## The Voters Dilemma

Posted: 20th September 2014 by seanmathmodelguy in Blog

For the last few years the city of Toronto has proved to be a very complex political arena. Attempting to predict election outcomes while quantifying the overlapping federal, provincial and municipal mandates has proven to be virtually impossible. Seemingly contradictory polls and the rhythmic beat of political rhetoric only succeed in obfuscating the issues for voters.

As an applied mathematician I found the issue of contradictory polls fascinating and by using the variation between polls, I was able to extract the most likely voting distribution of those not being polled. A key point in that analysis is realization that many rapid polls can skew the demographic of those polled, giving the false impression that views held by a precious few are applicable throughout Toronto.

The recent successful prediction of the US presidential election in contraction to many pundits is a testament to the predictive power of a well posed model and the luxury of a vast number of polls that can be systematically weighted according to their historically proven reliability. Unfortunately the mathematical theory of this approach falters when applied to the mayoral race in the city of Toronto due to a lack of data. With a significantly smaller number of polls, reconstruction of the true voting distribution is still possible but it must be done in a smarter way.

In my quest to attempt to build a prediction model for the mayoral race I have made some progress and had some insight as to some of the components that would be required. With respect to municipal politics in Toronto, one must contend with 44 virtually independent wards with their own unique set of issues. Prediction schemes that do not take this into account will simply not capture the multifaceted viewpoints presented at city council. If we also assume that voters are reasonable and only change their allegiance at isolated times then we nearly have a well-posed problem. What remains is to model a mechanism that instills changes in voting patterns. For this, inferring voter agency is key and is nuanced through how well an individual believes their issues are represented at city council contrasted with the block voting patterns of city councillors. The challenge is to treat the voting prediction as a hidden distribution that is simultaneously able to optimally recapture polling results while remaining faithful to the social-political reality of Toronto.

Direct evidence of just how contentious the voting public can be was made abundantly clear to me by watching a poll about policies be subverted into a conspiracy. Basically a textbook example of the politics of paranoia.

Searching for solutions that optimally resolve seemingly contradictory information rather than focussing on the contractions directly is a common theme in mathematics. With all mathematical models, they are only as good as the quality of the data they hope to model. By being well-informed of the issues and open to all sides of the debate the true voting distribution of Toronto can be revealed.