[EM] A more general chicken dilemma

[Kevin Venzke]

Hi Kristofer,

Kristofer Munsterhjelm via Election-Methods <election-methods at lists.electorama.com> a écrit :
> I've been investigating different criteria lately, and the chicken
> dilemma criterion seems to apply to very few elections in general (as a
> proportion of the number of elections possible with a given number of
> voters).
> 
> So I was wondering if the following would be a good generalization:
> 
> The following is required for an election to be applicable:
>     - There are three candidates and three factions, call them A, B, and C.
> Each faction prefers its corresponding candidate to everybody else (but
> may rank others coequal top based on the method, e.g. if it's Approval).
>     - The number of C-voters who prefer A to B is equal to the number who
> prefer B to A (i.e. they have no meaningful preference between the two).
>     - If the A-voters and B-voters express a full ballot, then A wins.
> 
> Then for every applicable election:
>     - If the B-voters truncate above A, then B must not win, otherwise the
> criterion is failed.
> 
> What do you think?

I think it's probably fine, but have you really broadened things much?

For purposes of testing compliance, you may find it difficult to cover all cases
of who is *or might be* an A-voter or B-voter, if they are ranking candidates
equal-top.

It is interesting, seeing it described like this, to wonder why the C voters
matter at all.

Your phrasing also makes one of my criticisms less intuitive. I tend to think it's
blatant cheating to require

- If the B-voters truncate above A, then B must not win

and not also require

- If the A-voters truncate above B, then A must not win

because I conceive of the situation as an A/B mutual majority which has to hang
together or else C wins as punishment.

But with your wording it's not clear that the B voters are even playing a role in
A's victory. If A can win single-handedly, why would those voters owe anything to
candidate B?

To me, a criterion with this name and concept should just say something like:

"If mutual majority doesn't apply, then the first-preference winner wins."
(otherwise follow mutual majority)

This waives the punishment if the first preference winner is part of the supposed
mutual majority, but otherwise it probably gets the punishment right.

Kevin
votingmethods.net