More on the technical side, but I really like the lecture notes from a course Don Knuth taught in 1987 called “Mathematical Writing.”

If I’d read the first few pages in the first year of my PhD it probably would have saved my reviewers some time... There’s also some very fun anecdotes :).

icymi they did indeed post the recording online! www.youtube.com/watch?v=5ZII...

fwiw, he gave a talk with the same title at JMM last year, and that's on youtube! www.youtube.com/watch?v=AayZ...

There is a *distribution* over candidates that is preferred over any other by a majority of voters, in expectation. It's called a Maximal Lottery. This phenomenon is a special case of the fact that Nash equilibria always exist with mixed strategies, but not always with pure strategies.

Before Arrow's Theorem there was Condorcet's Paradox, which says that there's not always a candidate that is preferred over any other by a majority of voters. (Even replacing "a majority" with 1% this is still true.)

But...

Thanks for the great choice!! To continue the interesting discussion, I thought I'd mention my usual answer to "what's one result about voting you wish more people knew?"

Tragically in voting theory, "optimality" is in the eye of the beholder.

That's a wonderful way to make the case for Borda! (And I wasn't aware of it so thanks for sharing 😃.) It is worth pointing out that Borda still does not satisfy many desirable properties, e.g., Condorcet consistency, and strategyproofness (though nothing really does; see Gibbard–Satterthwaite).