Utility and Relevance of Answers

How to answer a question? If the inquirer asks it in order to make a decision about something, then a wide range of reactions can be appropriate. If asked ‘Who of the applicants is qualified for the job?’, reactions may range from ‘Only Müller and Schmidt’, ‘At least Müller’, over ‘Müller has working experience in this field’, ‘Schmidt needs extra training’, to ‘The younger ones show more enthusiasm’, or even ‘The job needs an expert in PCF Theory’. This paper divides into two parts. The goal of the first part is to derive a measure of utility for answers from a game theoretic model of communication. We apply this measure to account for a number of judgements about the appropriateness of partial and mention–some answers. Under the assumption that interlocutors are Bayesian utility optimisers we see questioning and answering as a two-person game with complete coordination of preferences. Our approach builds up on work by A. Merin and R. v. Rooij on decision theoretically formulated measures of relevance. In the second part we study the relation between their approaches and our game theoretic model of answering. We are aiming for principled characterisations, and are especially interested in clarifying when and why we have to model this type of communication as a two–person game. There are a number of judgements about the appropriateness of answers that seem to be due to their utility in a specific pragmatic context. In our examples, we write ‘I’ for the inquirer, and ‘E’ for the answering expert. We use the following question (1a) as our main example: