[EM] Gross loser method

[Kevin Venzke]

Hi Forest,

Le vendredi 28 janvier 2022, 00:06:19 UTC−6, Forest Simmons <forest.simmons21 at gmail.com> a écrit :
> It is so omputationally simple that a small child can do it manually, given a
> copy of the pairwise matrix:
>
> Let k be the row containing the smallest entry in the entire matrix. [Too hard
> for a small child to find?] Cross out both row k and column k. [Kids like this
> kind of work.] Repeat until only one entry remains. Elect the candidate whose
> row is not crossed out.

> This method is due to Benham's modification of a non-Condorcet method whose
> name slips my mind at the moment.

Sounds like it could be Chris' complicated "MinLV" Condorcet method which I
could imagine having been inspired by Woodall's "MinGS", which just elects
whichever candidate has the greatest minimum votes-for.

> The name might be "Gross Loser Elimination"
> 
> The Gross Loser is the candidate that comes closest to being skunked in a pairwise
> matchup.
> 
> Elect the candidate that remains after repeatedly eliminating the Gross Loser.
> 
> Eleven words ... perhaps the best possible RCV method that can be defined so
> unambiguously and succinctly.
> 
> No need to mention Smith, but the fact remains it always elects a Smith member.
> 
> Here's a classic example of Chicken Defense:
> 
> 49 C
> 26 A>B
> 25 B (sincere B>C)
> 
> B subverts the sincere CW (A) by a chicken defection that creates a cycle 
> 
> A>B>C>A
> 
> RP, Schulze, MinMax, River, etc reward the defector by breaking the cycle at the
> A>B step, which is the weakest majority (26 to 25), allowing the defector to win
> with impunity.

Here is some criticism of that.

1. The method doesn't know whether anybody is strategizing, so the method
punishes the B voters even when they themselves believe they are sincere.

2. The method does not only punish the strategizers, it punishes the entire
majority. The A voters as well are confronted with an incentive: to NOT vote for
A next time, or to at least rank B above A. We have a very similar incentive in
FPP.

Somehow one needs to show that it's more likely that this punishment threat
causes the whole B faction to add on sufficient A preferences, than that the
majority decides before the election not to play with fire, and they withdraw
one of the candidates.

Personally I think this punishment dynamic does nothing but deter nomination.

3. Look at what happens if we switch the sizes of the A>B and B factions. Now B
wins and is NOT punished for defecting. This tells me that we didn't actually
fix the issue, because "not both" factions are required to cooperate. A faction
that "knows" they are the larger of the two, is exempt.

Probably the only real "chicken dilemma-proof" method is DSC. There if the
majority does not form a mutual majority, they just aren't going to win.

Kevin