There is a long-standing disagreement in the philosophy of probability and Bayesian decision theory about whether an agent can hold a meaningful credence about an upcoming action, while she deliberates about what to do. Can she believe that it is, say, 70% probable that she will do A, while she chooses whether to do A? No, say some philosophers, for Deliberation Crowds Out Prediction (DCOP), but others disagree. In this paper, we propose a valid core for DCOP, and identify terminological (...) causes for some of the apparent disputes. (shrink)

The coordinated attack scenario and the electronic mail game are two paradoxes of common knowledge. In simple mathematical models of these scenarios, the agents represented by the models can coordinate only if they have common knowledge that they will. As a result, the models predict that the agents will not coordinate in situations where it would be rational to coordinate. I argue that we should resolve this conflict between the models and facts about what it would be rational to do (...) by rejecting common knowledge assumptions implicit in the models. I focus on the assumption that the agents have common knowledge that they are rational, and provide models to show that denying this assumption suffices for a resolution of the paradoxes. I describe how my resolution of the paradoxes fits into a general story about the relationship between rationality in situations involving a single agent and rationality in situations involving many agents. (shrink)

There are decision problems in which rational deliberation fails to result in choosing a pure act. This phenomenon is known as decision instability and has been discussed in the literature on causal decision theory. In this paper we investigate another type of instability, called structural instability in dynamical systems theory. Structural instability indicates that certain qualitative features of the process of rational deliberation are under-determined in a decision situation. We illustrate some of the issues arising from structural instability with a (...) recent argument against causal decision theory proposed by Caspar Hare and Brian Hedden. We show that their argument is undermined by considerations arising from decision instability and structural instability. (shrink)

This paper applies the theoretical criteria laid out by D’Arms et al. to various aspects of evolutionary models of signalling. The question that D’Arms et al. seek to answer can be formulated as follows: Are the models that we use to explain the phenomena in question conceptually adequate? The conceptual adequacy question relates the formal aspects of the model to those aspects of the natural world that the model is supposed to capture. Moreover, this paper extends the analysis of D’Arms (...) et al. by asking the following additional question: Are the models that we use sufficient to explain the phenomena in question? The sufficiency question asks what formal resources are minimally required for the model to get the right results most of the time. (shrink)

I give a Dutch book argument for CDT thirders in the context of a generalized Sleeping Beauty scenario. In combination with the Briggs (2010) Dutch book for EDT thirders, this amounts to a purely decision-theoretic argument for halfing in Sleeping Beauty. In combination with the Hitchcock (2004) Dutch book for CDT halfers, this amounts to a Dutch book argument against CDT. The combined Dutch book against CDT invites a plausible diagnosis of the reasons for CDT’s failure: CDT is incompatible with (...) the Dutch book requirement because it allows the values of epistemically impossible outcomes influence one’s decision. (shrink)

Andy Egan has recently produced a set of alleged counterexamples to causal decision theory in which agents are forced to decide among causally unratifiable options, thereby making choices they know they will regret. I show that, far from being counterexamples, CDT gets Egan's cases exactly right. Egan thinks otherwise because he has misapplied CDT by requiring agents to make binding choices before they have processed all available information about the causal consequences of their acts. I elucidate CDT in a way (...) that makes it clear where Egan goes wrong, and which explains why his examples pose no threat to the theory. My approach has similarities to a modification of CDT proposed by Frank Arntzenius, but it differs in the significance that it assigns to potential regrets. I maintain, contrary to Arntzenius, that an agent facing Egan's decisions can rationally choose actions that she knows she will later regret. All rationality demands of agents it that they maximize unconditional causal expected utility from an epistemic perspective that accurately reflects all the available evidence about what their acts are likely to cause. This yields correct answers even in outlandish cases in which one is sure to regret whatever one does. (shrink)

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not (...) decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory. (shrink)

We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special consideration being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We extend this result to a type of Jeffrey conditioning where agents update on evidence that is uncertain but solid. However, merging (...) of beliefs does not generally hold for Jeffrey conditioning on evidence that is fluid. Several theorems on the asymptotic behavior of subjective probabilities are proven. Taken together they show that while a consensus nearly always emerges in important special cases, sustained rational disagreement can be expected in many other situations. (shrink)

Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...

