Optimal Paternalism: Sin Taxes, Internalities, and the Principle of Minimal Intervention

The section on mathematics begins with a question that morality alone cannot answer: if we are to intervene, then by how much?

Intuition: two types of consumers

The starting point of the O'Donoghue and Rabin model is a population in which some agents are rational and others suffer from self-control problems (hyperbolic discounting). The planner designs a common choice set and does not know who is who (Studying Optimal Paternalism, AER).

The internality

The key concept is the "internality": the harm a person inflicts on their future self through a present choice. Unlike an externality, it falls on the same person — yet it still justifies a corrective tax, as if it were harm to others (Journal of Behavioral Decision Making).

The sin tax as correction

The optimal "sin tax" solves two problems at once: it restrains overconsumption among people with self-control problems and redistributes the revenue back (for instance, as a lump sum), without penalising those who consume in moderation (Optimal Sin Taxes).

The asymmetry of orders

The main result is almost counterintuitive: even a small tax yields a first-order welfare gain (it eliminates overconsumption), while the distortion for rational agents is only second-order. That is why a moderate intervention is almost always preferable to complete inaction (O'Donoghue & Rabin).

The minimal sufficient intervention

From this follows a principle central to the whole site: the strength of paternalism should be calibrated to the degree of agents' errors. The stronger the distortions, the more aggressive the justified intervention; when errors are zero, the optimum converges to non-intervention. Paternalism is introduced not "just in case," but exactly to the extent that people systematically err.

Conclusions

A related framework is Thaler and Sunstein's "libertarian paternalism": to influence choice while preserving the right to opt out, taking people's own assessment as the welfare criterion. Here mathematics does not override ethics but gives it a measure: how much intervention is optimal and who pays its price.