[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

On 12.01.2022 20:47, Daniel Carrera wrote:
> 
> 
> On Wed, Jan 12, 2022 at 5:01 AM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>     Yeah, you would think so, but in practice it seems to work pretty well.
>     Perhaps this is an indication that if an election is susceptible to
>     strategy, the strategy usually is not very exotic?
> 
> 
> 
> That certainly seems to be the case. Yesterday I also added a "simple
> strategy" check where the ballot puts c_k at the top, w_A at the bottom,
> and the other candidates are randomized. So in my loop I first check
> whether that strategy works, and if it doesn't, I apply JGA's method,
> and I just keep track of that.

Maybe you could get a (very slight?) improvement by ranking the
candidates in reverse social order, e.g. if A is the winner and the
social order is A>B>C>D>E>F, then the B>A faction votes B>F>E>D>C>A.

Could be worth a try, at least; but 92% of the time for a 6-candidate
election is already pretty good!

Also, for IRV in particular, there's a shared ballot (JGA setting)
manipulation algorithm with worst case complexity of O(phi^c) where phi
is the golden ratio and c is the number of candidates.
https://courses.cs.duke.edu/fall09/cps296.1/csecon_hardness_barrier_to_manipulation.ppt

> I noticed that the simple strategy always worked, but I paid no heed
> because at the time I was doing tests with C=3 and the impartial
> model. But today I implemented the spatial model and ran several
> tests with more candidates and it really looks like the simple
> strategy works *almost* every time that JGA's method works:
> 
> Spatial model + Benham
> V=29, C=3 --> 0.1233-0.1365 (95% c.i.), simple=1.00, majority=0.73
> V=29, C=4 --> 0.2811-0.2989 (95% c.i.), simple=0.97, majority=0.52
> V=29, C=5 --> 0.4186-0.4384 (95% c.i.), simple=0.94, majority=0.37
> V=29, C=6 --> 0.5388-0.5575 (95% c.i.), simple=0.92, majority=0.26

That's odd: the results are quite close to my impartial culture ones,
and significantly removed from JGA's spatial model ones for IRV. Do you
get results closer to JGA's for V=99? Page 7 has the IRV spatial model
manip rates be around 10% at V=99, C=6; somewhat more with a low number
of dimensions.

-km