[EM] Proof idea that IRV can't be summable

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Dec 4 02:45:01 PST 2020

On 03/12/2020 19.04, Kevin Venzke wrote:
> Le jeudi 3 décembre 2020 à 04:20:54 UTC−6, Kristofer Munsterhjelm
> <km_elmet at t-online.de> a écrit :

>> If told to create something democratic without concern to current 
>> constraints, I'd probably just skip right to sortition. This would
>> not just invalidate single-winner methods, but voting altogether;
>> except, possibly, the method the assembly itself uses to decide.

> In this exchange "democratic" must mean that the assembly's seats are
> allocated proportionally. This leaves the issue of allocation of
> actual policy-making power as you suggest.
> Maybe there is a way to determine policy proportionally, and without
> using randomness. I don't think it can be based on decay of
> individual delegates' voting power (because if you use your power
> sub-optimally you may fail to influence policy) or on how many things
> you vote on (because proposals could be clones of each other etc.).
> So it might have to be based on time... A faction gets an amount of
> time in power.

One of the benefits of sortition is that how well you represent an
opinion with, say, 10% support among the people depends entirely on the
assembly size, not on the number of people you're drawing from[1]. So
the same process works on a city level as on a global level, and has the
same fidelity (assuming the same assembly size).

That given, the assembly must necessarily contain people with a mix of
opinions. So there's no easy way to determine who a certain faction
belongs to, and thus to give different factions different power. It'd be
analogous to if you elected a bunch of nonpartisan Condorcet winners to
an assembly: they're all consensus candidates, so how could you find any
factions to sweep the power over, over time?

Time can be used to diminish variance, though. Suppose you have an
assembly that uses Heitzig's nondeterministic consensus method. Then I
wouldn't be surprised if there exists a way to downweight the candidates
who got their wish in one election for the next, so as to reduce the
total swing over time while still having the same asymptotic properties.
Or in pure sortition, you can replace, say, 1/8 of the assembly every
1/8th of the period instead of all at once.

In a slightly related vein, I read a paper once suggesting to use voting
rights instead of money in a Clarke-Tullock system. The members who get
their way have to abstain from future influence depending on how much it
cost them to overrule the others. I have my doubts about whether CTT can
ever be useful, but it illustrates the principle.

Warren also suggested a party list method using time-based reweighting:
since you can't give every MP power exactly reflecting the number of
voters who voted for them (without weighted parliamentary votes),
instead adjust the quota so that if each MP of one party has too little
power, then eventually that party will get one extra.

[1] It's not entirely true if the assembly is very large compared to the
population because you're drawing without replacement. But if that's the
case, you have few enough people that you can just use direct democracy.

> But realistically there is probably a minimum faction size you would
> want to allow to wield power. And to prevent whiplash you'd probably
> want a minimum amount of time that a faction could be in power. Could
> a faction representing 25% of the voters be allowed to set policy for
> even a year? If not, can we defend that without invoking the
> principle of majority rule? (I doubt it... And for me that is always
> the limitation, that no matter what, you have to implement majority
> rule somewhere in the process.)

That sounds like variance. Your mechanism swings too much; a good method
continuously tracks what the people want, and changes the composition of
the representatives (or their power) just enough to reflect that. Loring
once compared two-party rule to a pendulum. To quote:

" A political pendulum swings; it cuts down forests and species,
families and towns. Agencies and businesses often lose wealth when a
council changes hands and changes laws.  These reversals are a major
cause of war-like politics. "

Reducing variance/entropy mitigates that kind of thing. But it shouldn't
be so reduced so much that the people can no longer hold the assembly
accountable. It's hard to get the balance right.

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