[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Mon, Jan 17, 2022 at 7:18 AM Colin Champion
<colin.champion at routemaster.app> wrote:

> Daniel – I’m a little unreassured by your figures, but it’s perfectly
> possible that the error is my own.
>

Yeah. I would take that last table of numbers with a huge grain of salt.
I'm ok with using the spatial model to get a rough measure of how easy it
is to manipulate the election, but I haven't studied the subject enough to
trust that I understand the rest. Speaking of not understanding, your page
says:

"Voters and candidates are drawn from the same mixture of 3 two-dimensional
gaussian components."

I don't understand what this means. In my program voters and candidates lie
in an N-dimensional issue space (N=4 in my last email) and each coordinate
is drawn from a standard normal distribution. So it's a multivariate
gaussian where the covariance is the identity matrix. Is your program
similar? I'm looking at your code (thank you for posting it) and I can't
figure out where the voters and candidates are generated.



    It’s true that false cycles were my example (based on my preference
> for minimax) but similar phenomena occur elsewhere. Condorcet/Hare comes
> pretty close to minimax for percentage correct under burying (and
> outperforms ranked pairs) while looking much worse than both methods
> under Euclidean loss. My explanation was that IRV makes huge errors
> under sincere voting (see Table 2) and this property is bound to carry
> through.
>

I just edited my program so it prints the Eucledian loss for sincere vs
tactical voting, but so far I cannot reproduce your result. The Eucledian
loss I get for Smith/IRV, Benham, Minimax, and IRV are not very different.
I might need to make a lot of changes to reproduce your result (e.g. number
of voters, number of dimensions, number of candidates, choice of tactics).

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