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
On Mon, Jan 17, 2022 at 7:18 AM Colin Champion
<colin.champion@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
