[EM] Quick and Clean Burial Resistant Smith, compromise

[Kristofer Munsterhjelm]

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). So e.g. if the honest
ballots are

10: A>B>C
10: C>B>A
 1: B>A>C

and A wins, then one of the C>B>A ballots can well be replaced by say,
B>C>A even though that ballot occurs nowhere in the honest election.

> That simple strategy increases the susceptibility to 0.0785, but
> that's still one order of magnitude off from the paper.

>     https://electowiki.org/wiki/Raynaud
>     <https://electowiki.org/wiki/Raynaud> suggests that all versions of
>     Raynaud pass ISDA, including Raynaud(GL). I agree, it would be useful to
>     have a table, but it wouldn't be practical to render it for all criteria
>     defined on electowiki; it would need some kind of interactive component
>     so you could select just the criteria (and methods) that interest you.
> 
> 
> I shouldn't get distracted with this right now, but maybe in a few
> months I could make a Google spreadsheet --- a poor man's interactive
> database.
> 
> -- 
> Dr. Daniel Carrera
> Postdoctoral Research Associate
> Iowa State University