[EM] Method X, bummer

[Kristofer Munsterhjelm]

On 8/5/23 19:21, Forest Simmons wrote:

> Do you consider Implicit Approval Chain Climbing to be burial resistant?

The "just barely" nature of implicit approval makes methods that use it 
a little unsatisfactory to me. I'd like methods to degrade gracefully in 
the sense that if everybody provides a full preference order, then they 
don't result in a perfect tie; and they don't give undue power to a 
single voter who doesn't provide a full preference order.

I guess that more generally, I consider honest equal-rank to be a voter 
saying "My opinions about A and B are so close it's not worth it to me 
to find out which it is"; and truncation to be "I know the rest are 
worse than those I listed, but I don't know much more about them".

Consider a voter whose honest full preference is A>B>C>D. The resistance 
of implicit approval methods, I would imagine (I haven't checked them), 
comes from that either the voter can say

A>B

which means "I want to direct some of my voting power to further 
separating {A, B} as acceptable candidates, from C and D, as less 
acceptable ones"; *or* that voter can say

A>B>C>D

meaning "I want to direct some of my voting power to be able to say 
that, even though I dislike both C and D, I still prefer C to D". The 
voter has to economize between the two and can't do both at once, which 
limits burial.

But this kind of underlying rationing of voting power introduces the 
problem of Approval - not just that there are multiple honest ballots, 
but that sincere voters have to deliberate *which* they should choose, 
because choosing the wrong one comes with consequences.

(Strictly speaking, any method with equal-rank and/or truncation has 
multiple honest ballots. But, at least to my mind, the stakes are lower 
when the method doesn't read a distribution of voting strength into 
which honest ballot the voter chooses to use.)


I haven't checked if implicit approval methods are burial resistant 
because I've been similarly focused on full preference domains for now, 
mainly IC. (I should write a spatial model, but haven't got around to do 
it.)

> In general, Agenda Based Chain Climbing is monotone when the agenda 
> formation is monotone ... so Borda and Kemeny Chain Climbing are also 
> Banks efficient monotone methods that are probably burial resistant, but 
> neither one is clone proof.

That sounds odd; I would imagine them to have the same "irrelevant 
candidate reordering problem" that IRV does. Perhaps I should code them 
up and see.

That problem is, e.g. suppose raising A on some ballot changes the 
ordering from ... > A > B > C > ... into ... > A > C > B > ..., then 
even though A wasn't harmed, this can affect A's opposition and possibly 
lead A to lose.

> In general, elimination with "take down" is Banks efficient ... but not 
> monotone unless based on a fixed (no renormalization between 
> eliminations) monotone agenda.
> 
> Implicit Approval is monotone and clone proof and UD, but just barely 
> UD. It is maddenly frustrating trying to find another UD monotone, clone 
> proof agenda forming method.

I think we'll need a more fundamental redesign, yes.

Perhaps X can be used for something else? I remember that Smith//IRV 
fails mono-add-plump; perhaps method X passes it? Or its "more monotone" 
nature can still be usable.

-km