Paradoxes in Probability Theory


Book Description

Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.​




Paradoxes of Rationality and Cooperation


Book Description

This anthology, the first to bring together the most importantphilosophical essays on the paradoxes, analyses the concepts underlyingthe Prisoner's Dilemma and Newcomb's Problem and evaluates theproposed solutions. The relevant theories have been developed over thepast four decades in a variety of disciplines: mathematics, economics,psychology, political science, biology, and philosophy. And theproblems these paradoxes uncover can arise in many different forms: indebates over nuclear disarmament, labour-management disputes, maritalconflicts, Calvinist theology, and even in the evolution of diseasethrough the "cooperation" of microorganisms. Thepossibilities for application are virtually limitless.













Introduction to Probability


Book Description

This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.




Paradoxes of Belief and Strategic Rationality


Book Description

The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions.




Good and Real


Book Description

Examining a series of provocative paradoxes about consciousness, choice, ethics, and other topics, Good and Real tries to reconcile a purely mechanical view of the universe with key aspects of our subjective impressions of our own existence. In Good and Real, Gary Drescher examines a series of provocative paradoxes about consciousness, choice, ethics, quantum mechanics, and other topics, in an effort to reconcile a purely mechanical view of the universe with key aspects of our subjective impressions of our own existence. Many scientists suspect that the universe can ultimately be described by a simple (perhaps even deterministic) formalism; all that is real unfolds mechanically according to that formalism. But how, then, is it possible for us to be conscious, or to make genuine choices? And how can there be an ethical dimension to such choices? Drescher sketches computational models of consciousness, choice, and subjunctive reasoning--what would happen if this or that were to occur? --to show how such phenomena are compatible with a mechanical, even deterministic universe. Analyses of Newcomb's Problem (a paradox about choice) and the Prisoner's Dilemma (a paradox about self-interest vs. altruism, arguably reducible to Newcomb's Problem) help bring the problems and proposed solutions into focus. Regarding quantum mechanics, Drescher builds on Everett's relative-state formulation--but presenting a simplified formalism, accessible to laypersons--to argue that, contrary to some popular impressions, quantum mechanics is compatible with an objective, deterministic physical reality, and that there is no special connection between quantum phenomena and consciousness. In each of several disparate but intertwined topics ranging from physics to ethics, Drescher argues that a missing technical linchpin can make the quest for objectivity seem impossible, until the elusive technical fix is at hand.




The Strategic Constitution


Book Description

Making, amending, and interpreting constitutions is a political game that can yield widespread suffering or secure a nation's liberty and prosperity. Given these high stakes, Robert Cooter argues that constitutional theory should trouble itself less with literary analysis and arguments over founders' intentions and focus much more on the real-world consequences of various constitutional provisions and choices. Pooling the best available theories from economics and political science, particularly those developed from game theory, Cooter's economic analysis of constitutions fundamentally recasts a field of growing interest and dramatic international importance. By uncovering the constitutional incentives that influence citizens, politicians, administrators, and judges, Cooter exposes fault lines in alternative forms of democracy: unitary versus federal states, deep administration versus many elections, parliamentary versus presidential systems, unicameral versus bicameral legislatures, common versus civil law, and liberty versus equality rights. Cooter applies an efficiency test to these alternatives, asking how far they satisfy the preferences of citizens for laws and public goods. To answer Cooter contrasts two types of democracy, which he defines as competitive government. The center of the political spectrum defeats the extremes in "median democracy," whereas representatives of all the citizens bargain over laws and public goods in "bargain democracy." Bargaining can realize all the gains from political trades, or bargaining can collapse into an unstable contest of redistribution. States plagued by instability and contests over redistribution should move towards median democracy by increasing transaction costs and reducing the power of the extremes. Specifically, promoting median versus bargain democracy involves promoting winner-take-all elections versus proportional representation, two parties versus multiple parties, referenda versus representative democracy, and special governments versus comprehensive governments. This innovative theory will have ramifications felt across national and disciplinary borders, and will be debated by a large audience, including the growing pool of economists interested in how law and politics shape economic policy, political scientists using game theory or specializing in constitutional law, and academic lawyers. The approach will also garner attention from students of political science, law, and economics, as well as policy makers working in and with new democracies where constitutions are being written and refined.