[EM] A Path to Success

[Kristofer Munsterhjelm]

On 3/9/23 23:14, Forest Simmons wrote:
> Kristofer suggested introducing a sequence of methods m0,  m1, m2, ... 
> forming a path of small steps gradually progressing from some simple 
> method m0 towards some ideal end method m_infinity.
> 
> Any ideas?

Here are some:

BTR-IRV to Benham (if the voters don't care about monotonicity or 
summability);
first preference Copeland to Benham (if they care about strategy 
resistance but not monotonicity);
Minmax to Schulze, Ranked Pairs or River (if failing Condorcet loser is 
not too tough a sell); possibly to some uncovered RP variant after this?
STAR to Smith,Range or Smith|Range (for cardinal ballots; X|Y is just 
notation I made up now for renormalizing after excluding everybody in 
the X set as I couldn't find a better designation for it)

These are all finite sequences. /Perhaps/ Approval -> STAR -> 
Smith,Range would work, but it would require a ballot format change.

On a related subject, as I understand it, FairVote likes to point out 
that their preferred single-winner method is a stepping stone to 
multiwinner. The IRV-likes above easily generalize to STV by adding the 
surplus election and redistribution steps, e.g. STV-ME (BTR-IV).

I once devised a multiwinner Ranked Pairs method with a polynomial 
runtime (in the number of voters and candidates), but in practice the 
polynomial is too large for large elections; it requires solving large 
linear programs. There's also CPO-STV and Schulze STV, but they're very 
complex.

Range has PRV, so possibly something like PRV -> Sequential Monroe -> 
Monroe (or PRV -> Sequential Ebert -> Ebert). For Majority Judgement or 
Bucklin there's BTV/EAR and my MCAB (though the latter is also pretty 
complex).

Condorcet methods in general? STV-CLE, but it feels kind of like 
cheating; the step from Condorcet to bolting it onto STV may feel a bit 
too artificial.

-km