24 April 2015

Applying the β distribution to voter characteristics

The first (and long) step in moving towards agent-based modeling is the creation of the agents themselves. While fictional, they must represent reality – meaning they need to behave like actual people. The main issue in voter modeling, however, is that since voting is private we do not know how individuals behave, only collections of voters – and we do not want them all to behave the exact same way. That is why one of the key elements of our work is the ability to create meaningful differences among our agents – particularly when it comes to the likes of issue positions and political engagement. 

The obvious difficulty is how to do that. In our model, many of our agents’ characteristics are limited to values between 0 and 1 (e.g., political positions, weights on given issues). Many standard distributions, such as the normal, would be cut off at these extremes, creating unrealistic “spikes” of extreme behaviour. We also cannot use uniform distributions, as the likelihood of individuals in a group looking somewhat the same (i.e., more around an average) seems much more reasonable than them looking uniformly different.

Which brings us to the β distribution. In a new paper, we discuss applying this family of distributions to voter characteristics. While there is great diversity in the potential shapes of these distributions - granting us the flexibility we need - in (likely) very extreme cases, the shape will not “look like” what we would expect. Therefore, one of our goals will be to somewhat constrain our selection of fixed values for α and β, based on as much empirical data as possible, to ensure we get this balance right.

A selection α-β combinations that generate “useful” distributions: