[EM] Chris BC reply

[Dave Ketchum]

Thanks, I learned a bit but:

I think cycles should not be hard to explain.  We get to A>B>C>A when the 
pairs are near ties and the wins of the pairs proceed around the circle, 
either right or left.

Minmax resolution of cycles does read easier than other methods.

That the winner does not have to come from the Smith set should shock only 
those who expect too much from that label.

Could there be a better name than "minmax"?

DWK

On Mon, 19 Feb 2007 19:04:09 +0200 Juho wrote:

> On Feb 19, 2007, at 10:42 , Michael Ossipoff wrote:
> 
> 
>>
>>Juho wrote:
>>
>>(There are good methods also on the other side of the fence,
>>
>>>like minmax(margins).)
>>>
>>I reply:
>>
>>But, when saying that minmax(margins) is good, you've got to say  
>>what it's good for. I've told what the wv methods are good for: The  
>>best ones meet SFC, GSFC, and SDSC.
>>
>>Mike Ossipoff
>>
> 
> Ok, fair enough.
> 
> My sympathies towards minmax(margins) come primarily from the way it  
> handles sincere votes. I'll address the behaviour with sincere votes  
> based on the two categorization criteria that I mentioned in my  
> previous mail.
> 
> A) how to measure preference strength between two candidates
> 
> Margins is a quite natural way of measuring the preference strength.  
> When comparing to winning votes I must say that defeat 0%-50% feels  
> worse than defeat 49%-50%, and that defeat 25%-75% feels quite  
> similar to 0%-50%. (One can always discuss what the intentions of  
> those voters that indicated a tie are, or if there are other better  
> ways to measure the preference strength than these two, but in any  
> case margins is quite decent.)
> 
> B) is there a philosophy to "fix" only the cyclic preferences and  
> keep the "straight" ones
> 
> Minmax does not follow this principle. It rather evaluates each  
> candidate in turn. I like this approach since trying to "linearize"  
> the preferences that are circular doesn't sound to me as natural. The  
> result that minmax gives is as follows. Elect the candidate that  
> would beat all the others. If there is no such candidate, elect the  
> one that would need least additional votes to beat the others. This  
> sounds like a natural utility function to me - at least for some  
> purposes (I accept that different utility functions may be best for  
> different elections).
> 
> I also find the path based explanations a bit clumsy since in real  
> life after the election it does not appear very natural to think that  
> the elected candidate is bad because there is a path where she could  
> be changed to X that could be in turn changed to Y etc. It is maybe  
> more natural to just see how the elected candidate looks with respect  
> to the other candidates (without imagined winner change paths).
> 
> Respect of the Smith set sounds natural when one images a picture of  
> the canidates and their preference relations drawn on a paper. The  
> most natural way to draw the figure is to draw the Smith set  
> candidates first in a group and only then the others below the Smith  
> set. It looks natural that one elects the winner from the Smith set.  
> But while respecting the fact that candidates outside the Smith set  
> lost to the Smith set candidates the description above totally  
> ignored the cyclic defeats. From minmax point of view they are just  
> as bad as the non cyclic defeats.
> 
> The disrespect of the Smith set leads to the possibility of electing  
> even the Condorcet loser in some extreme situations. This is the case  
> e.g. when there is a very strong loop between three candidates (Smith  
> set), and all these candidates beat a fourth candidate with a very  
> small margin. Electing the Condorcet loser sounds quite irrational at  
> first sight. One must however note that the Condorcet loser would in  
> this case need only few votes to beat all the others, i.e. it is not  
> that far of being a Condorcet winner. The others are much farther  
> from that target. The minmax utility function measures the distance  
> to being a Condorcet winner, and as already noted above this is a  
> quite natural utility function (at least for some uses). Electing the  
> Condorcet loser can thus be seen as a positive thing in some  
> situations (and methods that do not do so could be rejected based on  
> this criterion).
> 
> C) other stuff
> 
> Minmax is good also in the sense that it is easy to explain. "Least  
> number of additional votes to beat all others" is an explanation that  
> most peope understand and may agree to. It is better to have this  
> kind of understandable explanations to the results of the election  
> than just saying that there was a cycle (people don't understand what  
> that is) and it was solved by a very complex algorithm in favour of  
> some candidate (people don't understand this either).
> 
> The fact that the result for each candidate is a single number is  
> good since then people can see e.g. how much their favourite lost to  
> the winner. Referring to a complex algorithm and complex conditions  
> that would have changed the outcome is not as helpful and does not  
> explain which candidates got good/bad results.
> 
> One value for each candidate makes it also easy to display the  
> results, e.g. the intermediate results in TV during the vote counting  
> process. One can also easily see if some candidate still has  
> possibilities to win with the remaining votes that have not yet been  
> calculated (luckily with minmax(margins) one can actually see the  
> exact answer: number of additional votes needed (to beat all or at  
> least to pass the best result so far)).
> 
> 
> The comments above discussed the performance of minmax(margins) with  
> sincere votes. Let's cover also the strategy related aspects.
> 
> A) how to measure preference strength between two candidates
> 
> Some cases are worse for margins, some for winning votes. This  
> doesn't play strong role in my opinions about minmax(margins) (see  
> discussion at C below).
> 
> B) is there a philosophy to "fix" only the cyclic preferences and  
> keep the "straight" ones
> 
> Nothing special to comment here.
> 
> C) other stuff
> 
> In general Condorcet methods encourage sincere voting in most  
> situations and strategies are difficult to apply (especially in large  
> public elections). I tend to think that the strategy resistance of a  
> Condorcet method hopefully is good enough to put majority of the  
> voter on a sincere track. If large scale strategic voting starts to  
> appear in Condorcet methods, then maybe the situation is so bad that  
> it may be better do do some other tricks like agreeing on lesser  
> number of joint candidates or going for some other voting method  
> (wonder what that might be).
> 
> I also don't like discussions on counter strategies in association  
> with Condorcet. One of the key benefits of Condorcet methods is that  
> people can give their sincere opinions. If we go for (counter) 
> strategic votes in Concorcet methods, large part of their benefits  
> are lost.
> 
> In summary it would be good to use Condorcet methods in environments  
> where their natural strategy resistance gives good enough protection  
> and everyone can trust that the elections will not lead to anything  
> catastrophic (some small number of "uneducated" strategic votes will  
> probably always be present, but hopefully not leading to problems).
> 
> 
> This was a "short" description of reasons why minmax(margins) is a  
> method that may well be ok or even best for many uses. My  
> explanations are leaning in the direction that all Condorcet methods  
> are quite strategy resistant and may work fine in many elections.  
> Therefore it may be a good idea to pick a Condorcet method that has  
> good performance with sincere votes. Minmax(margins) is an exact  
> implementation of one quite natural utility function. Differences  
> between the strategy resistance of different Condorcet variants are  
> not big. And there are also the simplicity and understandability  
> benefits. Looks pretty good for me. (Maybe someone else can list the  
> bad points of minmax(margins). I maybe wrote this mail with only rosy  
> colours since that was the request.)
> 
> Although it is a common habit on this list to give a long list of  
> criteria that are a must I didn't provide one. I rather provided the  
> explanations (like why not meeting Condorcet loser may sometimes be a  
> good thing). The criteria also would force me to discuss the  
> difficulty of implementing the strategies, the probability of  
> success, the probability of certain vulnerabilities to appear in real  
> elections etc. That'd take years of your time (and it already has :-).
> 
> Juho

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  Dave Ketchum   108 Halstead Ave, Owego, NY  13827-1708   607-687-5026
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