Adventures in Democratic Decision Making
Though often taken for granted, democratic institutions have been subject to change and tinkering since their early days. The aim of the course is to look under the bonnet of voting systems, juries and apportionment rules, and see how the rules of the game have been questioned and refined over time. We will focus on a series of notable moments in democratic decision making, starting in Ancient Greece and ending with present day efforts to find a perfectly proportional representation system. The course will mainly follow George Szpiro’s Numbers Rule. The Vexing Mathematics of Democracy, from Plato to the Present, and structured as a series of weekly discussions on each chapter in the book. There will also be additional material on recent developments and trends.
Lectures
Week 1 (October 14, 2024)
We start out by introducing ourselves, followed by a breakdown of the logistics of the course. Main points are summarized in the slides, here.
We then have our first glimpse of social choice theory, and two ways of thinking about voting: as a procedure for finding society’s opinion about an unknown ground truth (epistemic voting), versus as a procedure for aggregating preferences into an expression of what voters want (non-epistemic voting). Slides here.
Week 2 (October 21, 2024)
We look at an early example of a functioning democracy: Ancient Athens. We see how Athenian democracy worked, and hear from one of its main critics, local thinker and would-be advisor to kings called Plato.
The readings are Chapter 3 of Lane (2014), for an overview of democratic Athens, and Chapter 1 from Szpiro (2010) for Plato’s alternative. As a bonus reading, also have a look at Chapter 4 of Melissa Lane’s book.
Adrian’s slides for how Athenian democracy functioned are here. Nestor’s slides for Plato’s alternative, based on Szpiro’s book, are here.
Week 3 (October 28, 2024)
We start getting into the weeds of voting, with an early example of trying to manipulate a collective decision: the trial of Afranius Dexter’s purported killers, as reported by Pliny the Younger. The reading is Chapter 2 of Szpiro (2010), and Victoria will be leading the discussion.
The takeaway from this week is that the rule used to determine the outcome of such a collective decision (plurality, or First-Past-the-Post) encourages tactical voting. Why? Because the outcome using this rule often mis-represents the preferences of the voters. There is a real possibility that the winner is hated by most of the voters, and the the upshot is that voters will be strategic about how they place their votes.
This is a broad phenomenon that afflicts many modern elections, not just trials in the Ancient world. Adrian’s slides are here.
Week 4 (November 4, 2024)
We read Chapter 3 of Szpiro (2010), which introduces us to the Catalan thinker Ramon Llull. Trying to find the most perfect way of electing an abbess, Llull put forward, around 800 years ago, not one, but two (!) voting rules. The first is based on counting the number of wins each candidate gets in pairwise contests with the other candidates, and is more commonly known today as Copeland’s method. Apart from the technicality of ties, which Llull hand-waived away, this problem takes up a lot of time and resources: we need to run an election for every possible pair of candidates. For 9 candidates, which was the number Llull was dealing with in his example, this amounts to 36 rounds of voting.
Lull tries to circumvent this problem by introducing a variant in which the loser in the first election is eliminated, while the winner is pitted against a new candidate, and so on, tournament style. This rule is known nowadays, unsurprisingly, as the tournament, or round-robin method of voting. While faster (with 9 candidates it requires only rounds of voting), it is sensitive to the order in which candidates are lined up.
Nicola is presenting. Her slides are here.
Week 5 (November 11, 2024)
We will be looking at Chapter 4 of Szpiro (2010). Lena is presenting.
Bibliography
- Szpiro, G. (2010). Numbers Rule. The Vexing Mathematics of Democracy, from Plato to the Present. Princeton University Press.
- Lane, M. (2015). The Birth of Politics: Eight Greek and Roman Political Ideas and Why They Matter. Princeton University Press.