LGRT 1681
Mathematics has many different ways of distinguishing “big” sets from “small” sets. I will introduce another, ultrafilters, and discuss their definition, construction, and some properties. Next, we will discuss different systems of voting, and criteria that good voting systems should follow. This is particularly relevant currently as many cities and states consider switching to ranked-choice voting. Massachusetts recently voted against a switch to ranked choice voting in 2020. Finally, we will see how the ultrafilter is surprisingly relevant to these considerations by using one to show that (ordinal) ranked-choice voting, while arguably an improvement over traditional first-past-the-post voting, is still a mathematically imperfect system.