[EM] 28 years of progress and a wakeup call

[Kristofer Munsterhjelm]

On 2024-05-21 22:30, robert bristow-johnson wrote:
> 
> 
>> On 05/21/2024 3:49 PM EDT Closed Limelike Curves <closed.limelike.curves at gmail.com> wrote:
>> This is true as long as voters use a strategy even a brain-dead
>> turnip could work out: set your approval threshold between the frontrunners.
> 
> But what are frontrunners?  How do you know who these candidates are
> under different ballot conditions?  Do you mean FPTP frontrunners?

I think the idea is somewhat like this. I haven't read the paper so I'm 
not sure I got it or its preconditions right. (There may be limits to 
convergence of the fixed point iteration mechanism.)

You do a preliminary Approval vote - a poll - without further 
instructions. The different voters' approval cutoffs fall at various 
points because there's zero info and the voters just do whatever.

Now suppose that the winner of the poll is A, and B is in second place.

Next poll, the voters set their cutoff to include A and exclude B (for 
those who prefer A to B) or to include B and exclude A (vice versa).

After this happens, candidate C has the highest approval count and D is 
in second place. Rinse and repeat.

Do this enough times and (if there's a CW,) some fixed-point candidate, 
W, will be in first place, and subsequent approval polls don't change 
who's the finisher and who comes in second. Then W is the Condorcet 
winner and nobody has any incentive to deviate from setting their 
approval cutoff between W and whoever comes in second.

Come the final election, people do as they did in the last poll, and 
then W, the Condorcet winner, wins.

So with Approval and enough polls, if there's a Condorcet winner (and 
given some assumptions about economic rationality) then Approval should 
find it. If there is a sincere cycle, then as I remarked, "round and 
round and round it goes; where it stops, nobody knows!" - the ultimate 
winner depends on the number of polls conducted and where the cycle started.

Or you could just run a Condorcet method and get the CW in one step 
without all this poll business.

Approval has very good method simplicity. But this process complexity -- 
sheesh, that's something else.

(Before someone says "but Monroe" -- IRV passes his criterion and I see 
no reason why a Condorcet prefix should void it.
Actual proofs that Condorcet does or doesn't void NIA would be welcome, 
of course... but checking NIA for a method that's part positional and 
part pairwise would require synthesizing Monroe's two pivotal strategy 
approaches, and that might be pretty tough.
In addition, "NIA-failing methods must fail in practice" does seem a bit 
counter to Debian's successful use of Schulze. Or the various other 
places and organizations that use it.)

> Lastly, I consider it disadvantageous to require any tactical 
> thinking or to incentivize any strategic thinking from voters.  Any
> more than what Arrow of Gibbard or Satterthwaite say we cannot get
> away from.

I agree. I find method complexity much more honest than process complexity.

We also really need a way to talk about process complexity in a 
principled way. When a method is intended to be the base layer of an 
induced method, then the properties of the base method can obscure the 
properties of the induced method.

E.g. if the iteration above settles into cycling between members of the 
essential set, then the induced method is nonmonotone, even if Approval 
itself is monotone. It is also nondeterministic[1] even if Approval isn't.

> This is why I am for strictly an ordinal ballot, where voters are
> not required to rank any candidate they don't want to rank, and
> where possible equal rankings are allowed (this is one reason I have
> sorta soured regarding BTR-IRV), and the Condorcet winner should
> always be elected whenever such candidate exists.

You could use fractional counting, e.g. if someone votes A=B>C, he gives 
half a point to A and half to B. Once either A or B is eliminated, the 
vote counts fully for the other candidate. Delemazure and Peters say 
that this way of handling ties may break clone independence 
(https://arxiv.org/abs/2404.11407), but BTR-IRV already fails it.

> I am still not committed about which Condorcet method, but, besides
> disincentivizing strategic or tactical voting, I am
> also concerned about the quality and conciseness of the legislative
> language to describe the method (that was the sole reason I had
> previously considered BTR-IRV).

A very simple modification to IRV would be Condorcet//IRV. Do you think 
that could work? Benham is better but needs more explanation.

The problem with Condorcet//IRV is that it's not cloneproof, and 
furthermore it fails in a very obvious way: clone the CW into a 
three-cycle and then C//IRV defaults to IRV, after which the cloned 
Condorcet winner can fail to be elected. Benham avoids that problem, but 
the Condorcet check has to be moved inside the loop, so to speak.

-km

[1] Or related to nondeterminism in the same way a pseudorandom number 
generator is related to actual randomness.