Independence is the condition that, if X is preferred to Y, then a lottery between X and Z is preferred to a lottery between Y and Z given the same probability of Z. Is it rationally required that one’s preferences conform to Independence? The main objection to this requirement is that it would rule out the alleged rationality of Allais and Ellsberg Preferences. In this paper, I put forward a sequential dominance argument with fairly weak assumptions for a variant of (...) Independence (called Independence for Constant Prospects), which shows that Allais and Ellsberg Preferences are irrational. Hence this influential objection (that is, the alleged rationality of Allais and Ellsberg Preferences) can be rebutted. I also put forward a number of sequential dominance arguments that various versions of Independence are requirements of rationality. One of these arguments is based on very minimal assumptions, but the arguments for the versions of Independence which are strong enough to serve in the standard axiomatization of Expected Utility Theory need notably stronger assumptions. (shrink)

Decision theorists have attempted to accommodate several violations of decision theory’s axiomatic requirements by modifying how agents’ choice options are individuated and formally represented. In recent years, prominent authors have worried that these modifications threaten to trivialize decision theory, make the theory unfalsifiable, impose overdemanding requirements on decision theorists, and hamper decision theory’s internal coherence. In this paper, I draw on leading descriptive and normative works in contemporary decision theory to address these prominent concerns. In doing so, I articulate and (...) assess several different criteria for individuating and formally representing agents’ choice options. (shrink)

The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which is both (...) the most commonly observed and a seemingly reasonable attitude to ambiguity---however supports a version of Egalitarianism, whose logical form is quite different from the theories defended by the aforementioned authors. Moreover, it turns out that the veil of ignorance argument neither supports standard Utilitarianism nor Prioritarianism unless we assume that rational people are insensitive to ambiguity. (shrink)

The basic Bayesian model of credence states, where each individual’s belief state is represented by a single probability measure, has been criticized as psychologically implausible, unable to represent the intuitive distinction between precise and imprecise probabilities, and normatively unjustifiable due to a need to adopt arbitrary, unmotivated priors. These arguments are often used to motivate a model on which imprecise credal states are represented by sets of probability measures. I connect this debate with recent work in Bayesian cognitive science, where (...) probabilistic models are typically provided with explicit hierarchical structure. Hierarchical Bayesian models are immune to many classic arguments against single-measure models. They represent grades of imprecision in probability assignments automatically, have strong psychological motivation, and can be normatively justified even when certain arbitrary decisions are required. In addition, hierarchical models show much more plausible learning behavior than flat representations in terms of sets of measures, which—on standard assumptions about update—rule out simple cases of learning from a starting point of total ignorance. (shrink)

There is currently much discussion about how decision making should proceed when an agent's degrees of belief are imprecise; represented by a set of probability functions. I show that decision rules recently discussed by Sarah Moss, Susanna Rinard and Rohan Sud all suffer from the same defect: they all struggle to rationalize diachronic ambiguity aversion. Since ambiguity aversion is among the motivations for imprecise credence, this suggests that the search for an adequate imprecise decision rule is not yet over.

This article is a critical survey of the debate over the value of the social discount rate, with a particular focus on climate change. The ma- jority of the material surveyed is from the economics rather than from the philosophy literature, but the emphasis of the survey itself is on founda- tions in ethical and other normative theory rather than highly technical details. I begin by locating the standard approach to discounting within the overall landscape of ethical theory, and explaining (...) the assumptions and simplifications that are needed in order to arrive at the model that is standard in the discounting literature. The article then covers the general theory of the Ramsey equation and its relationship to observed interest rates, arguments for and against a positive rate of pure time preference, the consumption elasticity of utility, and the effect of various sorts of uncertainty on the discount rate. Finally, it turns specifically to the ap- plication of this debate to the case of climate change, focussing on the recent controversy over the low discount rate used in the Stern Review of the Economics of Climate Change. (shrink)

Al-Najjar and Weinstein propose to scrutinize the implications of recent theories of ambiguity in dynamic settings. They conclude that such implications are so unreasonable as to cast doubts on the legitimacy of the theories under consideration. The present paper argues that the seemingly unreasonable implications highlighted by Al-Najjar and Weinstein can be understood as the result of basic trade-offs that arise naturally in the presence of ambiguity. In particular, Al-Najjar and Weinstein are uncomfortable with the possibility that an ambiguity-averse individual (...) may reject freely available information; however, this phenomenon simply reflects a trade-off between the intrinsic value of information, which is positive even in the presence of ambiguity, and the value of commitment. (shrink)

