People With Common Priors Can Agree to Disagree

Lederman, Harvey

doi:10.1017/s1755020314000380

Cited by 16 publications

(14 citation statements)

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“…For some generalizations of this result see Rubinstein and Wolinsky (1990) and Bacharach (1985). For a recent accessible and illuminating treatment see Lederman (2015). And for some further recent discussion Demey (2014) and Degrémont and Roy (2012).…”

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confidence: 89%

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Agreement Theorems for Self-Locating Belief

Caie

2016

The Review of Symbolic Logic

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Abstract. In this paper, I first outline Aumann's famous "no agreeing to disagree" theorem, and a second related theorem. These results show that if two or more agents, who have epistemic and credal states that are defined over algebras that do not include any self-locating propositions, have certain information about one another's epistemic and credal states, then such agents must assign the same credence to certain propositions. I show, however, that both of these theorems fail when we consider agents who have epistemic and credal states that are defined over algebras that do include self-locating propositions. Importantly, these theorems fail for such agents even when we restrict our attention to the credences that such agents have in non-self-locating propositions. Having established this negative result, I then outline and prove three agreement theorems that hold for such agents.Call a centered proposition one that may vary its truth-value not only across worlds, but also across individuals or times, and call an uncentered proposition one that may only vary its truth-value across worlds. 1 It is well-known that, for agents whose epistemic and credal states are defined over algebras of uncentered propositions, there are strict formal constraints on the extent to which such agents may rationally assign distinct credences to propositions, given knowledge of one another's epistemic and credal states. Interestingly, though, if one adds to such algebras centered propositions, then such formal constraints on rational disagreement, even concerning uncentered propositions, no longer obtain. 2 The purpose of this paper is to explore the extent to which there are formal constraints on disagreement amongst agents whose epistemic and credal states are defined over algebras that include centered propositions, given knowledge of one another's epistemic and credal states.Let us say, roughly, that a set of agents are epistemic confidants just in case (i) it is common knowledge amongst them what each agent knows, and (ii) it is common knowledge Received: November 10, 2015. 1 Examples of centered propositions include the proposition that I am hungry at time t, and the proposition that it is now raining in Matera. Examples of uncentered propositions include the proposition that NN is hungry at time t, and the proposition that it is raining in Matera at time t. One might notice that centered propositions are often expressed by sentences that contain indexicals like 'I' and 'now'. Given this, one might naturally wonder whether we should also allow propositions to vary their truth-values over locations. Such propositions may be expressed by sentences involving the indexical 'here'.The answer is that, while we can allow for this sort of variation, we need not take it as basic. Instead, we can take such variation in truth-value over location to be deriviative from variation over times and individuals. As we'll see, we can represent centered propositions by sets of world, individual, time triples. Given this, we can then, for exam...

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confidence: 89%

“…For an elegant proof of Aumann's theorem that makes explicit various assumptions that are tacit in Aumann (1976) and that notes various ways in which the result may fail if certain of these assumptions are relaxed see Lederman (2015).…”

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confidence: 99%

Agreement Theorems for Self-Locating Belief

Caie

2016

The Review of Symbolic Logic

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“…Then (GSTP) says that if player i makes the same decision d in all possible situations in S (i.e., i makes the same decision d based on information ℐ i ( ν ) for all ν ∈ S ), then they decide on d simpliciter . See Lederman (, section 8.2) for a discussion on a similar principle. I thank Harvey Lederman for pointing this out to me after he read an earlier version of this paper.…”

Section: Impossible To Disagreementioning

confidence: 99%

Two Tales of Epistemic Models

Liu

2019

Thought: A Journal of Philosophy

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This short paper has two parts. First, we prove a generalisation of Aumann's surprising impossibility result in the context of rational decision making. We then move, in the second part, to discuss the interpretational meaning of some formal setups of epistemic models, and we do so by means of presenting an interesting puzzle in epistemic logic. The aim is to highlight certain problematic aspects of these epistemic systems concerning first/third‐person asymmetry which underlies both parts of the story. This asymmetry, we argue, reveals certain limits of what epistemic models can be.

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“…Third, Aumann's result relies on controversial assumptions about knowledge and evidence, in particular positive and negative introspection. Lederman (2015) shows that without these assumptions, there are models in which agents with common priors and common knowledge of their posterior probabilities do differ in their posteriors.…”

Section: Reasons-based Rationalitymentioning

confidence: 99%

Reasons, Coherence, and Group Rationality

Hedden

2018

Philos Phenomenol Research

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If groups can have beliefs and other attitudes of their own, what determines which such attitudes the group rationally ought to have? A widespread presupposition is that group-level beliefs should be a function of the beliefs of the group's members, and similarly for other attitudes. But a host of impossibility theorems show that no such aggregation function can satisfy intuitively attractive constraints while ensuring coherent group-level attitudes. I argue that this presupposition is false. Group-level attitudes should be a function of group-level reasons (evidence, in the epistemic case), not individual-level attitudes. This allows for a theory of group rationality that (i) bypasses a host of pessimistic results in the literature on judgment aggregation and (ii) treats rational individual-level attitudes and rational group-level attitudes in parallel.

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People With Common Priors Can Agree to Disagree

Abstract: Robert Aumann presents his Agreement Theorem as the key conditional: "if two people have the same priors and their posteriors for an event A are common knowledge, then these posteri-

Cited by 16 publications

References 42 publications

Agreement Theorems for Self-Locating Belief

Agreement Theorems for Self-Locating Belief

Two Tales of Epistemic Models

Reasons, Coherence, and Group Rationality

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