[EM] A question about proportionality and... something else.

[Etjon Basha]

I'm unaware of Pereira's argument but it seems intuitively obvious that P33
and P67 are the optimal when picking two representatives.

I suppose there'd be no material difference between proportionality and
centrism in these simple models but in reality issues don't get decided one
by one in isolation, but in bundles, and in those cases, a proportional
assembly would (if at all it could) decide differently to a centrist one
and the practical outcomes would be quite different between the two.

Not to mention the nitty gritty of committee work, some of which might be
populated by skewed representations of the assembly by sheer chance in a
proportional system, a null issue under a proper centrist system, and so on.

If we ignore these issues, I see no difference between the Dutch and
Australian Assmeblies, and indeed no reason to have an assembly at all
beyond a single president (or perhaps a triumvirate of them).

Regards,


On Tue, 4 Nov 2025, 12:48 am Kristofer Munsterhjelm, <
km-elmet at munsterhjelm.no> wrote:

> On 2025-10-27 13:11, Etjon Basha wrote:
> > Sorry to hear Kristofer, I hope it's all resolved as best it can.
>
> I hope so too. Things are looking a bit better now, but I'm not sure
> yet. I'll try to reply to this, though, and hope I'm not pulled away again.
>
> > I'd say a qualified yes to both: at the extreme where random ballot is
> > used in the assembly (as opposed to electing the assembly itself), it
> > very much would matter how proportional the body is. Most would be quite
> > happy for a very majoritarian assembly in such conditions, I'd think, to
> > avoid the risk of being subjected to the vote of the 5% 5% of the time.
> >
> > At the other extreme of some complicated iteration of quadratic
> > negotiations or what have you, so some procedure that somehow irons out
> > all issues to produce an ultimately unanimous vote, proportionality
> > would also matter less.
> >
> > In practice neither of these two extremes apply, and so the
> > proportionality of the assembly matters to most, but in principle it
> > needs not.
> >
> > These are all ways to achieve utility, the intermediate steps are open
> > to improvement.
>
> What I found to be a problem with utility when I explored
> proportionality measures is that it's relatively weak.
>
> Here's an example: Suppose that the voter opinion distribution is a
> standard normal (i.e. one-dimensional). Suppose that the assembly
> reviews successive measures and that the representatives vote to accept
> or reject the measure by a majority vote.
>
> The people, could we ask all of them, will accept the measure if "yes"
> is closer to the mean/median opinion of zero than "no" is. But any
> assembly with an odd number of seats and a symmetric distribution of
> representatives around zero will also behave this way.
>
> So if a voter's utility for passing (failing) a measure is the negative
> of the distance between his position in opinion space and the measure's
> "yes" ("no") position in opinion space, then the balanced council
> accepts the measure iff the people does.
>
> In particular, the degenerate centrist case where every rep is at most
> an epsilon away from zero also does this, as long as the choice is
> symmetric around zero. So the model doesn't answer what level of PR is
> enough.
>
>
> As a simplification of what I'm (or was) trying to figure out, consider
> a similarly simple case: the people's opinion distribution is a standard
> normal, and just about every voter stands as a representative. The
> assembly has two seats, so by the argument above, the elected reps would
> be at quantiles 0.5-x and 0.5+x.
>
> But what is the correct level of PR? If x = 0, you get a pure
> centrist/bloc situation. x->0.5 gives a very polarized assembly. The
> k-median optimum is at 25% and 75%, and that's what Monroe does; but
> Toby Pereira argued that 33% and 67% is better (and he has a point).
>
>
> If I were asked what the benefits of PR are, I'd say that it keeps the
> representatives accountable, it keeps the factions from becoming too
> complacent, and allows shifting coalitions if the people's opinion space
> distribution is *not* simple.
>
> The first point is that the voters can see what the reps are accepting
> or rejecting, so they have a record of how each faction puts their money
> where their mouth is, so to speak. This can be hard to determine if all
> the negotiation happens inside the big-tent party.
>
> The second being that if we have a bunch of centrists, they may start to
> get sloppy because they're so ideologically similar; that they'll take
> each other's support for granted and thus may start to drift from the
> population's center. There's a lack of competition, so to speak, and
> it's worse if all the centrists come from the same party.
>
> And the third is pretty clear, and does happen in PR countries. But from
> a pure utility metric, one could imagine that sufficiently virtuous
> centrists would do this "inside their own heads", and track the popular
> center because that's what they were elected to do.
>
> But at least the first two of these points are hard to formalize and do
> simulations about. We could add parameters and say, suppose that similar
> reps lose contact with reality or get corrupted at some given rate, but
> different parameter choices would give different results about how much
> PR is too much: where the drawbacks of increased polarization start to
> outweigh the benefits of increased diversity of the representatives'
> positions.
>
> -km
>
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