Defining "degree of representation" in multi-winner elections

[rob]

I thought it might be appropriate to break this out into a separate thread from https://www.votingtheory.org/forum/topic/295/are-equal-ranking-condorcet-systems-susceptible-to-duverger-s-law, where this is straying off topic.

Below is a graphic I made to illustrate a point, showing voters and candidates in a multi-winner election. This is based on my voting simulator, where ideology-space is shown in two dimensions. (the crosshairs represent the median, the labeled dots represent candidates, the small dots represent voters)

In one scenario, A, B and C are elected to the 3 positions within a legislature. They are all close to the median, and would likely be the top 3 winners in a ranked choice election (preferably Condorcet compliant).

In another scenario, D, E and F are elected, as they might be in a party-list PR election. Each of these candidates are in a party, and the three parties are not particularly close to the median since parties don't tend to be right in the center.

Voter X is very much aligned with the ideological position of D and D's party, while quite distant from the other two candidates and parties.

The question is, in which scenario is voter X "more represented"? (and by extension, in which scenario is X better off?)

In the first scenario (which elects A, B and C), voter X is approximately equally represented by all three elected candidates. X neither loves nor hates any of the three.

In the second (electing D, E and F), X likes D a lot, but dislikes E and F.

[cfrank]

@rob I think certainly X achieves better representation in the second case. His interests are almost exactly embodied by one of the three candidates. So are the interests of the other voters near the two other candidates.

Ideally we would have a representative body whose ideological distribution is an informative compression of the electorate’s own distribution. Both centrist and more polar representatives would be present, not just one or the other. Middle ground representatives facilitate compromise while those further from the center contribute significantly to cognitive diversity and introduce issues to be compromised about.

This is just a half-formed spitball of an idea, but I think in the context of parties, it would be cool or at least interesting to have some kind of blocked and cross-over voting structure, where parties can win seats via at least two kinds of candidates, with one kind being elected solely from inside the party, and a second kind being elected solely from outside the party. This could basically set up a system of inter-party ambassadors and possibly encourage inter-communication and more compromise. In any case it would produce more representation of any ideological overlaps between parties.

[rob]

@cfrank said in Defining "degree of representation" in multi-winner elections:

@rob I think certainly X achieves better representation in the second case. His interests are almost exactly embodied by one of the three candidates.

So is it fair to say that, by your definition of representation, you only consider "positive representation"? You don't factor in the "negative representation" effects of candidates E and F, which are also elected and are ideologically very distant from voter X? That is, your only consideration for whether a voter has representation is how many people on their side are elected, while how many people on the opposite side are ignored.

I mean, that's fair, if that's how you define representation. (I resist defining it myself because I don't tend to use the word in this context) So you can say "X has more representation in scenario 2, but also has more opposition." Since both scenarios average out to roughly the same ideological position, my own view is that it isn't clear whether X is better off or worse off with either scenario.

The term "cognitive diversity" sounds like a positive. But so does its opposite, "like-mindedness." I know you are a fan of the concept of consensus.... I think "like-mindedness" and "consensus" are related concepts.

If I was a shareholder in a corporation, and we voted for officers of the company, I know I would choose scenario 1. I think like-mindedness means they can execute more effectively and probably increase profits (or whatever goal the corporation had, such as if it is a non-profit). This is why companies under a benevolent dictator often do well, such as Apple under Steve Jobs. (not that I would have wanted to work under him!)

I also suspect scenario 1 would be particularly effective for nations dealing with an adversary. I think Putin is currently exploiting the fact that the US is far from "like minded."

My highest priority is to "turn down the heat" in government, so you'd probably understand why I prefer scenario 1.

Regardless, assuming you agree with my characterization above, we made some progress here by clarifying the term "representation" as you use it.

[cfrank]

@rob that is true that I am more concerned with positive representation in Congress, I think cognitive diversity is a safe way to “turn down heat” in government while simultaneously offering routes for important or novel issues to be addressed. In my opinion, agreements between individuals of dissimilar ideologies are often more substantial and less controversial than those between like-minded individuals. I think those are the kinds of agreements that should be influence legislation. When it comes to things that need to get done quickly, nonpartisan executive authority is needed and I think that’s what that branch of government is for.

[rob]

@cfrank said in Defining "degree of representation" in multi-winner elections:

I think cognitive diversity is a safe way to “turn down heat” in government

Can't understand how having a wider ideological spread is going to turn down the heat compared to having a bunch of moderates.

@cfrank said :

simultaneously offering routes for important or novel issues to be addressed

Only to be shot down (or at least watered down to the point of uselessness) by those on the other side.

And just because you have moderates doesn't mean you don't have novel ideas. I think that's an erroneous assumption. I do think novel ideas have a much better chance when you have people working together rather against each other.

@cfrank said:

In my opinion, agreements between individuals of dissimilar ideologies are often more substantial and less controversial than those between like-minded individuals.

Even when those "like-minded individuals" are like-minded by virtue of them tending to all be moderates/centrists?

I'm having a hard time seeing that. At least on the "less controversial".... centrists aren't known for being particularly controversial. It's one thing if they are like minded if they are in a social-media bubble or the like. This is the opposite of this. You are actually electing the least controversial candidates.

