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.

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