[EM] Third Parties and Kristofer

[Kristofer Munsterhjelm]

On 2024-08-19 06:58, steve bosworth wrote:
> *Subject: [EM]Third Parties.*
> To: Kristofer Munsterhjelm and others. (km-elmet at munsterhjelm.no)
> FROM: Stephen Bosworth (_stevebosworth at hotmail.com 
> <mailto:stevebosworth at hotmail.com>_)

> I want fully to understand the relevant new ideas you offered in your 
> 7/30/2024 4:06 PM post. These ideas were especially prompted for me by 
> your words and phrases extracted and copied immediately below the next 
> paragraph.

> Currently, the intuitions or possibilities your words suggest to me, 
> once fully understood, might require either a rejection or a 
> confirmation of the proportional voting method published in 2020 by my 
> co-authors and myself 
> [/_https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3/ <https://www.jpolrisk.com/legislatures-elected-by-evaluative-proportional-representation-epr-an-algorithm-v3/>_/].

> That article offers a full account of evaluative-proportional 
> representation (EPR), including the algorithm for counting such an 
> election. Additionaly and in the last section of this post, I’ve added a 
> complementary and much shorter introduction to EPR . It explains, for 
> example, how electing a seven-member city council using EPR ensures that 
> every voter is most likely to see one of the elected candidates as 
> representing them accurately. Every party, voter, minority, and majority 
> of voters would be proportionally represented in the council exactly.

> Of course, I look forward to receiving as much feedback as possible from 
> you and from other EM contributors. In particular, I want to understand 
> why your “*VSE-like proportionality measure” *either falsifies or 
> supports my above paragraph’s last two sentences?

Bottom line first: the VSE measure is intended as a way to quantify how 
proportional a method is. Thus the only way to know whether it rules EPR 
in or out would be to test it. I haven't actually implemented my measure 
yet, though, and the parts you quote deal mainly with how the VSE idea 
could be extended to creating a proportionality measure for real STV 
elections.

However, more generally, you could probably devise an assignment where 
EPR doesn't perfectly represent the voters. I'll get back to that at the 
bottom, after explaining what my measure was about, and what the idea of 
applying it to real elections also was about. See [1].

----

My idea was that we draw the voters and candidates from an opinion 
space. For instance, a 2D opinion space might be like the classical 
authoritarian/libertarian and economic left/right of the political 
compass[2], and both voters and candidates would have a position on it.

I'm currently only talking about synthetic data, generated by a 
computer: not actual voter and candidate positions in opinion space. 
Thus the system doesn't need to know what the different dimensions stand 
for when evaluating a method.

If a method is proportional, then the distribution of elected candidates 
would tend, over a large number of elections, to be like the 
distribution of the voters. Suppose say 10% of the voters are quite 
socialist and neither authoritarian nor libertarian. Then a proportional 
method will elect 10% socialist balanced-authority candidates too, 
because the 10% of the voters will express a preference for them.

(It's a bit more complicated because there may not be a candidate at 
that position, so it's not just about first preferences. But it should 
give you the gist.)

So my VSE measure would use a computer to draw a bunch of voters and a 
bunch of candidates according to a normal distribution, and then judge 
the method according to whether the elected candidates ended up where 
you'd expect them to be based on the voter distribution of opinions. The 
"VSE" part is that it normalizes the score so that zero is what you get 
if you just picked people at random, and one is the best possible.

It uses the Sainte-Laguë index because Sainte-Laguë (Webster) is usually 
considered the best measure of proportionality.

----

That's the first part. In the second part, I basically say: we might be 
able to use this approach to quantify proportionality of an election in 
the real world, too.

For context: this is a real problem when using methods like STV. If you 
use party list, it's easy to determine proportionality. You just take 
ecah party's support and the fraction of seats it got, and use a 
standard measure like Euclidean distance or Sainte-Laguë. But for STV 
(and EPR, Schulze STV, QPQ, PAV, Phragmen, etc.), you can't do that, 
because later preferences matter. So people who report election results 
usually use party preference, but that can't easily tell you if the 
current election was proportional or not.

My idea would, if it could be implemented, solve that.

Say we ask a bunch of candidates and a bunch of voters a number of issue 
questions like, for example, "Farmers are paid too little" or "We need 
to give local government more of a say" and record how much they 
agree/disagree with them. Now we have a distribution of voter opinions 
and we know the opinions of every candidate. (This can be postprocessed 
to reduce the number of dimensions, but I won't get into that here.)

After the election is over and some of these candidates are elected, we 
could, in principle use the measure from above to determine how 
accurately the elected candidates mirror the voters' opinions. And this 
would work no matter what method you use for electing them.

Descriptive representation would be easy to add, as well. Just augment 
opinion space with additional properties - like class, ethnicity, 
gender, etc.

But it's not that simple. The Sainte-Laguë index is very sensitive to 
polling errors. For instance, if a libertarian was elected but (by sheer 
coincidence) none of the voters polled were libertarian, then the 
Sainte-Laguë index would be infinite, just because the polling missed 
the few libertarians who got that candidate elected. That's what I meant 
by the "zero opinion problem".

So that part is about "how to make real world measures of 
proportionality better" in a way that allows one to answer "but how 
proportional was the last election". It hasn't got anything to do with 
any method in particular.

-km

[1] Suppose, for instance, that a constituency has 10 parties of 10% 
support each, and every voter is perfectly partisan and vote their own 
party top and every other party bottom. Then you can't fit ten reps into 
seven seats and something has to go. It's very unrealistic, but it shows 
that having perfect representation all the time is impossible.

[2] Or, for that matter, the kind love/tough love and 
pragmatic/ideological axes of 
https://web.archive.org/web/20080212053747/http://politics.beasts.org/scripts/eigenvectors