The Public Good Provision Problem Re-Examined

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

A Theory of Experienced Utility and Utilitarianism

Abstract. I present a theory of measurement of preference intensity and use this measure as a foundation for utilitarianism. To do this, I suppose each alternative is experienced over time. An individual has preferences over such experiences. I present axioms under which preferences are represented by an experienced utility function equal to the integral of instantaneous preference intensity over time and unique up to a positive scalar. I propose an ethical postulate under which social preferences are utilitarian in experienced utilities.

Experienced Utility Under Risk and Uncertainty

Abstract. It is a common fallacy to view preferences under risk and uncertainty as a direct measure of preference intensity. Indeed, it is not unreasonable to imagine an individual with risk loving preferences over lotteries and diminishing marginal preference intensities over constant outcomes. It is then natural to wonder when an expected utility maximizer is in fact maximizing her expected preference intensity. Moreover, when this is the case, the decision maker is arguably neutral to risk—any concavity/convexity in her expected utility function comes entirely from her decreasing/increasing marginal preference intensity. This motivates a new definition of risk attitude that is net of the effect of preference intensities. In a recent paper, Fryxell (2019) shows how we may leverage preferences over experiences to measure preference intensity. I characterize preferences that admit an expected experienced utility representation (EEU), both in the case of (objective) risk and in the case of (subjective) uncertainty. I then propose a definition of risk attitude (for non-EEU maximizers) which is net of the individual's experienced utilities.

A Theory of Criminal Justice

Abstract. I propose a general framework with which to analyze the optimal 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. I first consider pure (costless) punishment. 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.

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).

The Average Location of Impact: A New Index and How to Use It

with Charlotte Siegmann

Abstract. The benefits of a policy change are often heterogeneous across several dimensions of interest. Two important dimensions are 1) the income level of the beneficiaries and 2) the time and generation at which the benefits occur. Summary statistics allow researchers to capture important features of an underlying distribution with a single number. We propose a summary statistic that measures the average location (e.g., income level or time) of a policy's impact, weighted by the amount of benefit occurring at each location. Importantly, the usual arithmetic mean cannot be used since benefits may be negative. We generalize the notion of an arithmetic mean to allow for both positive and negative weights. We call this the trimmed mean. We show that for absolutely continuous distributions, the trimmed mean exists and is unique. We discuss applications to inequality (using income level) and intergenerational equity (using time).