[EM] MinMax(AWP) and Participation

[Juho]

I still include minmax(margins) in the set of good Condorcet methods,  
also for practical elections. AWP style defeat strength measuring is a  
very interesting addition to the Condorcet family. It may be a bit  
tedious to the voters but in principle very interesting as said. Also  
variants of the AWP preference strength rule would be interesting.

In minmax(margins) I'm not very worried about those criteria that it  
violates and some other popular Condorcet methods meet since those  
situations are typically rare and often one may also argue that in  
those cases one actually should violate those rules. I won't cover the  
numerous details in this mail. I note also that different elections  
may have different needs on what kind of properties the winner should  
have, so different methods may be used for different needs. In  
addition minmax(margins) is simple, easy to understand, implements one  
very natural utility function (least additional votes to win all  
others) and the results can be shown nicely e.g. as histograms that  
clearly show how close each candidate is to winning the race at any  
point during the calculation process or when the results are final.

I do have some worries about minmax(margins). Some of the properties  
that are commonly mentioned as the key problems may sometimes be even  
like requirements to me (e.g. ability to elect sometimes outside the  
Smith set may well be a requirement in some elections). The problem  
that I refer to here (and that is usually not covered anywhere) is the  
possibility to artificially create a cycle or strengthen a cycle e.g.  
so that all candidates in the Smith set are strongly looped. As a  
result a candidate outside the Smith set may (strategically) win in  
minmax. I guess also this is not a major vulnerability in practical  
elections (requires too much coordination), but at least this is an  
additional vulnerability of minmax that most other common Condorcet  
methods do not have.

I like the minmax style of comparing the winning candidate to other  
potential winners (to measure in some (not perfect) way "the strength  
of opposition against the winner" after the election). The path based  
methods have some clone related properties that people may want but  
the philosophy of chained pairwise victories do not make as much sense  
to me (as a target) as direct (one step) comparison of candidates.

(As I recently wrote I also don't like heuristics that try to force  
the group opinions into some linear ordering (often called "breaking  
of the cycles"). Group opinions may be cyclic and there is no "right"  
non-cyclic preference order that would be more correct than the  
original cyclic opinion. We should learn to live with the idea that  
the group opinions are sometimes cyclic and we need to understand  
which candidate would be the best winner in that situation (not  
necessarily one of the top cycle candidates, as you can guess :-).)

In addition to listing the theoretical vulnerabilities of different  
election methods I put a lot of weight on real life like examples of  
the vulnerabilities. It is not easy to construct examples that would  
demonstrate obvious vulnerabilities in typical (large, public etc.)  
real life elections. All typical Condorcet methods are actually pretty  
good in typical real life elections. Many criteria are also  
incompatible with each others, and in these situations the real life  
like examples offer a reasonable basis to estimate which rule should  
be violated (to get the best winner with sincere votes or to defend  
against the most plausible strategy).


> If A wins and then another ballot with A ranked unique first is  
> added to the count,  A still wins.


This criterion seems to be a close relative of the "the candidate that  
needs least additional votes to win all others wins" rule (that  
defines minmax(margins)). The "additional votes" should be ones where  
that candidate is "ranked unique first".


Here's one example for minmax(wv).

1: A>B
2: B
2: C>A

A wins. Then we add one ballot with A ranked unique first.

1: A>C

A and C are tied. A doesn't necessarily win any more. Was the weak  
version intended to cover both minmax(margins) and minmax(wv)?


> Knowing that Beatpath satisfies the weaker version but not the weak  
> version may be an inducement for voters to bullet vote candidate A  
> to make sure that they avoid the no show paradox.  But MinMax is  
> free of this temptation; they wouldn't have to truncate the other  
> candidates.


Condorcet methods give good results only with good input. One should  
try to keep the level of bullet voting and truncation low (except if  
the voter really feels that the remaining candidates are practically  
equal (maybe equally unknown)). Minmax(wv) has some truncation  
incentives. I however do believe that in real life elections most of  
the truncation does not emerge because of the technical properties of  
the used method but for some more generic reasons like laziness to  
rank all candidates or (mainly irrational) fear that ranking a  
competitor of one's own favourite would somehow generally support that  
candidate and help him/her beat one's favourite candidate. The true  
properties of the method could be used in propaganda to encourage  
truncation, but as seen in real life the real life, propaganda is  
often not very rational. Quite as well the truncation arguments could  
be irrational and the (even marginally) rational arguments could be  
ignored :-). So, in real elections one should just try to make the  
voters feel comfortable with the idea that with the used (Condorcet)  
method it is wise to just sincerely rank numerous candidates and not  
truncate (and not try any stupid strategies that might hurt more than  
help).

Juho




On Apr 22, 2010, at 12:36 AM, fsimmons at pcc.edu wrote:

> I don't know if Juho is still cheering for MinMax as a public  
> proposal.  I used to be against it because of its clone dependence,  
> but now that I realize that measuring defeat strength by AWP  
> (Approval Weighted Pairwise) solves that problem, I'm starting to  
> warm up more to the idea.
>
> MinMax elects the candidate that suffers no defeats if there is one,  
> else it elects the one whose maximum strength defeat is minimal.
>
> There are various ways of measuring defeat strength.  James Green  
> Armytage has advocated one called AWP as making Condorcet methods  
> less vulnerable to strategic manipulation.
>
> If all ranked candidates on a ballot are considered approved, then  
> the AWP strength of a defeat of B by A is the number of ballots on  
> which A is ranked but B is not.
>
> Then more recently I was reading a paper by Joaquin Pérez in which  
> he shows that MinMax is the only commonly known Condorcet method  
> that satisfies the following weak form of Participation:
>
> If A wins and then another ballot with A ranked unique first is  
> added to the count, A still wins.
>
> Beatpath, River, Ranked Pairs, etc. fail this weak participation  
> criterion, but they do satisfy this even weaker version:
>
> If A wins and then another ballot with only A ranked is added to the  
> count, then A still wins.
>
> Proof:  First add a ballot in which no candidate is ranked.  The  
> above mentioned methods allow this, and it doesn't affect their  
> outcome since no mention of absolute majority is made in any of  
> them.  Then raise A while leaving the other candidates unranked.   
> This cannot hurt A since all of the above mentioned methods are  
> monotone.
>
> Knowing that Beatpath satisfies the weaker version but not the weak  
> version may be an inducement for voters to bullet vote candidate A  
> to make sure that they avoid the no show paradox.  But MinMax is  
> free of this temptation; they wouldn't have to truncate the other  
> candidates.
>
>
> ----
> Election-Methods mailing list - see http://electorama.com/em for  
> list info