Formal Epistemology Workshop
2024

Talks

Mitch Barrington (Michigan) - "Duty and Risk"

Abstract: According to absolutist moral theories, agents may not violate their duties for the sake of arbitrarily valuable consequences. Yet intuitively, it is permissible to take a sufficiently small risk of violation for the sake of the consequences. The Risk Problem is that it is notoriously difficult to give a principled account of how good consequences can justify the small risk, but no larger quantity of good consequences could justify the larger risk. I show that extant solutions to the Risk Problem have fatal flaws, then offer a theory that avoids these issues. The basic idea is that agents maximize rounded expected deontic weight (the degree to which, in some outcome, they uphold their duties) and use expected value to break ties. We find that absolutists have a generous helping of standard decision-theoretic resources at their disposal. Then, we use these resources to start doing absolutist decision theory, discovering surprising results about how absolutists should relate to preference axioms. They must, for instance, give up the Sure Thing Principle and the dominance principles it secures. Fortunately, as we come to see, these principles are unattractive—and arguments for them unconvincing—to the absolutist.

Paul Egré and Benjamin Spector (Institut Jean-Nicod) - "Explaining vague language"

Abstract: Why is language vague? Vagueness may be explained and rationalized if it can be shown that vague language is more useful to speaker and hearer than precise language. In a well-known paper, Lipman proposes a game-theoretic account of vagueness in terms of mixed strategy that leads to a puzzle: vagueness cannot be strictly better than precision at equilibrium. More recently, Egré, Spector, Mortier and Verheyen have put forward a Bayesian account of vagueness establishing that using vague words can be strictly more informative than using precise words. This paper proposes to compare both results and to explain why they are not in contradiction. Lipman's definition of vagueness relies exclusively on a property of signaling strategies, without making any assumptions about the lexicon, whereas Egré et al.'s involves a layer of semantic content. We argue that the semantic account of vagueness is needed, and more adequate and explanatory of vagueness.

Johan Gustafsson (UT Austin) - "Dynamic Causal Decision Theory"

Abstract: Causal decision theorists are vulnerable to a money pump if they update by conditioning when they learn what they have chosen. Nevertheless, causal decision theorists are immune to money pumps if they instead update by imaging on their choices and by conditioning on other things (and, in addition, evaluate plans rather acts). I show that David Lewis's Dutch-book argument for conditioning does not work when you update on your choices. Even so, a collective of causal decision theorists are still exploitable even if they start off with the same preferences and the same credences and will all see the same evidence. Evidential decision theorists who consistently update by conditioning are not exploitable in this way.

Simon Huttegger (UC Irvine), Sean Walsh (UCLA), and Francesca Zaffora Blando (Carnegie Mellon) - "Bayesian Randomness"

Abstract: In this article, we pursue two main goals. First, we develop a Bayesian perspective on algorithmic randomness, a branch of computability theory concerned with providing a formal account of the notion of a probabilistically effectively typical outcome. Second, we argue that adopting such a viewpoint leads to new insights for Bayesian epistemology--specifically, for one of the central pillars of Bayesian epistemology: the phenomenon of Bayesian convergence to the truth. We begin by arguing that computable probability theory provides a suitable framework for modeling the credences of computationally limited, and, thus, more realistic, Bayesian agents. We then show that adopting a Bayesian perspective on algorithmic randomness reveals that, for computable Bayesian agents--namely, for Bayesian agents whose credences are given by computable probability measures--the sequences of observations, or data streams, along which convergence to the truth occurs coincide with the algorithmically random data streams. More precisely, we show that, for several natural classes of effective inductive problems, a computable Bayesian agent's credences converge to the truth for all inductive problems in the given class if and only if the observed data stream is algorithmically random.

Michele Odisseas Impagnatiello (MIT) - "Representation Theorems and Expected Utility"

Abstract: One of the main arguments for Expected Utility Theory is the argument from representation theorems. This argument relies on the contentious premise that if an agent is representable as having a certain utility function, then the agent does have that utility function. In this paper, I argue that the basic insight behind representation theorems and their axioms can be used to give a better argument for Expected Utility Theory. By taking the agent’s utility function as given, and by adding plausible axioms that connect preference and utility, we can derive that the agent must prefer options with higher expected utility.

Ina Jäntgen (Cambridge) - "How effect sizes fail the risk-sensitive"

Abstract: Researchers often quantify the effectiveness of tested treatments using relative or absolute effect sizes, and these effect sizes inform decision-making between treatments, for instance, in clinical settings. This practice has an important and neglected problem: Absolute and relative effect sizes may fail to inform risk-sensitive rational agents sufficiently to decide which treatment is best. Effect sizes fail the risk-sensitive. This verdict holds for the standard view of rational decision-making -- Expected Utility Theory. It sets the ground for a much-needed debate on whether and, if so, how to use effect sizes in evidence-based decision-making.

