[EM] Method X, bummer

[Kristofer Munsterhjelm]

On 8/7/23 12:13, Filip Ejlak wrote:
> A note concerning monotonicity testing - even when there is no possible 
> pushover strategy for a voter/group of voters, it doesn't necessarily 
> mean that a given method is monotone.
> In these examples, changing ABC to BAC makes C the winner, so the change 
> doesn't make sense from the voter's point of view and will go under the 
> radar of any strategy detector, I guess.

You're right; I was using the Other strategy count as a proxy for what I 
really wanted, because I hadn't implemented an actual monotonicity check 
yet. It seemed to work for IRV (clearly nonmonotone), Adjusted Condorect 
Plurality, and the other nonmonotone methods I tested it with.

I was actually thinking about this earlier today, by analogy to the 
independence of clones criterion. If we have a B>A ballot, change it to 
A>B, and the winner goes from B to A, that's pushover (analogous to the 
types of cloning that can be exploited by running more or fewer 
candidates). But if the winner changes from A to C, then it's like 
crowding: still a failure but harder to strategically exploit.

James Green-Armytage did more general nomination incentive simulations 
to determine the incentive to entry and exit. The reasoning above 
suggests that there's a third way that nomination can affect the 
outcome: unpredictably but not obviously to anyone's advantage. If his 
"incentive to exit" is a more robust vote-splitting metric, and his 
"incentive to entry" is a more robust teaming metric, then there may be 
an "instability due to nomination" metric that corresponds to crowding.

> Another thing is that there are some election scenarios which an 
> impartial/spatial simulator might never notice. For the purposes of 
> strategy/critetia testing it might be good to include, for example, a 
> ballot generator that will produce random-size groups of voters, rather 
> that drawing voters one-by-one like a standard impartial generator does.

If a method passes scale invariance, impartial culture should have a 
chance of happening upon correlated electorate failures. That is to say, 
if you have defined voting groups, something like

  97: A>B>C>D
103: B>A>C>D

then that's not too far off
   1: A>B>C>D
   1: B>A>C>D

if the voting method only cares about the relative proportion of voters. 
But more generally, it's a good point; models that just draw voters from 
some distribution will only generate correlated behavior by chance, so 
it might be a good idea to create models that generate deliberately 
correlated voting.

-km