[EM] A thought about manipulability

[Kristofer Munsterhjelm]

On 6/26/23 02:14, Forest Simmons wrote:
> It seems to me that impartial culture is a very tenuous assumption for 
> public elections ... even less realistic than Yee diagram culture which 
> is generically cycle free ... not just free of a top cycle.

Yes; spatial models are probably the closest model we have, although 
they could be improved - e.g. voters may have a distribution of belief 
of the position of some given candidate, not just a point estimate, so 
that complete unknowns' positions are, well, unknown. Then they may be 
risk averse, which leads to a penalty to candidates who for some reason 
or other haven't got their position out there.

The question is more, I think, whether impartial culture is a good 
challenge for methods... a sort of "very hard difficulty" mode because 
it's more liable to produce near-ties than real elections, with the idea 
that if a method can handle anything IC has to throw at it, then it can 
definitely handle the real world...

... or if IC contains distortions that make it the wrong model to use, 
so that optimizing for strategy resistance with IC may lead to more 
real-world strategy vulnerability.

Complicating this is of course that don't even know how hardened a 
method has to be. If it's as weak as Plurality, we know it leads to 
Duverger. (I also think that IRV's center squeeze failure shows that it 
isn't good enough either.) But would Minmax or Ranked Pairs lead to 
stability and/or multi-party rule, or do single-member districts 
inherently lead to concentration? It's hard to tell, though top two 
runoffs in France (and Greek historical Approval use) seems to suggest 
that not all single-winner methods produce two-party rule. And Debian's 
use of Schulze seems to (weakly) suggest it's less likely to blowing up 
in one's face than IRV. At least such explosions aren't severe enough to 
lead to calls for a repeal.

If everything single-member does produce k-party rule then we don't 
really need to care about strategic situations involving more than k 
viable candidates. If honest Condorcet cycles are not just rare today 
(obviously they're rare with two-party rule), but will always be rare, 
then there's not much need to care about VSE for multi-Smith set 
situations. Etc...

But we don't know.

-km