This paper sheds new light on the subtle relation between probability and logic by (i) providing a logical development of Bruno de Finetti's conception of events and (ii) suggesting that the subjective nature of de Finetti's interpretation of probability emerges in a clearer form against such a logical background. By making explicit the epistemic structure which underlies what we call Choice-based probability we show that whilst all rational degrees of belief must be probabilities, the converse doesn't hold: some probability values (...) don't represent decision-relevant quantifications of uncertainty. (shrink)

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework generalises (...) the classical Dutch Book method. (shrink)

Second-order uncertainty, also known as model uncertainty and Knightian uncertainty, arises when decision-makers can (partly) model the parameters of their decision problems. It is widely believed that subjective probability, and more generally Bayesian theory, are ill-suited to represent a number of interesting second-order uncertainty features, especially “ignorance” and “ambiguity”. This failure is sometimes taken as an argument for the rejection of the whole Bayesian approach, triggering a Bayes vs anti-Bayes debate which is in many ways analogous to what the classical (...) vs non-classical debate used to be in logic. This paper attempts to unfold this analogy and suggests that the development of non-standard logics offers very useful lessons on the contextualisation of justified norms of rationality. By putting those lessons to work I will flesh out an epistemological framework suitable for extending the expressive power of standard Bayesian norms of rationality to second- order uncertainty in a way which is both formally and foundationally conservative. Contents. (shrink)

We argue in favour of identifying one aspect of rational choice with the tendency to conform to the choice you expect another like-minded, but non-communicating, agent to make and study this idea in the very basic case where the choice is from a non-empty subset K of 2 A and no further structure or knowledge of A is assumed.

This paper presents the results of an experiment on mutual versus common knowledge of advice in a two-player weak-link game with random matching. Our experimental subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilibrium. Our results are somewhat surprising and can be summarized as follows: in all our treatments both (...) the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 induces, under suitable conditions, successful coordination more frequently than common knowledge. (shrink)

Predicting the future state of a system has always been a natural motivation for science and practical applications. Such a topic, beyond its obvious technical and societal relevance, is also interesting from a conceptual point of view. This owes to the fact that forecasting lends itself to two equally radical, yet opposite methodologies. A reductionist one, based on first principles, and the naïve-inductivist one, based only on data. This latter view has recently gained some attention in response to the availability (...) of unprecedented amounts of data and increasingly sophisticated algorithmic analytic techniques. The purpose of this note is to assess critically the role of big data in reshaping the key aspects of forecasting and in particular the claim that bigger data leads to better predictions. Drawing on the representative example of weather forecasts we argue that this is not generally the case. We conclude by suggesting that a clever and context-dependent compromise between modelling and quantitative analysis stands out as the best forecasting strategy, as anticipated nearly a century ago by Richardson and von Neumann. (shrink)

We illustrate how a variety of logical methods and techniques provide useful, though currently underappreciated, tools in the foundations and applications of reasoning under uncertainty. The field is vast spanning logic, artificial intelligence, statistics, and decision theory. Rather than (hopelessly) attempting a comprehensive survey, we focus on a handful of telling examples. While most of our attention will be devoted to frameworks in which uncertainty is quantified probabilistically, we will also touch upon generalisations of probability measures of uncertainty, which have (...) attracted a significant interest in the past few decades. (shrink)

This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts.