[EM] Chris BC reply

[Juho]

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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