I'm sure you've seen this at some point, but for others...

Consider the following case:

On Twin Earth, a brain in a vat is at the wheel of a runaway trolley. There are only two options that the brain can take: the right side of the fork in the track or the left side of the fork. There is no way in sight of derailing or stopping the trolley and the brain is aware of this, for the brain knows trolleys. The brain is causally hooked up to the trolley such that the brain can determine the course which the trolley will take.

On the right side of the track there is a single railroad worker, Jones,who will definitely be killed if the brain steers the trolley to the right. If the railman on the right lives, he will go on to kill five men for the sake of killing them, but in doing so will inadvertently save the lives of thirty orphans (one of the five men he will kill is planning to destroy a bridge that the orphan's bus will be crossing later that night). One of the orphans that will be killed would have grown up to become a tyrant who would make good utilitarian men do bad things. Another of the orphans would grow up to become G.E.M. Anscombe, while a third would invent the pop-top can.

If the brain in the vat chooses the left side of the track, the trolley will definitely hit and kill a railman on the left side of the track, "Leftie" and will hit and destroy ten beating hearts on the track that could (and would) have been transplanted into ten patients in the local hospital that will die without donor hearts. These are the only hearts available, and the brain is aware of this, for the brain knows hearts. If the railman on the left side of the track lives, he too will kill five men, in fact the same five that the railman on the right would kill. However, "Leftie" will kill the five as an unintended consequence of saving ten men: he will inadvertently kill the five men rushing the ten hearts to the local hospital for transplantation. A further result of "Leftie's" act would be that the busload of orphans will be spared. Among the five men killed by "Leftie" are both the man responsible for putting the brain at the controls of the trolley, and the author of this example. If the ten hearts and "Leftie" are killed by the trolley, the ten prospective heart-transplant patients will die and their kidneys will be used to save the lives of twenty kidney-transplant patients, one of whom will grow up to cure cancer, and one of whom will grow up to be Hitler. There are other kidneys and dialysis machines available, however the brain does not know kidneys, and this is not a factor.

Assume that the brain's choice, whatever it turns out to be, will serve as an example to other brains-in-vats and so the effects of his decision will be amplified. Also assume that if the brain chooses the right side of the fork, an unjust war free of war crimes will ensue, while if the brain chooses the left fork, a just war fraught with war crimes will result. Furthermore, there is an intermittently active Cartesian demon deceiving the brain in such a manner that the brain is never sure if it is being deceived.

QUESTION: What should the brain do?

[ALTERNATIVE EXAMPLE: Same as above, except the brain has had a commissurotomy, and the left half of the brain is a consequentialist and the right side is an absolutist.]

Figuring out how to manipulate those intuitions in order to increase sales of Frosted Flakes.