[EM] "Possible Approval Winner" set/criterion (was "Juho--Margins fails Plurality. WV passes.")

[Juho]

On Mar 14, 2007, at 8:31 , Chris Benham wrote:

> I'm not suggesting that PAW be explicitly made part of the rules of  
> any method, and  the PAW
> criterion is met by most methods including the simplest. So I don't  
> see how it  "adds complexity".

Ok, if the election method already meets the criterion and the  
criterion is not used as part of the rules, then there is no impact.

> The Plurality criterion is about avoiding common-sense, maybe  
> "simple-minded" but nonetheless
> very strong and (IMO)sound complaints from a significant subset of  
> voters: the supporters of a candidate
> that pairwise beats the winner: "X ranked alone in top place on  
> more ballots than Y was ranked above
> bottom clearly equals 'X has more support than Y', so how can you  
> justify X losing to Y?!".

I think there are different kind of elections with different kind of  
rationale behind selecting the winner. For example the Condorcet  
winner could be different than the one with best average rating. =>  
One has to decide which needs to respect. Similarly the complaints of  
the voters could be based on different arguments. Some voters may  
complain about the number of "above bottom votes" (as above) but  
other voters might complain about the fact that the voters would like  
to change the winner to another candidate with a large majority.  
There are other other rational measures that can be used as a basis  
for complaints.

The plurality criterion is thus just one way of tying to characterise  
what kind of a candidate should be elected. It is typical that in the  
presence of cycles some rules that look obvious when there are no  
cycles, but things get more complicated and intuition easily fails  
when the cycles are present, and one needs to violate some of the  
criteria.

I liked the rationale you gave in support of the plurality criterion,  
the description of the situation after the election has been held. I  
think this is a good way to evaluate the methods (more natural than  
e.g. winner changing path based arguments) since typically we are  
seeking a candidate that would work well with the society and that  
would lead to a stable and happy state.

Note that the corresponding "state after the election" based  
justification of minmax(margins) (that fails the plurality criterion)  
for its behaviour is that it minimises the level of interest to  
change the winner to some other candidate (to one other candidate at  
a time). I think that property can be seen as a benefit for the  
society and as one possible justification to violate the plurality  
criterion. I don't claim that this minmax(margins) style of measuring  
utility is ideal, but at least it makes quite a lot of sense since it  
clearly provides best possible protection against one type of "after  
the election" risk/complaints.

I ended up again in discussing the benefits of different methods with  
sincere votes. But so did you :-). (I didn't yet catch if there are  
also some strategic issues that are closely linked to the plurality  
criterion.)

Juho



		
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