Thought experiment: Trading off risk, intragenerational and intergenerational inequality, and fairness

Jobst Heitzig (vodle.it)2 Sep 2023 23:32 UTC
9 points
6 comments3 min readEA link

This is a thought experiment designed to help clarify different aspects of one’s value system relating to intertemporal decision making under risk with large effects on different forms of inequality and fairness: ex ante inequality (“unfairness”), ex post intragenerational interpersonal inequality, and ex post intergenerational inequality. As every thought experiment, it is highly stylized and unrealistic to be able to focus clearly on the aspects under investigation.

The thought experiment is the following: Assume you are a decision maker who faces a choice between five possible interventions (e.g., different public health policies), only one of which you can enact. Each intervention would have severe consequences for everyone on Earth in the current and the next generation. Let us assume these two generations are roughly the same size and no later generations are affected.

An intervention’s effects may differ between homogametic/​XX (mostly female) and heterogametic/​XY (mostly male) subpopulations but will affect everyone inside one of these subpopulations in the same way, measurable by a per person gain or loss in WELLBYs (or, if you prefer, QALYs or DALYs).

All but one intervention’s effects are uncertain and depend on a “coin toss by nature” (landing heads or tails with roughly equal probability) that will only get known after the intervention is completed:

  • If intervention A “succeeds”, it gives everyone 10 additional WELLBYs, but if it “fails”, it costs everyone 5 WELLBYs.

  • Intervention B gives everyone in one generation 10 additional WELLBYs at the cost of −5 WELLBYs for everyone in the other generation. Nature decides which generation is the winning one in this case.

  • Similarly, C gives either every XX person in both generations 10 additional WELLBYs, or every XY person in both generations. Nature decides which. All others lose 5 WELLBYs.

  • D either makes the XX subpopulation of generation 1 and the XY subpopulation of generation 2 the winners, or makes the XXs of generation 2 and the XYs of generation 1 the winners. Again, nature decides which of the two scenarios applies.

  • Only intervention E gives each member of the current generation 10 WELLBYs but costs everyone in the next generation 5 WELLBYs without uncertainty.

The following table sumarizes these effects of all five interventions:

coin lands: h(eads) h h h t(ails) t t t
generation: c(urrent) c n(ext) n c c n n
subpopulation: XX XY XX XY XX XY XX XY
intervention: A +10 +10 +10 +10 −5 −5 −5 −5
B +10 +10 −5 −5 −5 −5 +10 +10
C +10 −5 +10 −5 −5 +10 −5 +10
D +10 −5 −5 +10 −5 +10 +10 −5
E +10 +10 −5 −5 +10 +10 −5 −5

Table 1: Gains and losses in WELLBYs (or, if you prefer, QALYs or DALYs) per person of five different hypothetical interventions with uncertain effects, by generation and subpopulation.

As you can see, for all you know all five interventions give the same expected net gain of +2.5 WELLBYs per person averaged over both generations’ total population.

Still, I suspect that you (like me) might find some of the interventions clearly or at least tentatively preferable to some others from the list, while between certain other pairs you might be undecided. Such preferences might relate to how different interventions would lead to different forms and degrees of risk, inter- or intra-generational inequality, equal or unequal chances (fairness), and different intertemporal distributions of gains and losses.

In order to clarify your values, you might want to first think about each of the pairs (A v B, A v C, B v C, …) separately and see whether one of the two seems clearly preferable, or both seem equally desirable, or neither of these three possibilities. It might be helpful to do this exercise first without applying some formal aggregation formula (such as a nonlinear welfare function).

Once you have written down your pairwise preference relation (which might turn out to be anything between a full ranking and a very incomplete, maybe even cyclic relation), you might then want to think of ways how the listed WELLBY quantities could be aggregated into an intervention’s overall evaluation (a “utility function”) that would be consistent with your pairwise preferences.

(In my case, I have a hard time with the latter task since my preference relation seem to contain two incomparable pairs: I can’t decide between B and C, and I can’t decide between B and D, but I clearly prefer D to C.)

As a last twist, you might also think about whether and how your preferences would change if “+10” was replaced by “live to the age of 150″ and “-5” was replaced by “die during infancy”, while “XX” and “XY” are replaced by “people with gene Z” and “people without gene Z”, where Z is a hypothetical gene occurring in roughly half the population, not correlated in any obvious way with their phenotype.

I’m very curious about your comments and preference disclosures!

PS: reacting to a comment by Roman (see below), I note that the “coin toss by nature” uncertainty need not be interpreted as aleatoric uncertainty manifesting after your choice, but can of course also be interpreted as purely subjective (“Bayesian”) probabilities representing your limited knowledge about some relevant aspects of the laws of nature that already exist before your choice.

Jobst Heitzig (vodle.it)2 Sep 2023 23:32 UTC
9 points
6 comments3 min readEA link