Choosing what to believe : belief change through the lens of rational choice

Abstract

Belief change, in the AGM tradition, gathers under a common methodological umbrella an array of operations, covering both single-agent and multi-agent processes. These operations are linked by the use of propositional logic as a lingua franca, are related by a network of interconnected rationality constraints and are united by the idea that they all describe, in some way or another, the dynamics of beliefs and information. In this thesis we want to see belief change, thus construed, as akin to making a decision: according to this perspective an agent, or group of agents, faced with new information must make a decision as to what part of the new information to adopt, in a manner that balances both the agents’ own positions, as well as certain rationality constraints, e.g., consistency. The parallel between changing a belief and making a decision is encouraged by the observation that both areas use the same underlying mechanisms of choices and preferences to rationalize their operations, in the process employing strikingly similar rationality constraints. Though we are not the first to make this observation, we argue that there is still space to explore its implications. Seeing belief change operators as choice procedures that rely on preferences over outcomes allows us to tap both a series of useful intuitions about what belief change operators do, and a set of properties, scattered throughout the rational and social choice literature, that can aid the design of new instruments for belief change. Thus, one side to our contribution to this thesis revolves around three existing prominent belief change operations, i.e., revision, update and merging, where these insights are employed in order to expand their range of application. For the case of revision we propose new postulates that deal with the way in which the prior information influences the revision process. For merging, which is a multi-agent operation, we adapt properties from the social choice literature, such as strategyproofness and proportionality, that formalize various aspects of fairness. We also look towards applications of revision and update to the Horn fragment of propositional logic, and extend existing work by studying weaker variants of the traditional postulates used in these cases. Another part of our contribution consists of a new type of belief change operation, which we call enforcement, and which we put forward both as a belief change operation in its own right and as theoretical background for a model of preference revision. In all these cases we use the usual belief change tools of logical postulates, which we reinterpret, as part of our choice perspective, as constraints on a choice function over possible outcomes. Through a set of representation results we are able to show, then, that the postulates can be rationalized in the familiar way using rankings on possible outcomes.