Dissertation
Dimensions of Value: Time, People, Risk
Imagine:
a world where anything that's best for me is also always best for you, best for her, best for him — in fact, best for everyone.
a world where anything that's best for me now is also always best for me tomorrow, best for me next year — in fact, best for me at all times.
a world where whenever we're unsure about how things will turn out, whatever's best on one possible way things might turn out is also best on another possibility — in fact, best on all possibilities.
In worlds like these, there'd be little need for distributive ethics or decision theory.
But our world isn't like any of these worlds. Competing considerations often require us to make trade-offs across people, across time, and across possibilities. From this arises the problem of aggregation: how do we combine what's good for each person, at each time, or on each possibility to determine how good things are overall?
By investigating issues at the interface of these dimensions and by unpacking some foundational assumptions in ethics, my dissertation offers a series of arguments for Additivism — roughly, the view on which value is summed up across people and time, and whose expectation is taken under risk.
Chapter 1: Replaceable Value in People and Time
How we aggregate value across time greatly constrains how we aggregate value across people. In fact, two plausible principles about time lead to a picture on which overall value is added up across both people and time. The first principle says that simply changing when a person lives shouldn't change how good things are. And the second says, roughly, that things can't be better unless they're better in some period of time or another. The best course of action for non-Additivists is to reject some underlying assumptions about value being freely replaceable.
Chapter 2: Risky Moral Decisions over Time
This chapter overlays considerations of risk on top of the dimensions of people and time. Cases involving uncertainty give rise to further problems for non-additive theories. Some non-additive theories predictably lead to outcomes that are guaranteed to be worse in situations where uncertainty is partially resolved over time. And others are sensitive to uncertainty about the distribution of value in the past in objectionable ways. This chapter shows that these problems are inevitable for non-additive theories—an axiomatic argument shows that the theories that avoid both problems are exactly the additive ones.
Chapter 3: Puzzles of Future People and Possible People
The third chapter furthers bolster the case for Additivism by exploring some ethical and metaphysical issues surrounding personal identity. A prominent critique of additive theories of value stems from the idea of the separateness of persons. Roughly, this is the idea that there is a difference, for instance, between:
(i) imposing a burden on me-now to benefit you-later; and
(ii) imposing a burden on me-now to benefit me-later,
and also between:
(iii) imposing a possible burden on me for a possible benefit to you; and
(iv) imposing a possible burden on me for a possible benefit to me.
The alleged difference between (i) and (ii) raises the much-explored question of personal identity over time: what is the special relation that connects me-now and me-later that doesn’t also connect me-now and you-later? Somewhat neglected is the question raised by the alleged difference between (iii) and (iv): what is the special relation that connects, say, actual-me and possible-me that doesn't also connect actual-me and possible-you or actual-me and actual-you?
Borrowing insights from work on personal identity and tools from modal metaphysics, the chapter explores various candidates for these special relations and shows how each raises difficult ethical puzzles for various non-additive theories.
Chapter 4: Additive Aggregation
The final chapter of the dissertation takes on technical questions concerning the general problem of aggregation. Aggregation problems like the ones above share a common abstract structure. The general problem is that of balancing trade-offs among different components—where these components could be interpreted as different people, times, possibilities, voters, reasons, and so on. A technical question concerns when the balancing of these components can be represented in an additive or linear form. The answer to this is of great relevance to many longstanding philosophical debates in ethics, epistemology, decision theory, social choice theory, probability theory, and beyond.
Versions of this technical question have been explored in economics, mathematics, and elsewhere. Building on some of these work, the final chapter of my dissertation proves a general mathematical result providing necessary and sufficient conditions for the existence of an additive or linear representation. This result unifies and improves upon various existing representation theorems in decision theory, welfare economics, comparative probability theory, and social choice theory.