[EM] Spatial models -- Polytopes vs Sampling

[Kristofer Munsterhjelm]

On 05.02.2022 00:22, Daniel Carrera wrote:
> 
> On Fri, Feb 4, 2022 at 3:38 PM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
>>     I don't know what this natural level would be, though, for something
>>     like Condorcet. I guess it would depend on to what degree dimensions
>>     follow geographical distinctions: if six districts have voters who care
>>     exclusively about economic issues, and four districts care exclusively
>>     about unitary state vs devolution issues, then that's going to give a
>>     different composition of issue space than if the unitary/devolved voters
>>     are represented by 40% in every district and the economic voters by 60%
>>     also in every district.
> 
>  
> Yeah. The eternal problem of single-member districts. One feature that I
> like about STV compared to other PR methods (and I realize STV is not
> 100% PR) is that in principle STV is sensitive to dimensions that might
> not be represented by political parties. If an electorate wants more
> women in power, STV can produce that without there necessarily being a
> "women's party".

Yes, I prefer STV for that reason too. It also pushes the parties to
follow the people to a greater degree (anticipating such voting).
Unfortunately, it can only be roughly proportional in that sense; party
list PR can be proportional down to say, one seat of 160, but it would
be impossible to ask the voters to rank 160 candidates.

>>     The concept of VSE is simply this:
>> 
>>     Suppose every voter assigns an absolute utility to each candidate. Then
>>     each candidate provides the electorate as a whole with some amount of
>>     total utility, were he elected.
>> 
>>     Now suppose there's a magic method that reads the voters' minds and
>>     always elects the best candidate.
> 
> 
> How do we decide who the best candidate is? Is it the one that maximizes
> total utility? I'm not sure I buy into the utilitarian argument. If
> making one person really miserable will make 10 people really happy, I
> would not necessarily consider that a good outcome. I'm also skeptical
> of the idea that one person's vote matters more if they feel more
> strongly about it. And that's not even taking into account the possible
> damage that a small extremist wing can have just by virtue of being
> extremist.
> 
> To put it differently, if moral philosophers cannot agree that
> utilitarianism is the way to go, why do I think that I can write an
> algorithm that solves the utilitarian problem?

Yes, you kind of need a presumption of how important it is. If you're
not a total utilitarian, then VSE performance is kind of like a voting
method criterion: all else equal, it's a good thing to have, but it's
not the one quality to rule all qualities.

>From that perspective, we could also imagine other sorts of VSE based on
other types of utilitarianism. The most obvious one would be "minmax
VSE", where the performance of some voting method in an election is the
utility to the voter who is the most displeased with the outcome. (That
one would be particularly hard to make robust to strategy.)

I would also think that even if utility is your objective, there are
better methods than the current proposed cardinal methods. If
incommensurability is a fundamental problem, then the current cardinal
methods ask for too much, which may lead them to false conclusions.
Properly constructed methods could take the limits of data into account
and lead to better outcomes (as well as being more honest about IIA
failure, as I've mentioned).

So for non-utilitarians, it would be interesting to see what the extreme
of VSE satisfaction looks like, in the same sense it's of interest to
know what strategyproof methods look like even if they wouldn't be
desirable in practice. And for utilitarians, the optimal methods may
improve on current cardinal methods or provide some ideas into how to do so.

(If, again, I can get such insights from the lookup tables that my
optimizer outputs... somehow.)

It would also be fun to outdo the current cardinal methods at their own
game :-)

> Concorcet and PR methods are nice in that they strike a balance between
> taking into account as much of the voter's preferences as possible
> without getting into the whole mess of computing utilities.

Yes. One of the advantages of ranked ballots, IMHO, is that I don't have
to consider whether my evaluation of say, candidate X as a 9/10 and Y as
an 8/10 is "really" the correct relative measure -- perhaps I should've
rated Y a 7/10 instead? On the other hand, ranking is easy: if I prefer
X to Y, then X>Y, done.

Some cardinal proponents say that rating is easier than ranking. I can't
say I've found that to be true, myself.

If I were asked to provide vNM utilities, I'd rather have the question
be phrased in terms of indifference lotteries, and even then it would be
a lot harder than ranking.

-km