Richard Bradley

Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation cannot be defined within them, on pain of collapsing probability into bivalence.

This article examines Becker's thesis that the hypothesis that choices maximize expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explains all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalized conditioning, allows for explanations in terms of changes in the values of all three variables. Key Words: preference change • decision theory • probability • desirability • attitude change.

Adams Thesis has much evidence in its favour, but David Lewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presuppose that the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is argued that the exact proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it might express, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents degrees of belief satisfyAdams Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals.

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.

An allocation problem is a type of aggregation problem in which the values of individuals' opinions on some set of variables (canonically a set of mutually exclusive and exhaustive possibilities) sum to a constant. This paper shows that for realistic allocation problems, namely ones in which the set of possible opinion values is finite, the only universal aggregation methods that satisfy two commonly invoked conditions are the dictatorial ones. The two conditions are, first, that the aggregate opinion on any variable depends only on the individuals' opinions on that variable and not on their opinions on any other variable and, secondly, that the aggregate opinion minimally preserves unanimous individual opinion. Connections between this result and similar ones in the literature on judgment aggregation are explored and their significance assessed.

This paper explores some aspects of the relation between different ways of achieving a consensus on the judgemental values of a group of indviduals; in particular, aggregation and deliberation. We argue firstly that the framing of an aggregation problem itself generates information that individuals are rationally obliged to take into account. And secondly that outputs of the deliberative process that this initiates is in tension with constraints on consensual values typically imposed by aggregation theory, at least when deliberation is modelled as process of learning from others compatible with Bayesian updating principles.

Multiple-vote majority rule is a procedure for making group decisions in which individuals weight their votes on issues in accordance with how competent they are on them. When individuals are motivated by the truth and know their relative competence on different issues, multiple-vote majority rule performs nearly as well, epistemically speaking, as rule by an expert oligarchy, but is still acceptable from the point of view of equal participation in the political process.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. A CASE FOR MULTIPLE-VOTE MAJORITY RULEVolume 9, Issue 1Richard Bradley and Christopher ThompsonDOI: https://doi.org/10.1017/epi.2011.5Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission.

Foundations of Bayesianism is an authoritative collection of papers addressing the key challenges that face the Bayesian interpretation of probability today. Some of these papers seek to clarify the relationships between Bayesian, causal and logical reasoning. Others consider the application of Bayesianism to artificial intelligence, decision theory, statistics and the philosophy of science and mathematics. The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the Bayesian approach. The upshot is a plethora of new problems and directions for Bayesians to pursue.The book will be of interest to graduate students or researchers who wish to learn more about Bayesianism than can be provided by introductory textbooks to the subject. Those involved with the applications of Bayesian reasoning will find essential discussion on the validity of Bayesianism and its limits, while philosophers and others interested in pure reasoning will find new ideas on normativity and the logic of belief.

Decision theory is the study of how choices are and should be made.in a variety of different contexts. Here we look at the topic from a formal-philosophical point of view with a focus on normative and conceptual issues. After considering the question of how decision problems should be framed, we look at the both the standard theories of chance under conditions of certainty, risk and uncertainty and some of the current debates about how uncertainty should be measured and how agents should respond to it.

As readers of this journal can attest to, although philosophers and economists are somewhat used to talking to and learning from each other, it tends to be the subset of philosophers working in decision theory, philosophy of science, and particular areas of ethics and political philosophy that contribute to our interdisciplinary field of research. The book that is the subject of this review symposium, Anna Mahtani’s The Objects of Credence (Oxford University Press, 2024), is a wonderful exemplar of what can be learned when a different branch of philosophy is brought to bear on central questions in this field. Both philosophers and economists talk about and work with credences, or degrees of belief, all the time. These are usually modelled as probabilities, which are in turn usually thought of as attaching to propositions. But it has long been argued by philosophers of language that propositions cannot be the objects of credence. Mahtani’s book is an investigation into all that begins to unravel once we accept this insight. The results have profound implications both for rational choice modelling and for welfare economics.

This dissertation interprets the lack of uniqueness in probability representations of agents' degrees of belief in the decision theory of Richard Jeffrey as a formal statement of an important epistemological problem: the underdetermination of our attributions of belief and desire to agents by the evidence of their observed behaviour. A solution is pursued through investigation of agents' attitudes to information of a conditional nature. ;As a first step, Jeffrey's theory is extended to agents' conditional attitudes of belief and desire by introduction of a definition of conditional desirability. The second step is an analysis of agents' attitudes to conditionals. Following Adams it is argued that the probability of a conditional is the conditional probability of its consequent given the antecedent. Since numerous 'trivialization' results show that no proposition could be such that this were the case, it is proposed that conditionals express a variable proposition as a function of the context in which they are asserted. The consequent technical treatment of conditionals as proposition-valued functions of sets of possible worlds delivers Adams' thesis as a natural consequence without fear of trivialization. ;Conditionals are the underlying objects of the decision theory that is presented in the final chapter. A representation theorem is proven for preferences defined over sets of such conditionals satisfying certain closure conditions, where an agent is understood to prefer one conditional over another just in case she prefers that the former by true rather than the latter. The theorem establishes that a rational preference ranking of conditionals implies the existence of a unique probability function and a desirability function unique up to choice of scale, that agree with the preference ranking, and that these functions satisfy both the axioms of Jeffrey's decision calculus and Adams' thesis. The theorem is interpreted as saying that elicitation of an agent's choices amongst conditional options suffices to determine our attributions of belief and desire to them