What I'm concerned about is situations, similar to today, where one party gets their way, then different people get elected, the balance shifts, and they undo what they did last time around. This seems far less likely when you have a bunch of moderates.

Maybe you could give an example of being "more substantial" while also being "less controversial." I'd say that typically, being substantial means it is a large change, and large changes are more likely to be controversial than small/evolutionary changes.

Anyway the one thing I can't figure out is how you advocate for consensualism while disliking like-mindedness. (or are you backing off on the consensus thing?) Because that's exactly what I'm advocating, electing consensus candidates.

[cfrank]

@rob I do think diversity can turn down the heat, since it will naturally introduce centrists and moderates. At the same time, individuals who are centrist will probably tend to have their own class of characteristic biases that can be checked by those further from the center. For example, centrists may consider certain issues unimportant, dismiss certain ways of thinking, be indecisive or even generally apathetic. I think it's better for the diverse perspectives to be heard and shot down by an equally diverse cohort than not to be heard at all. Rather than rely on a Condorcet method to identify the center, the moderate center could be allowed to emerge naturally.

I think novel ideas come from team work, and that cognitive diversity is the single most valuable resource available to a team. For example, teams have been shown repeatedly to outperform experts when it comes to solving hard and novel problems. Engagement with diversity tension and disagreement is what refines the directions of projects. It is true that teams tend to have fairly well-defined goals, so that there is naturally a degree of “like-mindedness” in a team. I think the goals of representative legislators should be to compromise to create laws that are congruent with the values and interests of their constituents.

Restricting to moderates might filter out the ideas and voices from less central ideological regions, which I think is bad, even if I disagree with what those voices might be saying. In fact, I think it's bad exactly because I might disagree with what those voices might be saying.

In terms of being more substantial and less controversial, I can only speak generally to the point that such agreements will be more informed and therefore more robust. I will try to think of an example but I am mostly operating on my own thoughts.

In terms of consensualism, I'm coming to believe that single-winner systems can't really accomplish that. I also think that allowing diversified representation would increase voter satisfaction and faith in government, since voters would be able to at least point to some group of people in office who more than just roughly embody their values in government, and know that their voices are being heard and addressed.

One can look at one of the core issues with our current system in Congress in two ways: one might think that the issue is a lack of moderation, or perhaps a lack of cognitive diversity. Both are true, I think, but I also think addressing cognitive diversity will naturally address the lack of moderation, and not necessarily the other way around.

[Toby Pereira]

Without getting into a definition of "representation" for now, I've always had the feeling that it's better to have a more diverse parliament that represents the electorate in a more proportional way than one that represents the electorate in the best way for a single candidate and then multiplying that by the number of candidates, if you see what I mean.

If you have single-winner constituencies and the single most representative candidate gets elected in each one, you could potentially end up with a lot of near-clones, and in a sense it seems to make having a large parliament a bit pointless.

In fact, it probably wouldn't end up that way because of geographical differences in voting behaviour, but that brings me onto the next point, which I believe is similar to that raised by @Andy-Dienes in the thread that this is an off-shoot from. You can get very different parliaments with exactly the same voting behaviour purely depending on the geographical distribution of the voters. You could end up with a bunch of near clones if there isn't much geographical difference in voter behaviour, or you could end up with something close to PR if you get geographical clusters of voters, or more likely something in between.

But since representatives make up the national parliament rather than simply act as an isolated representative for a group of people, I don't think such potential variation based on the same ballots is good voting method behaviour.

I think a method that gives similar results regardless of how one jumbles up the voters across the country is (all others things being equal) better than one that is very dependent on the geographical distribution of voters.

As Andy says, why split along geographical lines - why not let the voters just vote for what they want and the splits will come from that?

And as I said in the first paragraph, I think more diversity in parliament is good - and as for what diversity is, it's the diversity people vote for, not the predetermined things that people might have in mind like race, sex, age etc.

The "average" position in parliament is still going to be similar to what you'd have with Condorcet winners, but I think you'd get a wider range of issues considered and debated. It's not simply that you'd get "extreme" views and these would get voted down anyway. You'd get people raising people's consciousness on issues that might not otherwise be considered - issues that aren't based on "extreme" politics, but that people simply aren't very aware of and would be happy to support if they were.

And I'm not sure I would want too much like-mindedness in a parliament anyway. And I think you'd be more likely to get conforming behaviour where people go along with what they perceive to be the group view and don't question something until it becomes too late.

I think it's different for companies with their "benevolent dictator". Some companies succeed and some fail under a dictator, but a country is far too important to have the possibility of failing and you can't trust it to a dictatorship, even if in some cases it might work out.

[cfrank]

@toby-pereira I totally agree with you here. And a point to supplement or maybe just reiterate your stance on “benevolent dictators,” there’s a definite survivorship bias there. The business dictators who fail don’t show up in the news, while the ones who succeed are often lauded as geniuses without due regard for the role of pure luck or factors totally unrelated to their supposed acumen. The same goes for stock market investors—many who come out on top end up believing they have a special intuition to “outsmart” the market, but when compared with randomly generated portfolios, their inclinations usually fare no better, and often do worse (due to their relative lack of diversity, they are not as robust against market volatility).

So basically, when uncertainty is involved, failure doesn’t always indicate a poor strategy, not any more than success indicates a good one. This reduces my confidence that business dictatorships actually tend to promote the success of a company.