I've done a couple major runs of simulating voters and elections. I
think reviewing those models might help the discussion.
Most recently I've been doing the opinion space diagrams. They are
based on some two-dimensional world of political thought (possibly the
fiscal and social liberal-conservative axes that are sometimes
commented on, but more general than that it could be any issues).
Candidates and voters have various positions on these axes. The degree
to which a voter likes a candidate is directly proportional to the
nearness. "Closer to my views is better."
The candidates were placed by hand in a few configurations that seemed
interesting at the time. The populations of voters were gaussian
distributed around some central point. The results are here: http://bolson.org/voting/sim_one_seat/
Several years ago I started simulating by giving each voter a
uniformly distributed [-1.0 .. 1.0] opinion of each candidate. After
having done the spatial simulations, I think this is kinda lacking
because there's no consistency in how voters would asses various
choices. There would be no localities or coalitions. If I do these
over again, they'll be in various higher dimension opinion spaces (3+)
with randomly placed choices and voters, probably both with gaussian
distributions around some center. Without plotting the results, the
point would be to get bulk data about how often different methods
disagreed on the outcome.
One thing that a model of a voter as a collection of known opinions
that match up to choices or corresponding positions by choices means
that in the model voter intent and satisfaction is perfectly knowable.
In a recent post Mr Lomax brought up the topic of poorly informed
voters not being taken into account in various models, but I did
introduce such a factor in my early simulations. I added some amount
of 'error' as a uniformly distributed random variable to each opinion
a voter held and then voted based on that errant preference set. This
'error' factor could be interpreted as being misinformed, having
imperfect introspection, or having a ballot failure issue in the
polling place. Later summary happiness was measured based on the
original true preferences of each voter. Hopefully this should measure
how sensitive an election method is to these kinds of errors. And
indeed when graphed, my old favorite punching bag, IRV, did indeed
turn out to be more susceptible to error than other methods.
The old old results are here:
http://bolson.org/voting/sim.html
So, if I were to get around to it, I would go back to those bulk
simulations and run them based on a spatial model, probably in each of
3-8 dimensions to study the effect of dimensionality on the modeled
results. I might also separately study candidate-error and voter-
error. Candidate error would misrepresent their position to everyone
systemically, and voter error would affect each differently. Right now
I'd guess there's no solution for systemic candidate error but
different methods are more or less vulnerable to voter error.
Brian Olson
http://bolson.org/
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