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
The best way to kill a joke is to explain it. This is a series about explaining jokes. Each installment takes a game people enjoy and runs it through the machinery of cooperative game theory until the fun stops. The wager is that the autopsy is where the biology is — if you want to … Read more
The talk I’d come to Montreal for happened in a windowless hotel ballroom, and it opened with a small technical glitch. Behind Maggie the title slide read Revisiting Fairness Impossibility with Endogenous Behavior, and a live captioning system was transcribing the room along the bottom of the screen. As the chair read the title aloud, … 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
Wednesday’s post answered what selects: a stationary distribution, the wheel turning by no hand in particular. Knowing what the dynamics pick, though, is not the same as knowing whether they picked well. So step off the graph — out of the local view every node is stuck inside — and try to do the one … Read more
Last week I asked you to take your hand off the lever. The argument, compressed, was that the designer we kept reaching for — the planner who would tune the network so cooperation paid and nobody got fleeced — dissolves the moment you write him into the model. There is no seat at the controls. … Read more
TOKYO — Earlier this week I wrote that there was a man I meant to come back to before I left Japan. This is me keeping the promise. The meeting that Maggie and I came to Tokyo for is the gathering of the Society for Social Choice and Welfare, and at the turn of the … Read more
A confession before we start: I billed this as three posts, and the arithmetic has not cooperated (Ed.: You definitely know non-cooperation, John). The last two turned up a result and a question big enough that I’d rather run long than rush them, so the series will continue past today. This post is the third, … Read more
On Monday I split the payoff an agent earns into a part that travels with the strategy and a part that stays with the seat, \(f_i = \alpha_{s_i} + \beta_i + \varepsilon_i\), and promised that the positional term \(\beta\) has a closed form that takes about three lines to derive. Today we derive it. The … Read more
When you face a decision you don’t know how to make, you look sideways. You find someone who is doing well — the colleague who made tenure, the neighbor whose kids turned out kind, the friend who somehow retired comfortably a decade early — and you copy what they did. But the rule has a … Read more