Public Good Provision Re-Examined

Abstract. I write down the government's public good provision problem from first principles and find a unique solution, contrary to conventional wisdom. I call it the cost-sharing generalized pivotal mechanism. The cost-sharing generalized pivotal mechanism elicits individuals' private willingness to pay for the public good in dominant strategies, induces participation in dominant strategies, produces the welfare-maximizing quantity of the public good via a weighted benefit-cost analysis, finances exactly the cost of the public good, and taxes individuals fairly. Moreover, I show that the most well-known mechanism for public good provision, the Clarke mechanism, violates budget-balance, participation, fairness, and a basic principle I call no-extortion: if nothing is produced, no one should pay.

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 are maximizing the total XU across individuals. That is, LELO implies utilitarianism with respect to some utility representation and that representation is XU.

An Economic Theory of Criminal and Civil Law

Abstract. I propose a general framework to analyze the socially optimal response to criminal and civil wrongs. Each wrongful act, detected with some probability, generates a random piece of evidence and a consequent posterior probability of guilt for each individual. I show that with no assumptions on individual behavior, if the government prefers that, all else equal, innocent individuals face less punishment, incapacitation, rehabilitation, and reparations, then for each individual and each response the optimal policy must be non-decreasing in that individual's posterior probability of guilt. This implies that the optimal response for each individual depends solely on the quality of evidence against them, and not on their rank in the suspect list. I argue that distinguishing only between "innocent" and "guilty" significantly limits the scope of a multifaceted justice system, and may bias the system towards retributive rather than rehabilitative intuitions.

Infinite Ignorance

Abstract. I consider the problem of normative decision making in a world of potentially infinite value across space and time when every feasible action causes a finite change in value. It is well-known that many normative theories break down when applied to such worlds. In particular, all aggregative consequentialist theories suffer from infinite paralysis: ''If there is any positive probability the universe contains infinite moral value, then we should be morally indifferent among all our feasible actions.'' But many, if not all, aggregative consequentialist theories, including expected utility theory, are not grounded axiomatically in a framework which allows for infinitely good alternatives in the first place. Applying these theories in infinite worlds is applying them outside the scope in which they are grounded. I return to these foundations and construct a normative theory of decision making under risk and uncertainty in worlds which may contain infinitely good and bad alternatives. 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, then we should evaluate our feasible actions conditional on the universe containing finite moral value.'' As this prescription does not require that we actually know how to rank infinite worlds, I call this infinite ignorance.

Arbitrary Distributions

with Charlotte Siegmann

Abstract. We introduce the notion of an arbitrary distribution and propose a new class of summary statistics to describe such distributions. Arbitrary distributions extend the space of classical distributions beyond the usual probability and frequency domains. For example, consider the distribution of the benefits of a government policy across income levels or across time. Given such a distribution, we may want to compute its center of mass or its spread. The key challenge is that the benefits of a policy, or more generally the weights which constitute an arbitrary distribution, can be negative. For distributions with negative weights, it is not clear how to compute the center of mass or the spread. We propose a method which we call ironing—which converts an arbitrary cumulative distribution function into its nearest classical cumulative distribution function—as a natural solution to the problem. The ironed mean, variance, etc. of an arbitrary distribution is the mean, variance, etc. of the ironed distribution.

A Universal Characterization of the VCG Mechanism

Abstract. The Vickrey-Clarke-Groves (VCG) mechanism is the canonical mechanism within the class of strategy-proof and efficient mechanisms. What are its defining traits? Two characterizations are prominent. The first holds that the VCG mechanism is the unique mechanism which maximizes revenue among all mechanisms satisfying strategy-proofness, efficiency, and ex-post individual rationality. The second holds that the VCG mechanism is the unique mechanism which satisfies strategy-proofness, efficiency, universal participation, and no-deficit. I show that neither is true in general. What is true in general is that the VCG mechanism is the unique mechanism which maximizes revenue among all mechanisms satisfying strategy-proofness, efficiency, and universal participation.

XU with 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 full 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 budget-balanced. 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. One important case is the efficient allocation of a single good while raising as little revenue as possible. In this case, a cascading rebate mechanism generates revenue approaching zero as the number of players grows.