It is Monday and Johnson is anxious. He’s competing with several other managers for a promotion at Acme, Inc. They are so evenly matched in qualifications, Johnson learns, that the candidate who scores highest on a ruthlessness test everyone took last Friday will get the job. The results won’t be announced until this upcoming Friday.
Meanwhile Johnson’s charge, Parker, has missed his sales quota for the month. It’s a fluke, since Parker is his top earner, and Johnson knows it. Still, if he sacked Parker this would give Johnson evidence of his ruthlessness and therefore give him reason to believe he had scored well on the exam on which his promotion depends. He really wants this promotion.
So, assuming that the numbers are right, the expected value to Johnson from his firing Parker could be greater than the expected value from his not firing Parker, even though his firing Parker cannot causally influence the results of the ruthlessness exam.
Should Johnson sack Parker? If not, why not?
Alan Gibbard and Bill Harper (1978) presented examples like this and argued that there were two kinds of expected utility, one that measures how welcome the news is and another that measures the efficacy of an act for bringing about a desired state. So, firing Parker might bring welcome news to Johnson (“I am ruthless!”) but would do nothing to bring about his wished-for promotion, and would cost him his top earner if he didn’t get the promotion.
Another option is to argue that there is but one type of expected utility function for each of us, but the reference class is different depending upon whose utility function we consider and when. There is a contextualist flavor to this approach. The idea is that learning that Johnson sacked Parker might count as evidence to us that Johnson is ruthless, since it puts him in a new reference class (say, young executive who will stop at nothing to gain advancement) but the same act would not suffice to switch Johnson’s reference class, in so far as Johnson perceives his choice to fire or keep Parker as his own. For if he did take it as evidence for his ruthlessness, he in effect would be rejecting his belief that he exercised a free choice. This is Henry Kyburg’s take. But after Johnson chooses, say, to sack Parker, he can reflect on his action and think that perhaps he is ruthless after all. Which is a bit striking, I think. At the point of decision Johnson faces a dilemma (in so far as the first option is open to him, metaphysically) between exercising free will or treating his act as evidence, but after he makes his choice the dilemma disappears and he can view his choice as evidence while maintaining that it was freely made.