1 On the impossibility of amalgamating evidence

It is argued in this paper that amalgamating confirmation from various sources is relevantly different from social-choice contexts, and that proving an impossibility theorem for aggregating confirmation measures directs attention to irrelevant issues.

Synthese, 2013

Amalgamating evidence of different kinds for the same hypothesis into an overall confirmation is analogous, I argue, to amalgamating individuals’ preferences into a group preference. The latter faces well-known impossibility theorems, most famously Arrow’s Theorem. Once the analogy between amalgamating evidence and amalgamating preferences is tight, it is obvious that amalgamating evidence might face a theorem similar to Arrow’s. I prove that this is so, and end by discussing the plausibility of the axioms required for the theorem.

We discuss a potential application of Arrow's impossibility theorem to the amalgamation of the evidence provided by different experimental sources. It has been suggested that, as long as there are three or more theories and at least two sources of evidence, Arrow's negative result applies, and hence the aggregation of individual rankings is bound to coincide with the ranking delivered by one of the sources. Here we show that Arrow's result need not obtain when dealing with the amalgamation of the evidence. To do so we discuss how different types of sources typically require different attitudes on the part of researchers regarding various auxiliary statements. Due to confirmational holism, the set of items to be ordered by level of confirmation is actually a set of structured elements. We argue that this simple fact will often impose restrictions on the domain of a reasonable amalgamation function, thus violating one of Arrow's conditions. This phenomenon has interesting consequences at the time of considering the legitimacy of making meaningful comparisons among hypotheses that are rival in a radical way. We end by suggesting possible extensions of our framework to other contexts that require aggregating individual rankings, and in which Arrow's theorem can be said to apply.

Economics and Philosophy, 2015

One kind of deliberation involves an individual reassessing the strengths of her beliefs in the light of new evidence. Bayesian epistemology measures the strength to which one ought to believe a proposition by its probability relative to all available evidence, and thus provides a normative account of individual deliberation. This can be extended to an account of individual judgement by treating the act of judgement as a decision problem, amenable to the tools of decision theory. A normative account of public deliberation and judgement can be provided by merging the evidence of the individuals in question and calculating appropriate Bayesian probabilities and judgement thresholds relative to this merged evidence. But this formal epistemology for deliberation and judgement lacks substance without an account of how evidence can be merged. And in order to provide such an account, we need in turn an account of what the evidence is that grounds Bayesian probabilities. This paper attempts to tackle these two concerns. After finding fault with several views on the nature of evidence (the views that evidence is knowledge; that evidence is whatever is fully believed; that evidence is observationally set credence; that evidence is information), it is argued that evidence is whatever is rationally taken for granted. This view has consequences for an account of merging, and it is shown that standard axioms for merging need to be altered somewhat. §1 Deliberation and Judgement Bayesianism provides a natural account of certain questions to do with judgement and doxastic deliberation: Individual Deliberation. How strongly should I believe θ? Individual Judgement. Should I judge θ as true? Public Deliberation. How strongly should we believe θ? Public Judgement. Should we judge θ as true? Let us consider these questions in turn. 1 There is no need to assume a common prior probability function or common knowledge here (Aumann, 1976), merely a common interest.

Synthese (SYNT)

To say that evidence is normative is to say that what evidence one possesses, and how this evidence relates to any proposition, determines which attitude among believing, disbe-lieving and withholding one ought to take toward this proposition if one deliberates about whether to believe it. It has been suggested by McHugh that this view can be vindicated by resting on the premise that truth is epistemically valuable. In this paper, I modify the strategy sketched by McHugh so as to overcome the initial difficulty that it is unable to vindicate the claim that on counterbalanced evidence with respect to P one ought to conclude deliberation by withholding on P. However, I describe the more serious difficulty that this strategy rests on principles whose acceptance commits one to acknowledging non-evidential reasons for believing. A way to overcome this second difficulty, against the evidentialists who deny this, is to show that we sometimes manage to believe on the basis of non-epis-temic considerations. If this is so, one fundamental motivation behind the evidentialist idea that non-epistemic considerations could not enter as reasons in deliberation would lose its force. In the second part of this paper I address several strategies proposed in the attempt to show that we sometimes manage to believe on the basis of non-epistemic considerations and show that they all fail. So, I conclude that the strategy inspired by McHugh to ground the normativity of evidence of the value of truth ultimately fails.

Episteme, 2023

The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that if evidence can be unspecific, then an alleged counterexample to causal decision theory fails. This implies that what theory of decision we think is true may depend on our opinions regarding the nature of evidence. Even when we are theorizing about subjective theories of rationality, we cannot set aside questions about the objective nature of evidence.

Journal of Statistical Planning and Inference, 1990

We investigate conditions under which conditional probability distributions approach each other and approach certainty as available data increase. Our purpose is to enhance Savage's (1954) results, in defense of 'personalism', about the degree to which consensus and certainty follow from shared evidence. For problems of consensus, we apply a theorem of Blackwell and Dubins (1962), regarding pairs of distributions, to compact sets of distributions and to cases of static coherence without dynamic coherence. We indicate how the topology under which the set of distributions is compact plays an important part in determining the extent to which consensus can be achieved. In our discussion of the approach to certainty, we give an elementary proof of the Lebesgue density theorem using a result of Halmos (1950). AIMS Subject Classifications: Primary 60BlO; secondary 62M20. Key words: Merging of opinions. 0378.3758/90/$3.50 0 1990, Elsevier Science Publishers B.V. (North-Holland)

2010

In a previous issue of this journal, Yamada (2008) presents an interesting new model of combination of evidence called combination by compromise based on previous works published in Yamada (2006b,a).

Philosophy of Science, 2000

The requirement of total evidence is a mainstay of Bayesian epistemology. Peter Fisher Epstein argues that the requirement generates mistaken conclusions about several examples that he devises. Here we examine the example of Epstein’s that we find most interesting and argue that Epstein’s analysis of it is flawed.