## The Miners Puzzle

I expect many of you have heard of Parfit's "Miner Puzzle." Derek presented this in a (to my knowledge, never-published) manuscript from 1988, "What we together do". The puzzle was revisited by Niko Koldny and John MacFarlane in "Ifs and Oughts", JP 107 (2010), 115--43, which has prompted a lot of recent discussion. I'm told that there are similar cases in Regan's Utilitarianism and Cooperation (Oxford 1980), and in Jackson's "Decision-Theoretic Consequentialism and the Nearest and Dearest Objection," Ethics 101 (1991), 461--82.

I'll give a version of the case with some extra twists and whistles. Their motivations will emerge.

Ten miners are trapped; you know they're all together in shaft A or B or C, but you don't know which. A dam has broken upstream and the floodwaters are rapidly approaching. You have hold of a lever that can take any of five positions:

1. divert the water away from shaft A, sending most of it to shafts B and C
2. divert the water away from shaft B, sending most of it to shafts A and C
3. divert the water away from shaft C, sending most of it to shafts A and B
4. split the water equally between shafts A, B, and C
5. divert the water away from all the shafts, but it should then flood the area that you and fifty other emergency workers currently occupy

To remove any distracting effects of killing vs letting die, assume that the lever started out in position (e), but you've already taken hold of it and moved it to position (d), and are now rapidly trying to decide whether to leave it there or move it to another position. So you're already an active part of the process that determines where the water will end up.

Let's suppose you know that if the lever is left in position (d), half of the miners will drown. If the lever is returned to position (e), all the miners will survive but that would be incredibly reckless because you and all the other emergency workers would probably drown. If the lever is moved to one of positions (a)--(c), then if the water is in fact diverted from the shaft the miners are in, only one of the miners will drown. But if the water is diverted from a shaft the miners aren't in, all of the miners will drown.

Now, you have slightly better evidence (perhaps 4/9) for them being in shaft A than in each of the other shafts. Suppose you also sincerely and conscientiously believe you've seen a sign from God indicating that the miners are in shaft B. (If fact there is no God, and if there were He wouldn't want you basing moral choices of this sort on signs you think He's sent.) As a matter of fact, the miners are really in shaft C. Also, although bringing the waters down on yourselves and the other emergency workers would be incredibly reckless, and all your evidence says it would result in many more than ten deaths, as a matter of fact a freak accident would happen if you did this and nobody would die.

That's the scenario. Now:

• Which choice would in fact yield the best outcome? Choice (e), although it would be incredibly reckless and you'd merit criticism for making it, even after the fortunate results are known
• Which choice should you think would yield the best/optimal outcome, on the basis of your actual evidence? Choice (a). You have most justification for thinking this is the choice that would save 9 miners, although in fact it would kill them all. (Note that your justification for thinking this choice will succeed is still less than 1/2. And the "expected disvalue" of this choice is 6 deaths, a bit worse than choice (d).)
• Which choice should you think would yield the best outcome, given the (as yet unknown) fact that the miners are in shaft C? Choice (c). You're not in a position to know it, but that choice would save 9 miners. (It's not as good as choice (e), though, which would save everybody.)
• Which choice do you sincerely and conscientiously believe will yield the best outcome? I suppose choice (b), although you are somewhat unreasonable in thinking so, and in fact that choice would be as bad as (a).
• Which choice do most of us intuitively judge to be the appropriate one? Choice (d), although you know in advance this won't give the best/optimal outcome. Only five of the miners will survive.

That's a complex case, but I hope these normative claims sound right to you.

Now, a challenge: try to summarize those normative claims using the language of "what you objectively ought to do" versus "what you subjectively ought to do". I predict you will find that language too coarse to capture all the normative facts, and also that you will feel pulled in different directions about how to apply it, because we don't antecedently have a precise enough understanding of what the "subjective/objective" contrast should be, to settle whether it's (a) or (b) that captures the subjective side, or whether it's (e) or (c) that captures the objective side. And a case can be made for (d) being either the subjectively or objectively best choice, in some sense, though it's known it won't give the best outcome.

These kinds of difficulties make me very unhappy with the language of "subjective" vs "objective oughts". Usually the people reaching for that language have a good contrast in mind, but not always exactly the same contrast. I've found this language for labeling the contrasts to get in the way more than it helps.

We'll discuss this case, and the merits of the different choices, next week and onward through the term. But I wanted to get you thinking about the case (with the extra contortions I've added) ahead of time.