVM. In cases where strategy problems are less threatening we end up 
selecting a PVM that is close to the SVM.

Typically examples of strategic voting are handled as abstract examples 
that demonstrate that strategic manipulation of the end result is 
possible. In order to evaluate their real weight I would like to see an 
estimate on what the probability of each strategic voting case is in 
real life. One could for example look at some real life presidential 
election in some real country and then estimate how easy it would be to 
implement the strategy, how detailed information of the voters' 
preferences is needed, how many voters (and from which parties) would 
follow the strategy etc. In my opinion at least large scale public 
elections are not very easy to manipulate (in ranking based elections).

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).

As a response to your comment, I'm "willing to move away from Margins" 
in the PVM area if there are good reasons to do so (= to defend against 
strategies). Also other than margin based methods can be taken as the 
starting point (SVM) if they are properly justified. I picked the 
MinMax (margins) up because I think it is too often seen as a no good 
method although I think it is a good candidate for a SVM and possibly a 
well working PVM too.

I have tried to open a discussion on these topics by putting a mark on 
the opposite end of the playing field than where most players seem to 
be. I mean that it seems to be a typical thinking pattern to take 
Condorcet and Smith set as the only SC and then use all the remaining 
freedom and energy to find the most strategy resistant method (i.e. 
without caring which one of the remaining candidates would be most 
suitable for the job). The "MinMax (margins) as a PVM that is also the 
wanted SVM" approach represents the other end of the playing field.

Best Regards,
Juho


P.S. One more comment. I have criticized also the interest to force the 
group opinions into linear opinions (i.e. transitive, like we expect 
the individual voters' preferences to be). This linearization of group 
opinions may give a false feeling of finding a sincere "big brother" 
opinion. This thinking is problematic since we know that group opinions 
are not linear but may be cyclic. Better justification is thus needed 
if some group opinion linearization methods are claimed to be SVMs. Or 
maybe they are just PVMs. I don't know if anyone has claimed or wants 
to claim them to be SVMs.