[EM] Meta-criteria 6 of 9: Heuristics. #1, simplicity

[Juho]

On May 8, 2010, at 12:43 AM, Kristofer Munsterhjelm wrote:

> Juho wrote:
>> On May 7, 2010, at 7:11 PM, Kristofer Munsterhjelm wrote:
>>> Schulze's primary argument is that the use of paths let one make a  
>>> method that is very close to Minmax, yet is cloneproof and elects  
>>> from Smith. Thus, if one thinks the Minmax yardstick is a good  
>>> one, yet that Minmax's clone susceptibility means one has to  
>>> diverge from it in certain cases, Schulze is a good method.
>> Yes, Schulze has some such properties. If both criteria are  
>> considered important, then one should just estimate which method is  
>> closer to ideal. Minmax may ignore clones that have strong losses  
>> to each others (it puts more weight on the distance to being a  
>> Condorcet winner). Path based methods may defend "clones" also when  
>> there are no clones (and a candidate that meets neither criterion  
>> might win).
>
> Schulze also satisfies some "internal non-contradiction" criteria  
> that I like, such as reversal symmetry. It seems reasonable that a  
> method should handle "likes" and "hates" equally but opposite.  
> However, it would also be reasonable, at first observation, that a  
> voter can never be worse off by showing up, but that (Participation)  
> is very strict and almost no methods pass it.
>
> Perhaps there is an element of aesthetics to those criteria  
> (monotonicity, reversal symmetry, and also monotonicity). This would  
> fall within the legitimacy meta-criterion, I think; voters would  
> suspect something fishy is going on if raising a candidate makes him  
> lose, if polling for "who do you dislike" doesn't return the loser  
> of "who do you like", etc.

 From minmax point of view reversal symmetry is not an obvious  
requirement if there are cycles. If three candidates are in a cycle  
that is a bad thing. That is a bad thing irrespective of if one looks  
at the original or reversed votes. That would thus drop the cyclic  
candidates lower in both cases.

A world where voters may give the same answer to question "who should  
win" and "who should not win" doesn't appear very natural at first  
sight (from transitive opinions based point of view) but that seems to  
be possible in minmax. And the explanation is that cyclic defeats are  
considered to be as bad as any other defeats (i.e. cyclic clones or  
cyclic non-clones will not be treated as if there were no defeats  
among them), and the cycle exists when looking from either direction.  
In a way there is no agreement to do anything with the cycled  
candidates.

>
>>> As for your second part, there is naturally a tradeoff between  
>>> strong paths and short paths. Schulze considers paths equally no  
>>> matter their length, but the question is sensible. Methods that  
>>> focus on short paths are more like Copeland (which focuses on  
>>> "paths" of a single step), and methods that elect from the  
>>> uncovered set would have short paths from the winners to the  
>>> candidates not in the uncovered set.
>> I see the "one step philosophy" as answering to question "if we  
>> would elect x, would the society be happy with x or would it be  
>> interested in changing candidate x to someone else" (not on  
>> questions on if the society would be interested in multiple  
>> sequential changes). The philosophy of Copeland's method would make  
>> sense in principle. I guess the minmax philosophy can be said to  
>> focus only on the strength of the losses and not on the number of  
>> them because of the clone related problems that Copeland has. The  
>> number of losses also has no meaning if the intention is to check  
>> how close each candidate is to being a Condorcet winner.
>
> I can see three philosophies/approaches, and associated simple  
> methods (neither cloneproof):
>
> - The minmax approach: What matters is the worst outcome. Minmax is  
> its simple method. Schulze fits here because of the strength of a  
> beatpath being equal to the weakest link.

Yes, the philosophical difference is first step vs. multiple steps.

> - The Copeland approach: What matters is the number of short paths.  
> Second-order Copeland goes here as well.
> - The least reversal approach: What matters is the sum of victories  
> or defeats. Condorcet least-reversal fits here, as does the  
> "attacker's version" where the candidate with the greatest victory  
> sum wins. These methods seem to get low Bayesian Regret.
>
> Ranked Pairs, I'm not sure. Its idea is more complex, perhaps  
> embodied by the immunity against majority complaints criterion,  
> which goes like: If voters that support Y (and Y beats the winner X)  
> complain that Y should have won, not X, then those who support X can  
> point out that X beats Y at least as strongly through an indirect  
> path, no matter who Y is.
> It's possible to get Ranked Pairs closer to the Copeland approach,  
> as by Short Ranked Pairs (http://www.mail-archive.com/election-methods-electorama.com@electorama.com/msg04266.html 
> ).

The simplest explanation to Ranked Pairs might be that strongest  
opinions must be respected and weaker ones can be violated. Just like  
many other rules this seems very rational.

Actually I think the problems mostly come from the fact that people by  
nature see preferences as transitive preferences and therefore the  
impact of cyclic group opinions is confusing and many of their  
properties seem irrational. Many of the simple rules take one concept  
from the world of transitive opinions and then try to force that on  
the cyclic opinions. What would be needed is a change from Newtonian  
(transitive) rules to relative rules that are valid also in the cyclic  
cases.

> I have no idea where River fits into this - or Kemeny, for that  
> matter.


Kemeny seems to focus on the full raking of the candidates (not only  
on the winner) and finding the least distorting way to do this. If one  
wants to define a full ranking of the candidates then this approach is  
very natural. (But often the main target of single-winner methods is  
to just pick the ideal winner and full "transitivization" of the group  
opinion is not needed.)

Juho