[EM] Modeling Voters for Discussion and Simulation

[Brian Olson]

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/