On 04.02.2022 03:43, Forest Simmons wrote:

Yeah, my reluctance to base dimensions around the number of currently
existing parties in part stems from this. If we're supposed to improve
the state of politics, then we shouldn't take the current bundling of
issues as a given. To the degree it's possible, the method should get
out of the voters' way and let the natural number of dimensions reveal
itself through their actions.

FPTP doesn't do this.

Poll data would presumably be less contaminated by the
squashing-together effect of two party rule than actual election results
would be; and the results from New York's STV era also suggest that
there's room for multiple parties if the method just allows them to exist.

On another side note, I examined JGA's strategy paper a bit more closely
and I see that he has another synthetic model (IAC) which matches the
poll data well, at least for strategic resistance. I could check whether
it's as easy to construct exact probabilities for IAC as it is for IC; I
would expect so, since it's statistically very simple. However, I
couldn't easily construct exact probabilities for the utilities since
draws from a normal distribution need not be rational.

Perhaps if we make a method whose minimum VSE over a linear combination
of high dimensional spatial and IAC is maximized, we would have a
generally good method without overfitting too much. Same with
maximizing minimum relative strategy resistance, or some combination of
the two.

I say "make", but it's not that easy. The strategy generator could
possibly be fitted to do this, but inferring structure out of its lookup
table is still very hard, as I've said.

-km

I haven't followed this discussion - sorry if I'm missing something. I
quite like Jameson Quinn's model of an infinite number of dimensions of
progressively diminishing importance. On the other hand, if 'n
dimensions' is understood as meaning n dimensions of equal importance,
then it seems to me intuitively unattractive. As a first approximation I
might describe politics on a left/right axis; as a second I might
distinguish between economic and social liberalism but expect them to be
correlated (leading to a cigar-shaped 2D Gaussian) etc. (This doesn't
help Daniel who wants an upper limit.)

Quinn's model is on his vse page:
http://electionscience.github.io/vse-sim/VSE/

CJC

On 04/02/2022 09:55, Kristofer Munsterhjelm wrote:
<snip>

In terms of political realism, I might add that I also see considerable
merit in a GMM. If there is a racial divide in outlook then it's
hopeless to try to capture it with a smooth distribution.

CJC

On 04/02/2022 11:04, Colin Champion wrote:

On Fri, Feb 4, 2022 at 5:05 AM Colin Champion
colin.champion@routemaster.app wrote:

That's my intuition as well --- dimensions of decreasing importance. If you
wanted to make a cigar-shaped Gaussian, do you have any idea of how
elongated it should be? Like... should each dimension have half the
variance of the one before? Something else?

Let me also respond to Kristofer's comment about not taking the current
bungling of issues as a given. One could argue that the pragmatic approach
is to ask how a change in the electoral system would affect the fortunes of
minor parties that already exist, or how it might encourage a new party to
form. In the former case, you only need to model the sub-space spanned by
parties that already exist, and in the latter you only need 1 more
dimension than that.

I've read this page before and I dismissed it because I couldn't figure out
what the model actually was. Maybe it's obvious and I just don't see it,
but what is the actual formula for the VSE?

But in any case, the current conversation is about dimensionality, so you
are thinking of the “Hierarchical clusters” model, right?

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

On 04.02.2022 20:24, Daniel Carrera wrote:

I found a (very rough draft of a) paper that argues that political
positions are hierarchical down to infinity, i.e. that if you ask very
specific questions, different voters will have different opinions about
these, but that they can be grouped into larger categories that do make
sense in lower dimensional space.

https://garymarks.web.unc.edu/wp-content/uploads/sites/13018/2016/09/rovny-and-marks.-issues-and-dimensions.pdf

If that's true, then there should be some kind of effective limit to the
number of dimensions given by the degree that voters care to coordinate
and know the issues, and how strong a low-pass filter (so to speak) the
political mechanism provides. PR would allow for more distinctions than
FPTP.

In such a kind of model, I would imagine that any sort of single-member
district would have a definite attenuating effect on variety, but that
Condorcet would provide better reproduction for the unavoidable level of
quantization than would say, IRV or FPTP; i.e. that it's better at
finding consensus candidates.

If you want to directly represent an area of opinion space that 10% of
the voters care about in every district, then you would pretty much need
PR. IRV would either magnify or squash this 10% support based on its
"strongest wing of strongest wing" recursive logic, whereas Condorcet
would pull the consensus candidate somewhat in its direction.

So SMD would give you some degree of bundling, PR with thresholds give
you a lesser degree, and PR without thresholds an even lesser degree.

I'd imagine sortition would (on average) produce a very low degree of
bundling, since the representative sample should be accurate of the
people down to the variance provided by the size of the assembly itself.
It would also bypass whatever natural limit arises from the nature of
campaigning and party organization.

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.

(If the model is accurate, that is. Perhaps a properly designed poll
could determine whether it is; such a poll would ask various questions
within subcategories of subcategories of main categories and see if the
results are consistent with the hierarchical model.)

Yes. But if we're not careful, that's the kind of reasoning that leads
to IRV-type reform. Suppose that a method is stable for k parties and
then something bad happens at k+1. Once we're stuck at k parties, we may
ask for a reform that brings the well-behaved regime up to k+1. But then
we'll have the same problem at k+1.

It would be better, I think, to take into account scenarios all the way
up to n parties for some large n, so that there's plenty of room to grow
-- if we have that luxury as mechanism designers, of course.

The metaphor isn't completely fair to Condorcet because Condorcet passes
IIA whenever there is a honest CW and too few strategic voters to
disturb the presence of that CW. That could theoretically happen at any
dimension level. A Condorcet method can be stable at any dimension (best
case) and be unstable at any above one (worst case), so it's much harder
to tell how many parties it can support.

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. That method has 100% VSE by
definition. A method that picks candidates at random is defined to have
0% VSE. The VSE percentage of a method is its utility performance mapped
on this scale; most methods are above 0%, but it's possible for a truly
bad method to be less than 0%.

More info on wikipedia:
https://en.wikipedia.org/wiki/Social_utility_efficiency

Jameson summarizes his results here:
http://electionscience.github.io/vse-sim/VSEbasic/
Other people have also done VSE calculations. Here's John Huang's:
http://votesim.usa4r.org/summary-report.html

-km

This recent discussion about cigar-shaped Gaussians and
dimensionality gives me another idea: Instead of assuming that candidates /
parties are randomly selected from the electorate, you could imagine a
model that starts with two major parties divided along the major axis of
the Gaussian, and each new party picks a platform that is not random, but
is intended to maximize the number of voters that they can take from
previous parties.

Cheers,
Daniel

On Fri, Feb 4, 2022 at 5:05 AM Colin Champion
colin.champion@routemaster.app wrote:

--
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

On Fri, Feb 4, 2022 at 3:38 PM Kristofer Munsterhjelm km_elmet@t-online.de
wrote:

Thanks for the link! I'll read it over the weekend.

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".

Oh... Right... Yeah... I didn't think of that. Yeah, we need to make sure
election methods have room to grow.

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?

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.

Btw, thanks for the links. I'll go read those too.

Cheers,

Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University

On 05.02.2022 00:22, Daniel Carrera wrote:

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.

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.

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 :-)

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