Last time I ran the New York Times Spelling Bee through the machinery of cooperative game theory, treating each day’s word list as a weighted voting game: words are voters, points are votes, Genius is the quota, and a word has power when it’s the one that carries you across the line. The punchline was … Read more
Thursday’s post ended on a one-dimensional dial and a promise. The promise was that a single dimension is exactly what majority rule needs in order to behave. Turn an evaluation loose across many dimensions and it cycles — McKelvey and Schofield, the chaos in this blog’s masthead1 — but compress the whole question of equitable-versus-uniform … Read more
TOKYO — No guidebook leads with this, but Tokyo spent much of the twentieth century as one of the world’s quiet capitals of a strange and beautiful science: the mathematics of collective choice, the study of what a group of people actually do when they try to decide something together. The founding puzzle is older … Read more
“Should I put this in the junk drawer?” “I dunno. Do you think you could figure out where it goes?” That exchange is short enough to miss, and it is the entire subject of today’s post. The first post in this series introduced the junk drawer as a load-bearing component of any well-designed classification system, … Read more
The previous post used the phrase “local data” something like thirty times. The phrase did most of the heavy lifting in the argument: local data does not determine global structure, the more holes the underlying object has the more slack between local and global, and so on. I want to start this post by interrogating … Read more
This blog has been operating under the subtitle “Three Implies Chaos” since 2012. Long-time readers know the phrase pulls multiple duty: Li and Yorke’s period-three theorem from chaotic dynamics, Arrow’s theorem on preference aggregation, the Gibbard-Satterthwaite theorem on strategic manipulation, and the McKelvey-Schofield chaos theorem on multidimensional voting. Each of these results says, in its … Read more
In 1867, the French mathematician Pierre Ossian Bonnet asked a question that sounds like it should have an obvious answer. If you know the metric of a compact surface at every point — the intrinsic distances and angles, the things you could measure if you were a tiny ant walking on the surface — and … Read more