Communicating numeric quantities in context: implications for decision science and rationality claims.

Abstract

Perhaps more than most areas of cognitive psychology, the study of human judgment and decision-making relies heavily on experimental tasks communicated through written descriptions that convey numeric quantifiers as primary sources of information. Subjects in such studies usually are required to use such information to make choices, indicate preferences, or offer judgments. These responses are compared to normative benchmarks, resulting in the researchers drawing conclusions about the quality, coherence, or rationality of human judgment and decision-making (Arrow, 1982; Tversky and Kahneman, 1986; Stanovich and West, 2000). Most of this body of research has paid little attention (a) to how subjects interpret numeric information conveyed in writing and (b) to how those interpretations are influenced by context (Mandel and Vartanian, 2011; Teigen, in press). More often than not, researchers simply assume that subjects will interpret numeric quantities conveyed in experimental tasks as exact values, and also that subjects should interpret expressed numbers as precise quantities. Yet it is uncontroversial in linguistics that numeric quantifiers may be treated as exact or approximate values, and where their interpretations are approximate, they may be treated as one-sided (e.g., at least, which is lower bounded, or at most, which is upper bounded) or two-sided (e.g., roughly or about). Linguistic accounts of numeric quantifiers (e.g., Horn, 1989; Carston, 1998; Levinson, 2000; Geurts, 2006; Breheny, 2008) do not support the normative claim (or assumption) that a precise “bilateral” reading of such quantifiers consistent with exactly is the proper reading. Although linguistic accounts differ in what they posit as possible semantic defaults, even those proposing a bilateral semantics, such as Breheny (2008), specify pathways for pragmatically derived unilateral interpretations, such as interpreting a numeric quantifier, x, as at least x or at most x. More generally, the degree to which decision researchers seem confident in defining the meaning of linguistic terms for others runs counter to a fundamental idea in the philosophy of language, which holds that the meanings of words are definable only through their actual use in language (e.g., Wittgenstein, 1953; Austin, 1979). It also runs counter to psycholinguistic evidence indicating that even 5-year olds understand that numeric quantifiers should be interpreted as “at least” in some contexts (Musolino, 2004). And it runs counter to work in experimental pragmatics indicating that people develop context-sensitive scalar implicatures as they develop. For instance, they come to understand that although some logically entails all, it usually pragmatically excludes all because it would be infelicitous to use some if one meant all (Moxey and Sanford, 2000; Noveck, 2001; Noveck and Reboul, 2008).