[EM] No luck with simple monotone Heaviside methods, but a surprising idea

[Kristofer Munsterhjelm]

On 12/21/22 21:54, Forest Simmons wrote:
> "To boldly go where no man has gone before!"
> 
> It takes a very tenacious mind... with bulldog tenacity... to pursue an 
> idea this far into the wild unknown!

As the bulldog, I'm reminded of Barry Mazur's quote about number theory: 
"number theory swarms with bugs waiting to bite the tempted 
flower-lovers who, once bitten, are inspired to excesses of effort!".

Something like that, but not number theory in my case :-)

I've investigated a bit further, and it seems like every method (that's 
manipulable to begin with) becomes manipulable with probability 100% 
with enough voters and the impartial culture model. If I were to guess, 
I'd say this has to do with the the margins A>B-B>A approach zero 
(assume A beats B pairwise wlog). So it's very easy to overturn a 
pairwise victory. Perhaps that could be used to show that you can always 
make someone else the CW, and then use Durand's result to show that 
other majority methods can be no better than Condorcet methods at 
resisting strategy.

Anyway... with a limited number of voters, quadelect shows that the best 
monotone method is not far off the best nonmonotone (only 6% more 
manipulable for 97 voters). But I can't reproduce this with my simple 
Python simulator. So one of the two, or both, are wrong, and that needs 
further examination...

... which I probably won't get around to this year. There ought to be 
time for relaxing and enjoying holidays too! Not just satisfying one's 
curiosity.

(Also, datapoints from others' simulators would be very useful. In 
particular, what's the manipulability of the "two candidates share a 
majority, then A>B" method of my last post?)

-km