Dan Luu published an analysis of various discontinuities in systems such as tax brackets, benefits cliffs, and marathon race pacing, highlighting how these abrupt thresholds create unintended behavioral and distributional effects. This analysis matters because discontinuities are widespread yet often overlooked, causing inefficiencies and inequities in policy, finance, and even sports. By exposing these patterns, the article encourages designers to smooth transitions or anticipate behavioral responses. The article covers examples including US tax brackets, UK benefit tapering, marathon finish time spikes, and Polish language test score distributions. It notes that discontinuities often create 'cliffs' where small changes in input produce large jumps in output.
Background
Discontinuities in systems refer to points where a function jumps from one value to another without passing through intermediate values. Common examples include tax brackets (where marginal rates change abruptly) and benefits thresholds (where eligibility drops suddenly). Understanding these is crucial for designing fair and efficient systems.
Discussion
Commenters shared additional examples: UK tax cliffs creating >60% marginal rates, and the marathon pacemaker effect explaining finish-time clustering. Some argued for eliminating means-testing entirely to avoid cliffs, while others appreciated the humorous yet insightful marathon example.