XU

Abstract. An individual has preferences over experiences. I present axioms which are necessary and sufficient for the existence of an experienced utility (XU) representation in which the utility of an experience is equal to the integral of instantaneous utility over time. I propose a normative principle which states that what is best for society is what an ethical observer would most prefer if they were to live every life once. I call this the LELO principle. An ethical observer who respects LELO acts as if they seek to maximize the total XU across individuals. That is, LELO implies utilitarianism with respect to some utility representation and that representation is XU.

The Public Good Provision Problem Re-Examined

Abstract. I write down a government's public good provision problem from first principles and, contrary to popular wisdom, I find a solution. I call it the cost-sharing pivotal mechanism. Both the statement of the problem and the solution are new. The cost-sharing pivotal mechanism satisfies a new participation constraint, a new fairness principle, and is strategy-proof, efficient, and asymptotically ex-post budget-balanced in large populations. Moreover, I show that a commonly used methodological simplification in mechanism design is not without loss, standard participation constraints used in mechanism design are not well-suited for these environments, and the most well-known mechanism for public good provision, the Clarke mechanism, violates a basic fairness constraint---if nothing is produced, no one should pay.

Infinite Ignorance

Abstract. I consider the problem of ethics within potentially infinite worlds. It is well-known that ethical theories tend to break down when applied to infinite worlds. In particular, all aggregative consequentialist theories suffer from infinite paralysis: If there is any positive probability that the universe contains infinite moral value and individual actions can only cause a finite change in value, then we should be morally indifferent among all our actions. I take a different approach. I posit that there is some, possibly incomplete, moral ranking ⪰* over humanly-possible actions which give rise to probability distributions over universes or, more generally, to sets of possible universes. We may not fully know or understand ⪰*, but we can lay out a few axioms that we believe it should satisfy, narrowing the space of possibilities. This approach uncovers a positive result, reversing the statement of infinite paralysis: If there is any positive probability that the universe contains finite moral value and individual actions can only cause a finite change in value, then we should evaluate our actions conditional on the universe having finite moral value. As this does not require that we know how to rank infinite worlds, I call this infinite ignorance.

A Theory of Punishment

Abstract. I propose a general framework with which to analyze the optimal punishment as deterrence in response to crime. Each criminal act, detected with some probability, generates a random piece of evidence and a consequent probability of guilt for each citizen. I consider a utilitarian planner with no artificial moral constraints. In particular, I assume no upper bound on punishment—such a bound can only rise endogenously from the utilitarian objective. Punishment is pure, i.e., costless. If citizens are expected utility maximizers, a repugnant conclusion is reached—it is optimal to punish only with the realization of the most incriminating evidence. Allowing for more general behavior yields a weaker but more satisfactory result—optimal punishment is always decreasing in the quality of evidence.

Statistics for Arbitrary Distributions

with Charlotte Siegmann

Abstract. We introduce the concept of an arbitrary distribution and show how to apply descriptive statistics to them. Arbitrary distributions extend the domain of distributions on which statistics can be usefully applied beyond the usual frequency and probability distributions. For example, we can consider the distribution of the benefits of a policy across income levels and over time, and we can compute the center of mass and the spread of such a distribution. The key challenge is that such benefits, or more generally the weights within an arbitrary distribution, can be negative. We propose a method which we call ironing as a natural solution to the problem of statistics for arbitrary distributions.

XU, Risk, and Uncertainty

Abstract. Experienced utility (XU) is a utility representation built upon a decision maker's intensity of preference. Expected utility (EU) is a utility representation built upon a decision maker's attitudes towards risk. It is a common fallacy to view the latter as equivalent to the former. I characterize when this is precisely the case. That is, I characterize when XU = EU and hence when a decision maker maximizes her expected experienced utility (EXU). I do this both for the case of risk and uncertainty. The LELO principle is a normative principle which states that what is best for society is what an ethical observer would most prefer if they were to _live every life once_. I show that an ethical observer choosing among lotteries (acts) who respects LELO acts as if they seek to maximize the total EXU across individuals. That is, applied to lotteries (acts), LELO implies utilitarianism with respect to some utility representation and that representation is EXU.

The Shape of Social Impact

with Jacob Barrett

Abstract. As you and others dedicate more resources to a particular cause or movement, what is the shape of your expected marginal impact? Is it increasing, decreasing, or hump-shaped in the amount of resources that you or others dedicate? We introduce a general framework for thinking about this question and study in detail the case in which the benefits are realized at an uncertain threshold of investment. We find that the shape indeed depends on whether the resources are coming from 1) others or 2) you. 1) Your expected impact is generally hump-shaped in others' contributions, with its peak near the peak of your prior belief about where the threshold lies. 2) Fixing others' contribution levels, your expected impact is generally decreasing in your contributions if you are relatively optimistic that the threshold will be reached, and hump-shaped in your contributions if you are relatively pessimistic, with its peak farther out as you become more pessimistic.

Budget-Balancing the Groves Mechanisms

Abstract. When monetary transfers are available, one hurdle to achieving efficiency in mechanism design is balancing the budget. The Groves mechanisms characterize the class of strategyproof and allocatively efficient mechanisms, but no mechanism exists which is strategyproof and fully efficient—i.e., allocatively efficient and balances the budget. I characterize the class of Groves mechanisms which come as close as possible to balancing the budget without ever running a deficit. I call these cascading rebate mechanisms. Moreover, I show that in any domain, the pivotal mechanism uniquely maximizes ex-post surplus among all mechanisms which satisfy strategy-proofness, allocative efficiency, and universal participation, and that in a universal domain, the pivotal mechanism also uniquely minimizes ex-post surplus among all such mechanisms. That said, in restricted domains there exist mechanisms which come closer to budget-balance than the pivotal mechanism while never running a deficit. One important example is in an auction setting, in which the surplus-minimizing mechanism generates surplus approaching zero as the number of players gets large—significantly outperforming the pivotal mechanism (here, the second-price auction).