[EM] Anyone got a good analysis on limitations of approval and range voting?

[Juho]

On Nov 26, 2009, at 12:43 AM, Kristofer Munsterhjelm wrote:

> A final note is this: while the above may make it seem like I think  
> criterion compliance is pointless (after all, the failure could be  
> hidden in an obscure election scenario that will never happen),  
> that's not quite true. If a method passes Condorcet, you at once  
> know it will always pick the CW if one exists; you don't have to sit  
> down and reason whether the failure is acceptable by whatever metric  
> you are using. Thus, if we can pass criteria without having to pay  
> too much, we should; a method passing a criterion is a guarantee for  
> that method that it won't ever misbehave in the way drawn up by the  
> criterion, and such absolute guarantees are nice things to have. If  
> we can't have them, *then* we can start talking about whether or not  
> it matters, but in the ideal world, we would have a method that pass  
> the criteria that are worth passing.

I agree with this.

If some method breaks some criterion it would be good to understand  
also how often that is expected to happen and how serious the  
consequences are expected to be. (Even if some violations of this  
criterion (by other methods) would be serious the violations of this  
method might be minor. The violations might be so rare and  
consequences so mild that the problems are marginal or below the noise  
level.)

If there are multiple criteria that can not be met simultaneously it  
is possible that the best method violates all these criteria (instead  
of trying to meet as many of them as possible). It is possible that  
compatibility with some criteria makes the method violate some other  
criterion more. And this may lead e.g. to greater vulnerability to  
tactical voting (since the weakest link of the chain is now weaker  
than what it could be when all/many of the criteria are violated but  
only lightly).

In summary, it would be good to have some standard ways and common  
practices to give also some general estimates on 1) when / how often  
some criterion is violated and 2) how serious the consequences are.

We all would like e.g. "later preferences to never cause harm" and  
"election methods to be strategy free" but we just can't. Typically we  
need to sacrifice some properties in favour of some others, or simply  
accept that the laws of nature don't allow us to have everything that  
we would like to have. Some criteria are also double-edged. You may  
have problems both if you meet them and if you don't. Nice names of  
the criteria (that point in one direction only) and that use words  
with positive or negative tone may sometimes increase confusion (=> as  
if there would be a need to meet such a criterion always).

I addition I must note (the trivial fact) that the number of criteria  
that some method meets does not mean that it would be good (although  
there is some correlation). There may be e.g. criteria that point out  
some benefits that are marginal and that are in real life run over by  
some other bigger vulnerabilities. I think the true vulnerability of  
the methods can often be described in a more reliable way e.g. by  
giving some realistic (real life / in the intended environment)  
examples on how the method may fail. Such examples are of course often  
based on the basic information about theoretical vulnerabilities and  
whether or not the method meets some criteria but the real test is if  
those vulnerabilities will/can have some impact in the actual election.

Another summary. Maybe I was just saying that in many typical  
environments Condorcet methods are indeed "quite LNH" :-).

Juho