This is where you’ll get materials and external links.


For the first half of the course, we are loosely following Christoph Börgers’s book Mathematics of Social Choice. You should have free access to it in PDF form through Tisch Library (LINK). After you authenticate yourself with your Tufts account, you should be able to follow links for online access.


Week 1 – Ch 1/2
set, element, subset, proper subset, order, intersection, unionLINK (14 mins)
voting system, ballot, preference schedule, plurality, dictatorship, majority-fairness, interchangeable votersLINK (23 min)
runoff, elimination, Borda, PWC, sequential, “secondality,” interchangeable candidatesLINK (37 mins)
Week 2 – Ch 1/2
Condorcet cycles, Condorcet candidates, Condorcet-fairnessLINK (9 mins)
unanimity-fairness, and reasoning about when some system properties imply other system propertiesLINK (32 mins)
when to use examples or counterexamples? how to generalize? what should we demand of our democratic systems? intro to VRA * LINK (34 mins)
Week 3 – Ch 3
spoilersLINK (21 mins)
can any system be spoiler-proof? are spoilers so bad after all?LINK (19 mins)
Week 4 – Ch 4
Dominating sets, Smith sets, “strong” candidatesLINK (31 mins)
Week 5 – Ch 5-6
Smithification and “no weak spoilers”LINK (23 mins)
Introducing beatpathLINK (20 mins)
Transitivity and its consequences: beatpath has a winner, no weak spoilers, unanimity-fairLINK+LINK+LINK (44 mins)
Week 6 – Ch 7+
Favorable and neutral moves, monotonicity and strong monotonicityLINK (29 mins)
Runup to impossibilityLINK (20 mins)
Week 7 – Ch 9+
Proof of an Impossibility Theorem (Müller-Satterthwaite)
…with a small live audience of question-askers!
LINK (59 mins)
[0-41:20 lecture]
[41-end questions]
More on strategic voting and Impossibility
live audience
LINK (59 mins)
Week 8 – summing up our Voting Theory unit
Recap and big picture, plus STVLINK (56 mins)
More STV, plus reviewLINK (59 mins)
[0-29:40 more on STV]
[29:40-end review]
More midterm reviewLINK (60 mins)
Even more midterm review!LINK (55 mins)
Week 9 – Census and apportionment
Intro to census and apportionmentLINK (32 mins)
Apportionment and paradoxesLINK (56 mins)
Week 10 – Intro to redistricting
Wrap-up of apportionment, turn to redistrictingLINK (56 mins)
Compactness — Polsby-Popper and cut edgesLINK (51 mins)
Week 11- Fairness in redistricting
Shapes and fairnessLINK (45 mins)
Outcome metrics I: partisan symmetryLINK (54 mins)
Week 12 – More metrics
Outcome metrics II: PS continued, efficiency gapLINK (37 mins)
Why restate the formulas? And how do you put these metrics in context?LINK (53 mins)
Week 13 – Ensemble methods
A bit of final project discussion, then ensemble methodsLINK (65 mins)
Comparing redistricting approaches, the current state of play, and the big pictureLINK (73 mins)
Final exam prep
ReviewLINK (82 mins)
“Refresher”LINK (52 mins)


* Lecture on “when to use examples” at around 10:00, I gave the wrong winner for the Coombs method. After B is eliminated, C should win! So this example is inconclusive for whether Coombs is Condorcet-fair.

Thanks to Aira for catching the error!