The Abuse of Probability in Political Analysis: The Robinson Crusoe Fallacy

TLDR

Decision theory is often misapplied to real‑world problems such as staying home in the rain or speeding under police risk, a misuse I term the Robinson Crusoe fallacy that leads to widespread incorrect conclusions. The paper illustrates this fallacy in regulation, international sanctions, and organizational theory, arguing that it arises from inappropriate use of probability. In games without a pure strategy equilibrium, altering a player's payoffs shifts the opponent's equilibrium strategy rather than the player's own. Changing penalty size affects the frequency of law enforcement at equilibrium but leaves crime commitment rates unchanged.

Abstract

The decision to stay at home when you have no umbrella and rain is probable is an appropriate problem for decision theory. The decision to speed when you are in a hurry and the police might be patrolling is a game against a rational opponent. Treating the latter like a problem for decision theory is what I call the Robinson Crusoe fallacy. It is quite common and leads to incorrect conclusions. If the game has no pure strategy equilibrium, changes in the payoffs to a player affect not that player's strategy but the strategy of the opponent in equilibrium. For example, modifying the size of the penalty does not affect the frequency of crime commitment at equilibrium, but rather the frequency of law enforcement. I provide examples of this fallacy in regulation, international economic sanctions, and organization theory and argue that it stems from inappropriate use of the concept of probability.