According to the so-called ‘deliberation crowds out prediction’ thesis, while deliberating about what you’ll do, you cannot rationally have credences for what you’ll do – you cannot rationally have option-credences. Versions of the thesis have been defended by authors such as Spohn, Levi, Gilboa, Price, Louise, and others. After registering a number of concerns about the thesis, I rehearse and rebut many of the main arguments for it, grouped according to their main themes: agency, vacuity, betting, and decision-theoretical considerations. I (...) go on to suggest many possible theoretical roles for option-credences. -/- I locate the debate about the thesis in a broader discussion: Are there rational credence gaps – propositions to which one cannot rationally assign credences? If there are, they spell trouble for various foundations of Bayesian epistemology, including the usual ratio formula for conditional probability, conditionalization, decision theory, and independence. According to the thesis, credence gaps are completely mundane; they arise every time someone rationally deliberates. But these foundations are safe from any threat here, I contend, since the thesis is false. Deliberation welcomes prediction. (shrink)

Sufficient conditions are given under which ratifiable acts exist.

I explore the prospects for modelling epistemic rationality (in the probabilist setting) via an epistemic decision theory, in a consequentialist spirit. Previous work has focused on cases in which the truth-values of the propositions in which the agent is selecting credences do not depend, either causally or merely evidentially, on the agent’s choice of credences. Relaxing that restriction leads to a proliferation of puzzle cases and theories to deal with them, including epistemic analogues of evidential and causal decision theory, and (...) of the Newcomb Problem and ‘Psychopath Button’ Problem. A variant of causal epistemic decision theory deals well with most cases. However, there is a recalcitrant class of problem cases for which no epistemic decision theory seems able to match our intuitive judgements of epistemic rationality. This lends both precision and credence to the view that there is a fundamental mismatch between epistemic consequentialism and the intuitive notion of epistemic rationality; the implications for understanding the latter are briefly discussed. (shrink)

A one-boxer, Erica, and a two-boxer, Chloe, engage in a familiar debate. The debate begins with Erica asking Chloe: ‘If you’re so smart, then why ain’cha rich?’. As the debate progresses, Chloe is led to endorse a novel causalist theory of rational choice. This new theory allows Chloe to forge a connection between rational choice and long-run riches. In brief: Chloe concludes that it is not long-run wealth but rather long-run wealth creation which is symptomatic of rationality.

Harold Jeffreys' ideas on the interpretation of probability and epistemology are reviewed. It is argued that with regard to the interpretation of probability, Jeffreys embraces a version of logicism that shares some features of the subjectivism of Ramsey and de Finetti. Jeffreys also developed a probabilistic epistemology, characterized by a pragmatical and constructivist attitude towards notions such as ‘objectivity’, ‘reality’ and ‘causality’. 1 Introductory remarks 2 The interpretation of probability 3 Jeffreys' probabilistic epistemology.

I present a decision problem in which causal decision theory appears to violate the independence of irrelevant alternatives (IIA) and normal-form extensive-form equivalence (NEE). I show that these violations lead to exploitable behavior and long-run poverty. These consequences appear damning, but I urge caution. This decision should lead causalists to a better understanding of what it takes for a decision between some collection of options to count as a subdecision of a decision between a larger collection of options. And with (...) this better understanding of subdecisions in hand, causalists will not violate the IIA or the NEE. This decision will also teach causalists that, in sequential decisions, a rational agent may be led to make a series of choices which are causally dominated by some other sequence of choices they could have made instead. I will encourage causalists to recognise this as an intrapersonal tragedy of the commons. (shrink)

I respond to a dilemma for Causal Decision Theory (CDT) under determinism, posed in Adam Elga's paper “Confessions of a Causal Decision Theorist”. The treatment I present highlights (i) the status of laws as predictors, and (ii) the consequences of decision dependence, which arises natively out of Jeffrey Conditioning and CDT's characteristic equation.My argument leverages decision dependence to work around a key assumption of Elga's proof: to wit, that in the two problems he presents, the CDTer must employ subjunctive-suppositional (rather (...) than evidential) transformations of a shared prior. (shrink)

Dynamo: Diagrams for Evolutionary Game Dynamics is free, open-source software used to create phase diagrams and other images related to dynamical systems from evolutionary game theory. We describe how to use the software’s default settings to generate phase diagrams quickly and easily. We then explain how to take advantage of the software’s intermediate and advanced features to create diagrams that highlight the key properties of the dynamical system under study. Sample code and output are provided to help demonstrate the software’s (...) capabilities. (shrink)

