[EM] Hey guys, look at this...

[Kristofer Munsterhjelm]

On 22.02.2023 19:44, Forest Simmons wrote:

> This formulation with the top and bottom counts determined before any 
> candidates are stricken from the list ... makes for a method that is 
> (unlike IRV) a one pass, precinct summable, monotonic method.
> 
> Did I mention clone proof and ISDA?

That does sound pretty good (and I may have to check it in detail, or if 
it could be used to move Friendly closer to ISDA). But from a cursory 
glance, if top count is used for the initial order, would it pass ISDA? 
Imagine the "everybody ranks himself first as a write-in" idea: all of 
the single first preference candidates are Smith-dominated, but they 
completely obscure the top counts (first preferences). So the bottom 
count tiebreaker would be used, which would presumably give a different 
order than the top count with Smith candidates eliminated.

In any case, by referring to vNM utilities, I was thinking of methods 
that take preference strength into account. Such a method must fail 
Condorcet, much less ISDA. Consider the usual weak centrist vs Condorcet 
winner contention point, our ordinary LCR with a very weak C-first count:

50: L>C>R
40: R>C>L
  5: C>R>L

IRVists say C must lose because C is a milquetoast baby-kissing 
candidate. Condorcet proponents say that C still beats everybody else 
one-on-one. With preference strengths, we could theoretically 
distinguish the strong centrist scenario:

50: L (9) C (8) R (0)
40: R (9) C (8) L (0)
  5: C (9) R (3) L (0)

from the weak centrist:

50: L (9) C (1) R (0)
40: R (9) C (1) L (0)
  5: C (9) R (3) L (0)

and elect the CW in the first scenario but not the second -- at least as 
long as the method's strategic distortions aren't too severe.

(An interesting side question would be: suppose we have a two-player game:
50: L (9) C (x) R (0)
40: R (9) C (y) L (0)
  5: C (9) R (3) L (0)
where the two players are the L and R factions and their moves are 
choosing some value for x or y. For which lp-norm cumulative vote 
methods is the Nash equilibrium significantly different for strong and 
weak centrists, so that the method can tell them apart even under 
strategy? I've heard that Euclidean normalization is particularly 
strategy resistant, but I haven't verified this.)

-km