Your brain is divided, and each half is transplanted into the body of one of two people whose brains have been fatally injured. Each of the resulting people would, if the transplant succeeds, be psychologically (and phenomenally) continuous with you as you are now.Footnote 1 Call the person that would have the left half of your brain ‘Lefty’ and the person that would have the right half of your brain ‘Righty’.Footnote 2 Let’s assume that each year in Lefty’s and Righty’s lives would be of equal positive well-being.

Consider, first, an outcome where both transplants succeed:

  • Double Success   Lefty lives for 40 years, and Righty lives for 40 years.

Given the transitivity of identity, you can’t be identical with both Lefty and Righty, who are plausibly distinct people.Footnote 3 And, since your relation to Lefty is much the same as your relation to Righty, you can’t plausibly be identical with one of them but not the other. So you are neither identical with Lefty nor identical with Righty. Even so, Derek Parfit argues that this outcome is prudentially better for you than an outcome where both transplants fail:

  • Double Failure   Neither transplant succeeds.

Parfit claims that Double Failure is prudentially worse for you than an outcome where one transplant succeeds:

  • Single Success   Lefty lives for 40 years, and the transplant to Righty does not succeed.

In this outcome, there’s only one survivor. And it seems that, in principle, you could survive a brain transplant and that you could survive with just half of your brain. Hence it’s plausible that you survive in Single Success and that surviving in Single Success is prudentially better for you than dying in Double Failure.Footnote 4 But, if Single Success is prudentially better for you than Double Failure, then your relation to Lefty in Single Success must contain what matters in survival.

Next, note that your relation to Lefty is the same in Double Success as in Single Success—the only difference being the lack of uniqueness. Since the relation that matters is plausibly intrinsic, it shouldn’t depend on uniqueness. The addition of Righty should not make it the case that your relation to Lefty no longer contains what matters in survival. And, as we argued earlier, your relation to Lefty in Single Success does contain what matters in survival. So your relation to Lefty in Double Success must also contain what matters in survival. And, by symmetrical reasoning, your relation to Righty in Double Success must contain what matters in survival. Accordingly, Parfit concludes, Double Success should be prudentially better for you than Double Failure.Footnote 5

But how does Double Success compare to Single Success? As we have seen, your relation to Lefty in Double Success contains what matters in survival. And your equivalent relation to Righty in that outcome also contains what matters.Footnote 6 Nevertheless, even though both your relation to Lefty and your relation to Righty contain what matters, we may still doubt that Double Success is prudentially better for you than Single Success. For example, consider the following (at first glance compelling) view:Footnote 7

  • The Prudential Average View   Let the chancy equivalent of an outcome be a prospect where all fission events are replaced by an even-chance lottery of being any of the fission products. The prudential value of an outcome is equal to the expected prudential value of its chancy equivalent.Footnote 8

In other words, the Prudential Average View regards the prudential value of splitting into Lefty and Right as equal to the expected prudential value of an even lottery between becoming Lefty or becoming Righty—in other words, the average between Lefty’s and Righty’s well-being.

The Prudential Average View entails that Double Success is prudentially equally as good for you as Single Success, since Lefty and Righty have equally good lives. We will argue, however, that Double Success is prudentially better for you than Single Success. Thereby, we show that the Prudential Average View is false.Footnote 9

Consider a case where only the transplant to Righty succeeds but there is a slight mishap in this transplant so that Righty only lives on for 20 years:

  • Half Success   Righty lives for 20 years, and the transplant to Lefty does not succeed.

The earlier argument that Single Success is prudentially better for you than Double Failure also shows, changing what needs to be changed, that Half Success is prudentially better for you than Double Failure.

Now, consider the following variation, where both transplants succeed overall but (as in Half Success) there is a slight mishap in the transplant to Righty so that Righty only lives on for 20 years:

  • One-and-a-Half Success   Lefty lives for 40 years, and Righty lives for 20 years.

Your relation to Lefty is the same in One-and-a-Half Success as in Single Success. And it must be prudentially good for you to stand in that relation to Lefty, since Single Success is prudentially better for you than Double Failure. Likewise, your relation to Righty is the same in One-and-a-Half Success as in Half Success. And it must be prudentially good for you to stand in this relation to Righty, since Half Success is prudentially better for you than Double Failure. So, from a prudential perspective, One-and-a-Half Success differs from Single Success only in that you also stand in a relation to Righty which contains what matters in survival—and this, as we have seen, is prudentially good for you. Since the relation that matters in survival is plausibly intrinsic, the prudential value of standing in that relation to a future person should not be diminished by your standing in that relation to some other person.Footnote 10 Accordingly, One-and-a-Half Success has everything that is prudentially good for you in Single Success and, in addition, you stand in a relation to Righty that is prudentially good for you. Therefore, One-and-a-Half Success should be prudentially at least as good for you as Single Success.Footnote 11

Next, compare One-and-a-Half Success to Double Success. From a prudential perspective, the only difference between these outcomes is that one of the people to which you stand in the relation that matters (namely, Righty) has a better life in Double Success than in One-and-a-Half Success. Since the relation that matters in survival is plausibly intrinsic, the prudential value for you of standing in the relation that matters to Lefty shouldn’t be affected by the change in Righty’s life. And it is prudentially better for you to stand in the relation that matters to Righty in Double Success than to Righty in One-and-a-Half Success, because Double Success is better for Righty than One-and-a-Half Success. Consequently, Double Success should be prudentially better for you than One-and-a-Half Success.Footnote 12

Now, since One-and-a-Half Success is prudentially at least as good for you as Single Success and, moreover, Double Success is prudentially better for you than One-and-a-Half Success, it follows by the transitivity of prudentially at least as good as that Double Success is prudentially better for you than Single Success.Footnote 13

Among other things, this result rules out the Prudential Average View. We can show that, other things being equal, having more fission products with good lives is prudentially better for you.Footnote 14 Given that each person involved has a good life, fission is not only prudentially better for you than death, it is (other things being equal) prudentially better for you than survival without fission.Footnote 15