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

[Forest Simmons]

Very interesting questions!

With regard to the ISDA question ...

It would be very strange for most voters to use up all of their equal-first
options without including at least their favorite Smith candidate as a
compromise.

Indeed, it's hard to see how the frivolous top voting could happen without
the bottom preferences hijacking the determination of the Smith set.

But here's the way to look at it: the method is just agenda based chain
climbing in disguise.

Until you reach the worst Smith item on the agenda, everything is
irrelevant to the final outcome.

-Forest

On Wed, Feb 22, 2023, 1:25 PM Kristofer Munsterhjelm <km_elmet at t-online.de>
wrote:

> 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
>
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