The Roots of the Equation

Discrete Math and Democracy, Week 2

So we ended the first week with a proof of May’s Theorem, but really only in the case of an even number of votes. I assigned the proof with an odd number for homework, and none of them where able to quite get it on their own but a majority got close.

(As an aside, here’s the chart I mentioned that we did in the previous post, but filled in.)

Then we started talking about voting systems with three or more candidates. In particular, not only how to tabulate the winner by hand, but how to tabulate automatically using spreadsheets. First, the slides:

When I first worked on these problems over the summer, my spreadsheet solutions were definitely…inelegant, let’s say. Compare what I did then vs. what I did this week with the students.

Summer: https://docs.google.com/spreadsheets/d/1Z0s_cQ9vAUZRDTXB_8BFCNlbjrrjVo8aoW8fjm9XH7Y/edit?gid=2074741057#gid=2074741057

Better: https://docs.google.com/spreadsheets/d/11XoeRwnayoBUOO6psc2n4fGoKtOrDIDmWzkNwLCMKGE/edit?gid=0#gid=0

What’s especially nice about the newer version is how it displays who wins or is eliminated in a particular round – learning the XLOOKUP command was pretty hand.

Anyway, going through those methods and implementing them in spreadsheets took the whole week, on top of additional practice with the second election preference schedule. (We did the Apple one as a class and then I assigned them the Alli/Bell/Choi/Diaz one to do on their own.)