An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.

This book offers a comprehensive overview of the structure, strategy and methods of assessment of orthodox theoretical economics. In Part I Professor Hausman explains how economists theorise, emphasising the essential underlying commitment of economists to a vision of economics as a separate science. In Part II he defends the view that the basic axioms of economics are 'inexact' since they deal only with the 'major' causes; unlike most writers on economic methodology, the author argues that it is the rules that (...) economists espouse rather than their practice that is at fault. Part III links the conception of economics as a separate science to the fact that economic theories offer reasons and justifications for human actions, not just their causes. With its lengthy appendix introducing relevant issues in philosophy of science, this book is a major addition to philosophy of economics and of social science. (shrink)

In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities (...) and I argue that in it these expectations give no grounds for a decision to swap since that decision must be based on a summation of all the expectations. But this sum yields a non‐convergent series that has no meaningful value. The conflicting recommendations – that it is to one or the other player's advantage to swap – arise from different ways of grouping terms in the sum that yield an illusion of convergence. I describe a generalized exchange paradox, explore some of its properties and display another example. (shrink)

This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...) rationality and prudence. The sensible lover imitates the older literary example of Ulysses' tying himself to the mast. (The example belongs therefore to the class of problems treated in Elster (1979)). Both this lover and Ulysses foresee that under certain possible future conditions, their opinions, values and preferences will or would differ from what they are now, in a very definite fashion. To what extent is such foresight possible? Correspondingly (when we do not claim foreknowledge) to what extent is such opinion reasonable, rational, coherent, or consistent in some suitably broad sense? It is not easy to understand exactly what is possible or even logically permissible in this respect. In an earlier paper, "Belief and the Will", I argued for a principle ("Reflection") to govern such deliberation. Here I will both generalize the treatment of opinion in "Belief and the Will" and respond to criticism. Critical examples mainly resembled the story of Ulysses who foresaw a period of dysfunction (at the sound 2 of the sirens) in his epistemic and/or doxastic future. Other criticism focused on the model of opinion used (precise numerical subjective probability) and on the merits of Dutch Book arguments. The present argument will not rely on Dutch Book arguments and strategies, and the Reflection principle will be formulated so as to apply also to vague opinion. (shrink)

In the exchange paradox, two players receive envelopes containing different amounts of money. The assignment of the amounts ensures each player has the same probability of receiving each possible amount. Nonetheless, for each specific amount a player may find in his envelope, there is a positive expectation of gain if the player swaps envelopes with the other player, in apparent contradiction with the symmetry of the game. I consider a variant form of the paradox that avoids problems with improper probabilities (...) and I argue that in it these expectations give no grounds for a decision to swap since that decision must be based on a summation of all the expectations. But this sum yields a non‐convergent series that has no meaningful value. The conflicting recommendations – that it is to one or the other player's advantage to swap – arise from different ways of grouping terms in the sum that yield an illusion of convergence. I describe a generalized exchange paradox, explore some of its properties and display another example. (shrink)