The Roots of the Equation

I totally purposefully combined these two weeks because they were short due to holidays, and not because I forgot about week 3. Yep.

First was our first quiz on what we covered in the first 7 days. (My quizzes are always slightly lagging, in all of my classes.) It was…longer than I anticipated. I think my usual metric for how long students need for work doesn’t apply to this class, because it’s so new to them. It was also testing some spreadsheet commands they needed to learn, so I made it an online quiz. I did it by sharing it through Google Classroom, highlighting cells they needed to fill in, and having them turn off their Wi-Fi once they opened the quiz. See below:

https://docs.google.com/spreadsheets/d/1qyLIkmBhQqvS-Zk4VsEivnQuTDUsYn_-BPJbXpW5iFw/edit?usp=sharing

We started off my returning to some of the criteria we looked at for two-candidate systems, now applied to the multi-candidate systems. We started filling out the chart in the first slide below.

We worked through counterexamples for why IRV/et al fails monotonicity, and why Borda and Survivor fail majority. I also discovered this website that both calculates winners and has a bunch of example elections, which has been very handy: https://rob-legrand.github.io/ranked-ballot-voting-calculator/

We also read this argument about why IRV failing monotonicity doesn’t matter: https://archive3.fairvote.org/reforms/instant-runoff-voting/irv-and-the-status-quo/how-instant-runoff-voting-compares-to-alternative-reforms/monotonicity-and-instant-runoff-voting/

Then we got to Condorcet, which took the bulk of our time. We learned how to make pairwise comparison matrices both by hand and using spreadsheets, which we see in the Pairwise Matrices tab of my example spreadsheet: https://docs.google.com/spreadsheets/d/11XoeRwnayoBUOO6psc2n4fGoKtOrDIDmWzkNwLCMKGE/edit?usp=sharing

This took the bulk of the time, and also I realized I needed to give more practice so we did more for the RCV election systems and the matrices.

The last thing we covered was using the pairwise matrix to find the Condorcet winner, loser, and also to resolve the results of a tournament/pairwise agenda election. We hinted at the idea that the person who sets the agenda/seeds the tournament has a lot of power to determine the winner, but that’s an idea we’ll dig into more this week.