Description:

If you live in a country that is governed by electoral democracy, you probably have noticed that sometimes a system that is supposed to elect the leaders most preferable to its population seems to do the exact opposite. Even worse, most of the time these outcomes aren't due to fraud or voter manipulation, they are the result of the system working exactly as designed. 

As with many structural issues, it's easy to resign oneself to saying that these issues with democracy are deeply ingrained in the fabric of society-- that making meaningful change will require a total overhaul of education, of government, of the media, of economic systems. Though there may be some truth to this perspective, it does risk turning problems that are solvable into seemingly almost immutable characteristics of the social world.

This is where mathematical methods come in. If we can identify the incentives and outcomes we think are undemocratic and build the appropriate measurements to identify and capture them, we can sometimes construct new systems of social choice that, purely by the way they are designed, disincentivize or even prohibit these kinds of outcomes. 

In this course, we look at two different social choice issues from this mathematical perspective. First, we investigate systems of voting, and investigate what kinds of desriable properties various alternative voting systems may or may not have. We describe when seemingly reasonable notions of fairness actually secretly contradict one another, and how careful uses of mathematics can help us find an achievable middle ground. Then, we move on to the much more complicated issue of redistricting, and the way that geography and the distribution of people across a country can impact their political power. 

Neither of these issues has a purely mathematical solution, nor can we propose a 'perfect' and fair system, but through this analysis we can learn how to precisely imagine and describe which alternatives are possible.

Background Needed:

Some simple algebraic manipulation and the ability to read graphs needed. Knowledge of currently implemented voting systems in representative and/or parliamentary democracies encouraged.

Soft Skills Learned Along the Way:

Set theory and basic proof writing, propositional logic, compuational sampling, mathematics communication.

Disclaimer:

Parts of the content of this course has been slightly simplified or given in slightly less generality than possible for the intended audience. A more accurate and nuanced version of the material can be found in the textbooks and papers referenced.

This page contains materials originally designed on a Canvas site. Some references to this remain.