Journal Club - Proportionality and Strategyproofness in Multiwinner Elections
So, it may not completely shock you to learn I try and spend some time reading academic papers relevant to my interests reasonably often. In a perfect world, every day -- but this world is far from perfect. Nonetheless, I was reading a totally unrelated thing (about the use of SAT solvers in academia -- that doesn't really matter for this discussion) when I was linked to this paper.
What does it say? #
It begins by pointing out a weakness of approval voting: it can fail to be even approximately proportional. If you select 3 winners, 51% approve {a, b, c} and 49% approve {d}, you'll choose {a, b, c}, even though, intuitively, seems like d should be in the winner set, as >1/3 of voters approved only of d. It shows a classic correction to this (based on diminishing returns of multi-winner states) that leads to the election being vulnerable to strategic voting or manipulation. Notably, the strategy of not approving someone you'd like to see as a winner, to improve the chance of getting what you want. The paper is about providing an upper bound on how these combine, notably that even weak forms of proportionality and strategyproofness cannot coexist.
You might think we want to avoid strategies that get a higher number of approved members on the committee. Those are the most obvious to want to avoid. But you can weaken this to, don't have strategies where the number of approved candidates goes up by simply adding additional winners to what they'd otherwise get. Then you can weaken that even further to say, let's only prevent strategies where people don't lose the candidates they'd otherwise get, and just get more candidates they approve of as winners, and only because they failed to list some candidates they actually like and did no other tactic. I think you'll agree that this is pretty straight-forward: they're not trying to prevent all strategies, but really just one: pretending a candidate they like is one they don't like, so if they're selected anyway, they can (in analogy) say "well, I didn't get anyone I want, at least include one". This is called Hylland free riding, and you can understand how the "I didn't get anything I wanted, you should include at least one" sounds a lot like what proportionality will ensure.
The proportionality requirement is surprisingly weak though. It's literally that, in the case where everyone is party-line voting for k candidates, if at least 1/k of the people vote solely for candidate c, then c should be in the winner pool. It's only for when people vote party-line (so either people completely agree or completely disagree on candidates), only for the single-approval case, and only when that exact ballot gets enough votes to reasonably deserve the seat. That's enough to trigger the impossibility.
The result also holds if the proportionality requirement is simply that, if there are few enough parties that they can all get a seat, every party does get a seat, even if we throw out any other sense in which it might be proportional or representative. These are really small asks, and that neither is possible alongside strategyproofness is surprising, even to me, and I've seen plenty of social choice theory impossibility proofs. (For technical reasons they have to include the rule that if someone wins, at least one voter approved of them -- reasonably so.)
Unsurprisingly, this holds when the number of winners is 3 or more, and at least one person has to not-win -- simpler voting systems have their own impossibilities -- but fascinatingly appears to require the number of voters is a multiple of the number of winners. Extremely weird, and the authors appear to think this might disappear as the number of voters increases.
In practice, you'd have to be extremely strategic to have a strategy that relies on the precise number of voters in a real election, but conversely you'd have to be extremely meta-rules oriented to have a rule saying we'll adapt the vote counting policy to be the only one meeting requirements A, B, and C depending on how many people vote. In balance, we should take the claim of tradeoffs seriously.
Why did this catch my eye? #
Because I've been reading about how decision-making in animal brains might well be modelled with something like this. We have many internal systems that encourage us towards the variety of things we care about, and wish to balance those against each other to decide on the multiplicity of things we're actually working towards on any given day (or moment).
The analogy might be somewhat strained, but consider: weak efficiency, in this metaphor, implies that if you do something there is some reason you wanted to do that. I think this is true and non-trivial enough that I think some people would benefit from hearing it. Strategyproofness, as formulated above, is about avoiding internal motivations from artificially demotivating you to more closer steer behavior (I think anyone who regularly uses their phone in bed can attest it seems like a plausible risk -- you could scroll social media just as well on the exercise bike). And the proportionality requirement suggests, as a metaphorical counterpart, that we make time for all high-bidding activities in the medium-term, a very much desirable trait we also see ourselves failing at occassionally. To learn these are mutually incompatible, in a deep sense, is useful knowledge. And since it's not true of decision-making in general, only this sort of decision-making, I think it's probably worth bringing to the attention of others.
I think a lot of ink has been spilled about akrasia, willpower, and the techniques people use to try and align moment-to-moment preferences with meta-preferences or preferences abstracted from time (what I want to want, or what I want to have done, respectively). Perhaps that approach isn't getting the impact we want because we are not seriously considering the diplomatic work of trying to align ourselves in this way. I do not think Internal Family Systems is precisely what I would recommend -- it sounds like the precise type of procedurally generated faux-internal-depth that can be very distracting for little purpose at all. If there aren't big thoughts motivating someone's addiction, I think you can probably handle those impulses as though they're thoughtless, as a professional would (slowly ramp down dosage until eliminated, the impulse lagging but dropping over time as well).
But perhaps more interestingly, I think this also hints that we could do the opposite: cultivate desire for the things we wish to seek. I think very few people are competent at this -- they will fail to notice what the assignment even is -- but some people succeed. I am not aware of a great deal of non-social ways to achieve this, but not none. I encourage you to brainstorm how you have built interests in the past. I think people deny we can learn to love things, even as they have a personal history of acquired tastes and hobbies they adopted as adults.
If this paper gives any hints, in my metaphor, it's that you might want to deliberately avoid making space for strategic demotivation (strict approval voting), even if that means neglecting comparatively minor concerns. Or the opposite! (For instance, trying to address all concerns at their level of seeming importance regardless of demotivation.) But I think not choosing a strategy is leaving people making weird tradeoffs they don't intend.