We use probability-matching variations on Ellsberg’s single-urn experiment to assess three questions: (1) How sensitive are ambiguity attitudes to changes from a gain to a loss frame? (2) How sensitive are ambiguity attitudes to making ambiguity easier to recognize? (3) What is the relation between subjects’ consistency of choice and the ambiguity attitudes their choices display? Contrary to most other studies, we find that a switch from a gain to a loss frame does not lead to a switch from ambiguity (...) aversion to ambiguity neutrality and/or ambiguity seeking. We also find that making ambiguity easier to recognize has little effect. Finally, we find that while ambiguity aversion does not depend on consistency, other attitudes do: consistent choosers are much more likely to be ambiguity neutral, while ambiguity seeking is much more frequent among highly inconsistent choosers. (shrink)

The menu-dependent nature of regret-minimization creates subtleties when it is applied to dynamic decision problems. It is not clear whether forgone opportunities should be included in the menu. We explain commonly observed behavioral patterns as minimizing regret when forgone opportunities are present. If forgone opportunities are included, we can characterize when a form of dynamic consistency is guaranteed.

Al-Najjar and Weinstein argue that the extant literature on ambiguity aversion is not successful in accounting for Ellsberg choices as rational responses to ambiguity. We concur, and propose that rational choice under ambiguity aims at robustness rather than avoidance of ambiguity. A central argument explains why robust choice is intrinsically context-dependent and legitimately violates standard choice consistency conditions. If choice consistency is forced, however, ambiguity-aversion emerges as a semi-rational response to ambiguity.

I argue that many of the priority rankings that have been proposed by effective altruists seem to be in tension with apparently reasonable assumptions about the rational pursuit of our aims in the face of uncertainty. The particular issue on which I focus arises from recognition of the overwhelming importance and inscrutability of the indirect effects of our actions, conjoined with the plausibility of a permissive decision principle governing cases of deep uncertainty, known as the maximality rule. I conclude that (...) we lack a compelling decision theory that is consistent with a long-termist perspective and does not downplay the depth of our uncertainty while supporting orthodox effective altruist conclusions about cause prioritization. GPI Working Paper No. 2-2019. (shrink)

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons (...) to be uncertain about updating, rationality can require you to prefer ignorance. (shrink)

I argue that many of the priority rankings that have been proposed by effective altruists seem to be in tension with apparently reasonable assumptions about the rational pursuit of our aims in the face of uncertainty. The particular issue on which I focus arises from recognition of the overwhelming importance and inscrutability of the indirect effects of our actions, conjoined with the plausibility of a permissive decision principle governing cases of deep uncertainty, known as the maximality rule. I conclude that (...) we lack a compelling decision theory that is consistent with a longtermist perspective and does not downplay the depth of our uncertainty, while also supporting orthodox effective altruist conclusions about cause prioritization. (shrink)

We analyze the role of ethical values in the determination of the social cost of carbon, arguing that the familiar debate about discounting is too narrow. Other ethical issues are equally important to computing the social cost of carbon, and we highlight inequality, risk, and population ethics. Although the usual approach, in the economics of cost-benefit analysis for climate policy, is confined to a utilitarian axiology, the methodology of the social cost of carbon is rather flexible and can be expanded (...) to a broader set of social-welfare approaches. [Open access]. (shrink)

This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, is the (...) general approach taken for resolving sequential decision problems { we make explicit what the key alternatives are and defend our own approach. Furthermore, we endorse a resolution of the aforementioned puzzle { we privilege decision theories that merely permit avoiding free evidence over decision theories for which avoiding free evidence is uniquely admissible. Finally, we situate this particular result about free evidence within the broader `dynamic-coherence' literature. (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

We distinguish three qualitatively different types of uncertainty—ethical, option and state space uncertainty—that are distinct from state uncertainty, the empirical uncertainty that is typically measured by a probability function on states of the world. Ethical uncertainty arises if the agent cannot assign precise utilities to consequences. Option uncertainty arises when the agent does not know what precise consequence an act has at every state. Finally, state space uncertainty exists when the agent is unsure how to construct an exhaustive state space. (...) These types of uncertainty are characterised along three dimensions—nature, object and severity—and the relationship between them is examined. We conclude that these different forms of uncertainty cannot be reduced to empirical uncertainty about the state of the world without inducing an increase in its severity. (shrink)

How should an impartial social observer judge distributions of well-being across different individuals when there is uncertainty regarding the state of the world? I explore this question by imposing very weak conditions of rationality and benevolent sympathy on impartial betterness judgments under uncertainty. Although weak enough to be consistent with all the main theories of rationality, these conditions prove to be sufficient to rule out any heterogeneity in what is good for individuals, to require a neutral attitude to uncertainty on (...) the part of the social observer, and to require that both individual and social betterness be strongly separable. (shrink)

Imprecise probabilities are an increasingly popular way of reasoning about rational credence. However they are subject to an apparent failure to display convincing inductive learning. This paper demonstrates that a small modification to the update rule for IP allows us to overcome this problem, albeit at the cost of satisfying only a weaker concept of coherence.

Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the ambiguous bet (...) and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process. (shrink)

Knowledge-first epistemology includes a knowledge norm of action: roughly, act only on what you know. This norm has been criticized, especially from the perspective of so-called standard decision theory. Mueller and Ross provide example decision problems which seem to show that acting properly cannot require knowledge. I argue that this conclusion depends on applying a particular decision theory which is ill-motivated in this context. Agents’ knowledge is often most plausibly formalized as an ambiguous epistemic state, and the theory of decision (...) under ambiguity is then the appropriate modeling tool. I show how to model agents as acting rationally on the basis of their knowledge according to such a theory. I conclude that the tension between the knowledge norm of action and formal decision theory is illusory; the knowledge-first paradigm should be used to actively select the decision-theoretical tools that can best capture the knowledge-based decisions in any given situation. (shrink)

Gerd Gigerenzer and Thomas Sturm have recently proposed a modest form of what they describe as a normative, ecological and limited naturalism. The basic move in their argument is to infer that certain heuristics we tend to use should be used in the right ecological setting. To address this argument, we first consider the case of a concrete heuristic called Take the Best (TTB). There are at least two variants of the heuristic which we study by making explicit the choice (...) functions they induce, extending these variants of TTB beyond binary choice. We argue that the naturalistic argument can be applied to only one of the two variants of the heuristic; we also argue that the argument for the extension requires paying attention to other “rational” virtues of heuristics aside from efficacy, speed, and frugality. This notwithstanding, we show that there is a way of extending the right variant of TTB to obtain a very well behaved heuristic that could be used to offer a stronger case for the naturalistic argument (in the sense that if this heuristic is used, it is also a heuristic that we should use). The second part of the article considers attempts to extending the naturalistic argument from algorithms dealing with inference to heuristics dealing with choice. Our focus is the so-called Priority Heuristic, which we extend from risk to uncertainty. In this setting, the naturalist argument seems more difficult to formulate, if it remains feasible at all. Normativity seems in this case extrinsic to the heuristic, whose main virtue seems to be its ability to describe actual patterns of choice. But it seems that a new version of the naturalistic argument used with partial success in the case of inference is unavailable to solve the normative problem of whether we should exhibit the patterns of choice that we actually display. (shrink)

Are foundations of models of ambiguity-sensitive preferences too flawed to be usefully applied to economic models? Al-Najjar and Weinstein (2009) say such is indeed the case. In this paper, first, we point out that many of the key arguments by Al-Najjar and Weinstein do not apply to quite a few of the ambiguity preference models of more recent vintage, and therefore to that extent do not undermine the foundational aspects or applicability of ambiguity models in general. Second, we argue the (...) focus in that paper on Ellsberg examples is an overly narrow concern; the Ellsberg examples have their uses but they are not the best context to understand why reasonable real-world agents may find acting in an ambiguity-sensitive manner normatively or prescriptively appealing. Finally, normative considerations aside, we submit that Al-Najjar and Weinstein are unduly dismissive of the power of such preferences to provide illuminating positive analyses of economic phenomena. (shrink)

This paper constructs a simple model of decision-making that accounts for the paradoxes of Ellsberg and Machina. It does so by representing decision makers’ beliefs on the vector space $${\mathbb{R}}\times {\mathbb{R}}$$ R × R and by providing a reasonable decision rule with axiomatic foundations. Moreover, the model allows for a characterization that clearly distinguishes between the two paradoxes. The interesting feature of the paper is that the ‘resolution’ of the paradoxes is along the lines suggested by the eponymous authors themselves. (...) This is to say, the decision rule derived from the axioms corresponds to Ellsberg’s own rule in the narrow set of circumstances that he explored, and the decision rule embodies Machina’s injunction that we treat choice under uncertainty in a similar manner to the way we treat standard consumer theory. That the paper cleaves to the advice of both authors is a little surprising given that it utilizes a two-dimensional vector space that neither author deployed. (shrink)

There are few models of price competition in a homogeneous-good market which permit general asymmetries of information amongst the sellers. This work studies a price game with discontinuous payoffs in which both costs and market demand are ex ante uncertain. The sellers evaluate uncertain profits with maximin expected utilities exhibiting ambiguity aversion. The buyers in the market are permitted to split between sellers tieing at the minimum price in arbitrary ways which may be deterministic or random. The role of the (...) primitives in determining equilibrium prices in the market is analyzed in detail. (shrink)