Three implies chaos is not a warning. It’s a description.
Li-Yorke proved in 1975 that in any dynamical system, a three-cycle implies the existence of chaos. Arrow proved in 1951 that any collective choice rule over three or more alternatives is either dictatorial or manipulable. McKelvey proved in 1976 that in a spatial voting model with three or more issue dimensions, majority rule can reach any point in the policy space from any other. Three is where the comfortable mathematics ends and something more interesting begins.
This blog exists because those results are not merely mathematical curiosities. They are structural descriptions of how institutions actually behave — descriptions that show up, in recognizable form, in the news every week, in legislation, in court decisions, in algorithms, in markets. The formal results are the map. The news is the terrain. The blog tries to show that the map and the terrain are the same place.
I’m John Patty, a professor of political science and data & decision sciences at Emory University. My research uses formal models — game theory, mechanism design, social choice — to study how institutions shape behavior. My academic page, including research papers and CV, is at johnwpatty.net.
I write here when something in the news is so perfectly illuminated by the theory that I can’t not. The posts are long by internet standards. The footnotes are real footnotes, not decorations. The mathematics is kept in the background unless it’s doing necessary work. The blog is uncomfortable for everyone, which I take as a sign that something is working.
The blog ran actively from 2012 to 2016, then went quiet for reasons that are mostly between me and my therapist. It returned in early 2026. Some of the people who used to read it — colleagues, friends, people I admired — aren’t here anymore. Part of what brings me back is the sense that the kind of work this blog tries to do matters more now than it did when I left.
How to read this blog
Posts come in two forms. The longer essays develop a single formal argument in full — they run long because the argument requires it, not because I enjoy writing long posts (I do not). Dispatches from the Underground is a shorter recurring feature — three to five items connecting current events to the underlying structure, followed by a couple of things we’re watching.
If you’re new here, the By Theme page is the fastest way to find the argument you’re already having. The full chronological archive is here.
Get in touch
I read everything sent to jwpatty@emory.edu. I respond to most of it, eventually. If you see a theorem in the news that belongs on this blog, I want to know about it.
The blog has an email subscription — the sign-up is in the sidebar. New posts arrive in your inbox when they’re published, which is more often than it used to be and less often than I’d like.