Personal vs. institutional decision analysis#

Part 2 · Stage 7 · 🗳️ Data Collection & Decisions · Lesson 061 of 144 · intermediate

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Important

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Whose utility?#

Expected-utility maximisation presumes a utility function. But whose? A homeowner deciding whether to remediate radon and a public-health agency deciding what to recommend nationally face the same posterior and reach different optimal actions — not because one is irrational, but because their utilities and their information genuinely differ.

Three ways they diverge#

The value of a risk reduction varies between people. The dollar amount an individual will pay to remove a given increment of lung-cancer risk is not universal; it varies with wealth, age, risk aversion and belief. An institution must adopt a single figure; the individual has their own.
Individuals condition on more. A homeowner knows their basement, their habits, whether they smoke (radon risk is far higher for smokers). Their posterior for their own exposure is sharper than the agency’s posterior for a house drawn from their county.
The decision spaces differ. The individual chooses an action; the institution chooses a rule, applied to millions of houses. A rule optimal in aggregate is not optimal for most of the individuals it binds.

Aggregating individual decisions#

The subtle point is that a policy is not evaluated by its expected utility for a typical house, but by the aggregate consequences of the individual decisions it induces. Set a recommendation threshold and some households will remediate who need not, and others will not measure who should. The distribution of outcomes across the population is the object of interest, and it must be simulated:

import numpy as np
remediation_cost = 2000.0                               # dollars per house
# posterior predictive radon for each of many houses, from the hierarchical model
radon = ppc["radon"]                                    # (S draws, n houses)
for threshold in [2.0, 4.0, 8.0]:                       # pCi/L action level
    remediate = radon.mean(axis=0) > threshold          # rule applied per house
    cost = remediate.sum() * remediation_cost
    exposure = radon[:, ~remediate].mean()              # residual risk borne by the rest
    print(threshold, cost, exposure)                    # the trade-off a policy makes

Where the two must disagree#

An institution’s recommendation is rationally more conservative in some directions (it bears reputational and legal cost for under-warning) and less in others (it cannot price an individual’s risk aversion). It also faces genuinely collective considerations — equity across households, the cost of a programme, the credibility of future advice — which never appear in a personal utility.

The Bayesian contribution is not to dissolve this conflict but to make it explicit. The posterior is shared; the utilities are not. When a personal and an institutional analysis disagree, the disagreement should be traceable to a named difference in utility or information — and that is a far healthier disagreement than one hidden inside a threshold nobody can justify.

Hint