When we deliberate about what to do, we appear to be free to decide on different options. Three accounts use ordinary beliefs to explain this apparent freedom—appealing to different types of ‘epistemic freedom’. When an agent has epistemic freedom, her evidence while deliberating does not determine what decision she makes. This ‘epistemic gap’ between her evidence and decision explains why her decision appears free. The varieties of epistemic freedom appealed to might look similar. But there is an important difference. Two (...) rely on an agent's ability to justifiably form beliefs unconstrained by evidence, and identify decisions as beliefs—either beliefs about acts or about decisions. But, when used to explain apparent freedom, these accounts face serious problems: they imply that agents have epistemic freedom over evidence-based beliefs, and rely on a faulty notion of justification. Underlying these troubles, it turns out that these accounts presuppose an unexplained apparent ability to form different beliefs. A third variety of epistemic freedom uses ignorance conditions instead (Levi and Kapitan). We appear free partly because we’re ignorant of what we’ll decide. Ignorance-based accounts avoid the above problems, and remain a promising alternative. (shrink)

A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences.

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should (...) be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, (...) a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility. (shrink)

In sequential decision problems, an act of learning cost-free evidence might be symptomatic, in the sense that performing this act itself provides evidence about states of the world it does nothing to causally promote. It is well known that orthodox causal decision theory, like its main rival evidential decision theory, may sanction such acts as rationally impermissible. This paper shows that, under plausible assumptions, a minimal version of ratificationist causal decision theory, known as principled ratificationism, fares better in this respect, (...) for it never labels symptomatic acts of learning cost-free evidence as rationally impermissible. (shrink)

A computer simulation runs a model generating a phenomenon under investigation. For the simulation to be explanatory, the model has to be explanatory. The model must be isomorphic to the natural system that realizes the phenomenon. This paper elaborates the method of assessing a simulation's explanatory power. Then it illustrates the method by applying it to two simulations in game theory. The first is Brian Skyrms's (1990) simulation of interactive deliberations. It is intended to explain the emergence of a Nash (...) equilibrium in a noncooperative game. The second is Skyrms's (2004) simulation of the evolution of cooperation. It is intended to explain cooperation in assurance games. The final section suggests ways of enhancing the explanatory power of these simulations. (shrink)

Since Ernest Sosa's (1980) seminal paper, a variety of views on the nature of intellectual virtues and their role in one's epistemic theory have emerged. These views, including Sosa's original, largely draw from moral counterparts for their motivation, articulation, and defense. Consider two broad accounts of intellectual virtues: -/- Consequentialist Conception (CC): An intellectual virtue is a stable disposition, ability, or power to reliably acquire epistemic goods (e.g., true belief and knowledge). -/- Aristotelian Conception (AC): An intellectual virtue is a (...) character trait involving an underlying psychological and behavioral structure directed at various epistemic goods. (shrink)

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich (...) the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden, and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions. (shrink)

Nobody's going to object to the advice "Do the right thing", but that doesn't mean everyone's always going to follow it. Sometimes this is because of our volitional limitations; we cannot always bring ourselves to make the sacrifices that right action requires. But sometimes this is because of our cognitive limitations; we cannot always be sure of what is right. Sometimes we can't be sure of what's right because we don't know the non-normative facts. But sometimes, even if we were (...) to know all of the non-normative facts, we'd still not be sure about what's right, because we're uncertain about the normative reasons those facts give us. In this dissertation, I attempt to answer the question of what we're to do when we must act under fundamentally normative uncertainty. It's tempting to think that, in such circumstances, we should do what we regard as most probably right. I argue that this view is mistaken, for it is insensitive to how degrees of actions' values compare across different normative hypotheses; if an action is probably right, but, if wrong, is terribly, terribly, wrong, it may be rational not to do that action. A better answer is that we should do the action with the highest expected value. I spend the first part of the dissertation providing arguments for and rebutting arguments against this view of action under normative uncertainty. I spend the next part of the dissertation explaining what degrees of value are, and showing how they can be compared across normative hypotheses. In the remaining parts of the dissertation, I consider two questions related to our primary question -- first, what is one required, or obligated, to do under normative uncertainty; and second, what is it rational for one to do when one is not only normatively uncertain in the way we've been discussing, but also uncertain about what it is rational to do under this sort of normative uncertainty. (shrink)