[EM] Definite Approval/Disapproval

[Kristofer Munsterhjelm]

On 07.05.2022 07:20, Forest Simmons wrote:
> That's a good template for all of us to imitate in our outreach to the
> proletariat!

"Arise ye workers from your slumbers", eh? :-)

> Let me see how well I can imitate it for my latest attempt in the
> fpA-gpC vein:
> 
> Candidates are arranged into
> one-on-one match-ups like runoffs where the candidate who would win a
> runoff with only the two wins. If there is a candidate who wins every
> runoff he's part of, he is elected. 
> 
> Otherwise candidates get reward value for every matchup they win or tie,
> but lose value for every matchup they lose.
> 
> The candidate with the greatest net reward value is elected.
> 
> Specifically, a candidate's prize/reward value is proportional to its
> estimated formidability as an opponent in these matchups. You get your
> opponent's prize value when you defeat or tie him in a matchup.
> Otherwise, you pay out that value.
> 
> The formidability of a candidate is gauged as a function of its
> respective first and last place showings on the ballots.

Yeah, it would have to be something like that. For fpA - sum fpC:

A candidate starts out being as strong as his first preference votes,
but he loses strength by being beaten by other candidates, according to
*their* first preference votes. The strongest candidate wins.

On an aside, your definition makes me think of an interesting recursive
primitive for Condorcet-compliant methods. Suppose X's score is f(X) and
let f(X) be some monotone nondecreasing function of f of all the
candidates X beat (or the strongest such candidate). Then there exist
very broad subsets of monotone nondecreasing functions so that the CW
always wins by f score (e.g. sum or max, possibly any p-norm for p>=1 as
long as f(X) >= 0 for all X). Similar broad proofs can probably be had
for the case where f(X) is some monotone nonincreasing function of f of
the candidates who beat X pairwise. However, cycles would require
finding equilibrium points, which can be pretty hard to explain.

-km