The Unreliability of Foreseeable Consequences: A Return to the Epistemic Objection

Abstract

Consequentialists maintain that an act is morally right just in case it produces the best consequences of any available alternative. Because agents are ignorant about some of their acts’ consequences, they cannot be certain about which alternative is best. Kagan (1998) contends that it is reasonable to assume that unforeseen good and bad consequences roughly balance out and can be largely disregarded. A statistical argument demonstrates that Kagan’s assumption is almost always false. An act’s foreseeable consequences are an extremely poor indicator of the goodness of its overall consequences. Acting based on foreseeable consequences is barely more reliably good than acting completely at random.

Technical Appendix

We model the choice situation as a binomial distribution and compare the various probabilities of consequences resulting from actions A and B. Situations in which the action with the best consequences are those that result from A are those in which the net utility of selecting A minus the net utility of selecting B is greater than 0.

Let n be the number of unforeseen consequences. The probability (for both actions A and B) that there will be k beneficial unforeseen consequences is determined by the following:

$$ {P}_n^k=\frac{n!}{2^nk!\left(n-k\right)!} $$

As the number of unforeseen consequences increases, the factorials become extremely large. One way to calculate them is with the following recursive function.

$$ \begin{array}{c}\hfill {P}_n^0=\frac{1}{2^n}\hfill \\ {}\hfill {P}_n^k={P}_n^{k-1}\left(\frac{n-k+1}{k}\right)\hfill \end{array} $$

Let V _a and P _a represent distinct net utile values and the probability that that net utile value will occur respectively for action A. Similarly, let V _b and P _b represent distinct net utile values and the probability that that net utile value will occur respectively for action B. The overall probability Q that action B will have a greater utility than action A will is given by the following:

$$ Q=\sum_{k_1=0}^n\sum_{k_2=0}^n\left[\kern1em \begin{array}{c}P{a}_{k_1}\cdot P{b}_{k_2}\left(\mathrm{if}\kern0.28em V{b}_{k_2}>V{a}_{k_1}\right)\kern1em \\ {}\kern1em 0\left(\mathrm{otherwise}\right)\end{array}\kern1em \right] $$

for n unforeseen consequences. Due to the difficulty in calculating binomials for n > 1000, it is useful to use a normal approximation. The results of the binomial probability and the normal approximation are given in the table below:

n	Binomial Probability	Normal Probability
20	0.04035	0.05692
50	0.13563	0.15866
100	0.21838	0.23975
200	0.29119	0.30854
500	0.36399	0.37591
1000	0.40286	0.41153

If there are 1000 unforeseen consequence there is a greater than 40 % chance that action B has better consequences than action A does. The fact that the foreseeable consequences are such that A has 10 more utiles than B does is hardly a reliable indication that A will be better. And as the number of unforeseen consequences passes 1000, the odds that A is the best course of action decrease still further—approaching 50 %.