Population Ethics under Risk

Population axiology concerns how to evaluate populations in terms of their moral goodness, that is, how to order populations by the relations “is better than” and “is as good as”. The task has been to find an adequate theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. So far, this field has largely ignored issues about uncertainty and the conditions that have been discussed mostly pertain to the ranking of risk-free outcomes. Most public policy choices, however, are decisions under uncertainty, including policy choices that affect the size of a population. Here, we shall address the question of how to rank population prospects—that is, alternatives that contain uncertainty as to which population they will bring about—by the relations “is better than” and “is as good as”. We start by illustrating how well-known population axiologies can be extended to population prospect axiologies. And we show that new problems arise when extending population axiologies to prospects. In particular, traditional population axiologies lead to prospect-versions of the problems that they praised for avoiding in the risk-free settings. Finally, we identify an intuitive adequacy condition that, we contend, should be satisfied by any population prospect axiology, and show how given this condition, the impossibility theorems in population axiology can be extended to (non-trivial) impossibility theorems for population prospect axiology

How valuable are chances?

Chance Neutrality is the thesis that, conditional on some proposition being true (or being false), its chance of being true should be a matter of practical indifference. The aim of this paper is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centrepiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality but that Linearity is not; and hence, that Chance Neutrality is not rationally required

How valuable are chances?

Chance Neutrality is the thesis that, conditional on some proposition being true (or being false), its chance of being true should be a matter of practical indifference. The aim of this paper is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centrepiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality but that Linearity is not; and hence, that Chance Neutrality is not rationally required

Counterfactual Desirability

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. We end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles

Hierarchical Finite State Machines for Efficient Optimal Planning in Large-scale Systems

In this paper, we consider a planning problem for a hierarchical finite state machine (HFSM) and develop an algorithm for efficiently computing optimal plans between any two states. The algorithm consists of an offline and an online step. In the offline step, one computes exit costs for each machine in the HFSM. It needs to be done only once for a given HFSM, and it is shown to have time complexity scaling linearly with the number of machines in the HFSM. In the online step, one computes an optimal plan from an initial state to a goal state, by first reducing the HFSM (using the exit costs), computing an optimal trajectory for the reduced HFSM, and then expand this trajectory to an optimal plan for the original HFSM. The time complexity is near-linearly with the depth of the HFSM. It is argued that HFSMs arise naturally for large-scale control systems, exemplified by an application where a robot moves between houses to complete tasks. We compare our algorithm with Dijkstra's algorithm on HFSMs consisting of up to 2 million states, where our algorithm outperforms the latter, being several orders of magnitude faster.Comment: Accepted to ECC 202

Fairness and risk attitudes

According to a common judgement, a social planner should often use a lottery to decide which of two people should receive a good. This judgement undermines one of the best-known arguments for utilitarianism, due to John C. Harsanyi, and more generally undermines axiomatic arguments for utilitarianism and similar views. In this paper we ask which combinations of views about (a) the social planner’s attitude to risk and inequality, and (b) the subjects’ attitudes to risk are consistent with the aforementioned judgement. We find that the class of combinations of views that can plausibly accommodate this judgement is quite limited. But one theory does better than others: the theory of chance-sensitive utility

The Economics and Philosophy of Risk

Neoclassical economists use expected utility theory to explain, predict, and prescribe choices under risk, that is, choices where the decision-maker knows---or at least deems suitable to act as if she knew---the relevant probabilities. Expected utility theory has been subject to both empirical and conceptual criticism. This chapter reviews expected utility theory and the main criticism it has faced. It ends with a brief discussion of subjective expected utility theory, which is the theory neoclassical economists use to explain, predict, and prescribe choices under uncertainty, that is, choices where the decision-maker cannot act on the basis of objective probabilities but must instead consult her own subjective probabilities