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Posted on Monday, 1 November 2010

Cost-Benefit Analysis

When faced with a choice, cost-benefit analysis asks:

  1. What are the possible outcomes?
    \{ \text{outcomes} \}
  2. Who benefits and who is harmed in each of these outcomes?
    \{ \text{outcomes} \} \to \scriptsize \begin{pmatrix} \text{person}_1 \\ \text{person}_2 \\ \text{person}_3 \\ \vdots \end{pmatrix}
  3. How much is the benefit or harm in each case?
    \{ \text{outcomes} \} \to \scriptsize \begin{pmatrix} \text{person}_1 \text{ ---} \ \$_1 \\ \text{person}_2 \text{ ---} \ \$_2 \\ \text{person}_3 \text{ ---} \ \$_3 \\ \vdots \end{pmatrix}
    (Sometimes the harm might be multi-dimensional — measured in money, health, outrage, opinions about what happens to others, & more. But you ultimately must reduce all of that to an actionable ranking of alternatives — mathematically, a total order ⪰.)
    \scriptsize {\begin{matrix} \text{health} \\ \$ \; \$ \; \$ \\ \text{outrage} \\ \text{envy} \\ \text{concern} \\ \vdots \end{matrix} } \ \to \ \, \succeq
  4. What is the likelihood of each outcome?
    \begin{pmatrix} \text{prob}_1 \leftarrowtail \text{outcome}_1 \\ \text{prob}_2 \leftarrowtail \text{outcome}_2 \\ \text{prob}_3 \leftarrowtail \text{outcome}_3 \\ \vdots \end{pmatrix} , \quad \sum_i \text{prob}_i = 1

This is a pretty reasonable way of doing things, I think. It lays out why hard choices are so hard.

(Should I harm this one in order to aid this one? Is it better to do this kind of harm, or that kind of harm? Etc.) I’ll write more about cost-benefit analysis, Pareto optimality, and morals another time.

15 notes

  1. isomorphismes posted this