Utility, Informativity and Protocols

Recently, quantitative notions of relevance have been proposed for questions and assertions and, based on an assumption of optimal relevance, used for linguistic applications. BarHillel and Carnap’s (1953) notion of informativity (their ‘inf’ value) has already been used in traditional pragmatics of natural language; Merin (1999a,b) proposes that the relevance of a proposition q should be seen as argumentative value with respect to an hypothesis h and measured by Good’s (1950) notion of the weight of evidence, log P (h/q) P (¬h/q) ; and van Rooy (1999,2001b) measures the utility of interpretations of questions and answers in terms of the value of sample information and the reduction of entropy. These measures are used to determine what is actually expressed by an expression with an underspecified semantic meaning, and to account for certain pragmatic inferences, especially conversational implicatures (e.g. Parikh, 1992; Merin, 1999b; van Rooy, 2001b, and Schulz, 2002). In an inspiring paper, Bernardo (1979) showed that the expected informational value of an experiment/question is the natural special case of its expected utility value. The first contribution of this paper is to extend this investigation in several ways. The second contribution is to measure the relevance/utility of non-partitional questions, and show how different proposals (using either protocols or likelihood functions) come down to the same thing.