Petra Kosonen (UT Austin) - " Bounded Utilities and Ex Ante Pareto"

Abstract: This paper shows that decision theories on which utilities are bounded, such as standard axiomatizations of Expected Utility Theory, violate Ex Ante Pareto if combined with an additive axiology, such as Total Utilitarianism. A series of impossibility theorems point toward Total Utilitarianism as the right account of axiology, while money-pump arguments put Expected Utility Theory in a favorable light. However, it is not clear how these two views can be reconciled. This question is particularly puzzling if utilities are bounded (as standard axiomatizations of Expected Utility Theory imply) because the total quantity of well-being might be infinite or arbitrarily large. Thus, there must be a non-linear transformation from the total quantity of well-being into utilities used in decision-making. However, such a transformation leads to violations of Ex Ante Pareto. So, the reconciliation of Expected Utility Theory and Total Utilitarianism prescribes prospects that are better for none and worse for some.

Adrian Liu (Rutgers) - "Avoiding Polarization"

Abstract: Epistemic agents have higher-order uncertainty when they are unsure what the rational credences are. If higher-order uncertainty is rationally permissible, then in theory agents can obey many standard constraints on epistemic rationality, yet fail to match their current credences and their expected future credences. Two agents who fail to match and do so in different directions will polarize their opinions. Exploiting this possibility, Dorst (2023) proposes a mechanism in which asymmetries in when evidence is ambiguous – when it allows higher-order uncertainty – generate polarization. He hypothesizes that the mechanism can explain real-world cases of political belief polarization. I argue that the asymmetries in question do not generate polarization. While they allow polarization, the asymmetries do not generate rational pressure to polarize nor eliminate rational pressure to avoid polarization.

Zhen Ma (Peking University) - "Local Deference and Multiple Experts"

In a recent series of articles, Kevin Dorst has defended what he calls Trust, a Goldilocks principle that can strike a balance between the value of evidence and rational higher-order uncertainty (namely, modesty). This paper is a natural extension of Trust in a prior framework with multiple expert functions, and the conclusions are (i) Trust, unlike other reflection principles, proves effective in addressing the challenge of expert disagreement. (ii) The prior framework with multiple expert functions presents a promising path for exploring local deference.

Ioannis Polychronopoulos (LMU Munich) - "Regularity and Non-Linear Probabilities"

Abstract: One of the conditions that have been proposed as rational constraints for an agent's probability assignments is Regularity. Regularity states that apart from contradictions, no proposition should be assigned probability 0. The obvious issue with this suggestion is that there are often far too many propositions for an agent to assign non-zero and real probability to all of them. A promising but controversial solution advocated by the proponents of regularity is to allow for probabilities with infinitesimal values. In this paper, I will make the case for regularity and defend it from past objections, most notably Williamson's (2007) argument and Easwaran's (2014) discussion of it. As I will argue, the argument shows that there are pairs of propositions that are not equiprobable, but neither of which is more likely than the other. Formalizing such a phenomenon requires a novel approach to infinitesimal probabilities. Therefore, I will propose a non-linear probability theory preserving the intuitive structure of standard probability theory, while also accounting for probabilistically incomparable propositions.

Hayden Wilkinson (Oxford) - "Flummoxing Expectations"

Abstract: Expected utility theory often falls silent, even in cases where the correct ranking of options seems obvious. For instance, it fails to compare the Pasadena game to the Altadena game, despite the latter turning out better in every state. Decision theorists have attempted to fill these silences by proposing various extensions to expected utility theory. As I show in this paper, such extensions often fall silent too, even in cases where the correct ranking is intuitively obvious. But we can extend the theory further than has been done before--I offer a new extension, Invariant Value Theory, which deals neatly with those problem cases and also satisfies various desirable conditions. But other prima facie desirable conditions, including Independence, the theory violates. Is this a problem for the proposal? It may not be--in a new impossibility result, I show that no theory can satisfy Independence in full generality without violating several other conditions that together seem just as plausible.

Xin Hui Yong (MIT) - "Adapting Decision Theory: A Fragmentationist Model of Adaptive Evaluative States"

Abstract: Kim is strong-minded, empowered and rational save her desire for risky cosmetic surgeries. Why? Have her evaluative states been harmfully distorted, and should people intervene? The adaptive preferences (AP) literature's attempts to answer this have been criticized: misdiagnosing Kim's evaluative states is not only disrespectful of her rationality, but could also result in harmful interventions. This has led theorists like Serene Khader to call for a careful differentiation between the different reasons an agent perpetuates their own harm. But *how* exactly to draw this distinction remains a thorny problem.

I propose a novel solution to this problem that adapts fragmentation, a concept drawn from decision theory (Elga and Rayo 2022). On this account, not just practitioners, but Kim *herself* has the tools to autonomously evaluate and intervene on her adaptive preferences. By synthesizing two literatures, I provide resources relevant to practitioners and theorists alike.