William L. Harper

This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances

Skyrms' investigations of dynamic deliberation are traced through his book of 1990 and his subsequent investigation of dynamic deliberation based on inductive rules to his recent results about chaos generated by evolutionary game dynamics. It is argued that the dynamics studied in the book, and the inductive dynamics as well, need to be supplemented to yield the correct recommendation in an example game. Some features about information feedback are pointed out. Finally, it is suggested that more work is needed to assess whether Skyrms' results about chaos have any interesting implications for plausible game theoretic representations of interactions among human agents.