Fractional Treatment Rules for Social Diversification of Indivisible Private Risks

Should a social planner treat observationally identical persons identically? This paper shows that uniform treatment is not necessarily desirable when a planner has only partial knowledge of treatment response. Then there may be reason to implement a fractional treatment rule, with positive fractions of the observationally identical persons receiving different treatments. The planning problems studied here share some important features: treatment is individualistic, social welfare is a strictly increasing function of a population mean outcome, and outcomes depend on an unknown state of nature. They differ in the information that the planner has about the state of nature and in how he uses this information to make treatment choices. In particular, I compare treatment choice using Bayes rules and the minimax-regret criterion. Following the analysis, I put aside the literal notion of a planner who makes decisions on behalf of society and consider the feasibility of implementing fractional treatment rules in functioning democracies.

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