[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Mon, Jan 10, 2022 at 11:27 AM Kristofer Munsterhjelm <
km_elmet at t-online.de> wrote:

> On 10.01.2022 01:14, Daniel Carrera wrote:
>
> > Hmm... The numbers I'm getting are a lot smaller than those in the
> > paper. I'm using Benham, V=99, N=1, C=6 and the voters and candidates
> > follow a standard normal, just as in the paper. I chose those parameters
> > because Table 1 gives a strategic susceptibility of 0.622 which should
> > be easy to detect, but I'm only getting 0.00196; so off by over two
> > orders of magnitude. I don't have as many iterations (numiter =
> > 100, strategy_iters = 100) but that should not change the overall scale.
>
> Try using impartial culture (every preference order is equally likely;
> just do a standard shuffle on the order of candidates to get the ballot
> order) and both iter counts = 1000. This should be easier to test than
> Gaussian; I remember I got different results than JGA on Gaussian myself.
>
> For comparison purposes, here are some results from quadelect for
> Condorcet,IRV. The ranges are a 95% c.i.:
>
> Gaussian, sigma = 0.2: 15 voters, 3 candidates: 0.0784-0.0862
> Gaussian, sigma = 0.2: 30 voters, 3 candidates: 0.0784-0.0862
> Gaussian, sigma = 0.2: 100 voters, 3 candidates: 0.0404-0.0462
> Gaussian, sigma = 0.2: 1000 voters, 3 candidates: 0.0256-0.0303
>
> Impartial culture: 15 voters, 3 candidates: 0.1101-0.1191
> Impartial culture: 30 voters, 3 candidates: 0.1491-0.1593
> Impartial culture: 100 voters, 3 candidates: 0.2428-0.2550
> Impartial culture: 1000 voters, 3 candidates: 0.1588-0.1692
>
> And to try to reproduce JGA's results under impartial culture:
>
> 29 voters, 3 candidates: 0.1363-0.1461 (JGA: 0.099)
> 29 voters, 4 candidates: 0.2838-0.2967 (JGA: 0.188)
> 29 voters, 5 candidates: 0.3936-0.4074 (JGA: 0.282)
> 29 voters, 6 candidates: 0.5065-0.5206 (JGA: 0.355)
> 29 voters, 7 candidates: 0.5761-0.5901
>
> The JGA figures aren't entirely comparable because they're for Benham,
> Woodall, and Smith-IRV, while one would expect Condorcet-IRV to be
> slightly more manipulable. I probably get higher values because I'm not
> restricted to a single ballot for the strategizers' choice.
>
> And 99 voters:
>
> 3 candidates: 0.1353-0.1451 (JGA: 0.088)
> 4 candidates: 0.261-0.2735  (JGA: 0.180)
> 5 candidates: 0.3779-0.3916 (JGA: 0.255)
> 6 candidates: 0.4602-0.4743 (JGA: 0.312)
> 7 candidates: 0.5245-0.5386
>
> This is with numiters=1000, strategy_iters=512.
>
> > It's hard to see how randomly shuffling ballots would be a strategy. I
> > tried changing the strategy: after the random ballot is generated,
> > candidate c_k is moved to the top and w_A to the bottom.
>
> It sounds like you interpreted my "random preference order" to mean
> "some other random ballot in that election"... I mean just a random
> preference order (drawn from impartial culture).


No, I understood that part. However, looking at your pseudocode again, I
just realized that you choose the random ballot once per strategy_iters and
reuse that ballot for every single voter that did not prefer w_A:

for 1...strategy_iters:
        e_B = e_A
        b_B = random preference order
        for every ballot B in e_B:
                if B ranks c_k ahead of w_A:
                        B = b_B
        w_B = winner of e_B according to method M
                if w_B = c_k:
                        then strategy successful

That makes a lot more sense now. Now I see what the paper means when it
says that it gets every voter in the strategic coalition to cast the same
ballot. When I read your first pseudocode I thought it meant that every
single voter with c_k > w_A would draw a different random permutation. So
you see why I was confused and why it didn't work. So I fixed this, and
fixed other bugs. I also followed your advice and switched to "impartial
culture".

Impartial culture: 15 voters, 3 candidates:

Your result:  0.1101-0.1191
My result:  ~0.06

So I'm still off by a fair bit, but at least now I'm in the correct
magnitude range. I'm going to look around to see if I find another bug.

Cheers,
-- 
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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