1. Psychological experiments on the interpretation of vague expressions. Not Exactly refers to a few papers (by Toogood, by Berry, and by Gigerenzer) discussing psychological experiments on the interpretation of vague expressions. My colleagues Advaith Siddharthan and Matt Green recently pointed me to a number of other papers in this tradition. Much of this work focusses on the expression of probabilities (e.g., risks), for example in connection with side effects of medicins ("These side effects are rare".) One intriguing paper in this area is Ellen Peters et al. (2009), ``Bringing meaning to numbers: the impact of evaluative categories on decisions'', in Journal of Experimental Psychology: Applied; a closely related paper is B.Zikmund-Fisher et al. (2007) ``Does labeling prenatal screening test results as negative or positive affect a woman's responses?'', in American Journal of Obstetrics and Gynecology 197; then there is the ancient (and ultra brief) article by J.H.Toogood (1980) ``What do we mean by "usually"?, in The Lancet. In a nutshell: evaluative words (like ``good'') help medical decision making, but the psychological mechanism responsible for this phenomenon is proving difficult to pin down.
In April 2011, a paper by H. Mishra and A. Mishra and B. Shiv came out in the journal Psychological Science entitled ``In Praise of Vagueness: Malleability of Vague Information as a Performance Booster''. The paper reports on a series of intriguing experiments showing that subjects' behaviour is sometimes influenced more effectively by information if this information is offered less precisely (e.g., where they are told that a certain value lies between values x and y) than if it is offered to them more precisely (e.g., where they are told that a certain value equals z). In the non-precise condition, for example, subjects who were trying to loose weight were told that their BMI (in fact, a variant of the conventional BMI scale) was between 25 and 30 . The authors explain their result arguing, essentially, that imprecise feedback allowed subjects to convince themselves that they are close to their weight-loss goal, which kept them optimistic even if they fell short of this goal. While these results are extremely interesting, they may not be as directly relevant to the subject matter of my book as the title of the paper suggests, because saying that a number lies between 25 and 30 is not vague in the usual sense (i.e., which hinges on the existence of borderline cases). Instead, the results appear to tell us something about granularity of information, to use a term coined by Jerry Hobbs and often used in Artificial Inteligence.
Work on the expression of probabilities includes an often-cited paper by Robert Hamm (1991) ``Selection of verbal probabilities: a solution for some problems of verbal probability expression'', in the journal Organizational bahavior and human decision processes. Hamm's experiments showed that some English phrases which express likelihood vaguely (such as "very unlikely") are interpreted with remarkable unanimity. Hamm's work was the basis for later studies, including Dieckmann et al. (2009) The use of narrative evidence and explicit likelihood by decisionmakers varying in numeracy, in Risk Analysis, and Bisantz et al. (2005) Displaying uncertainty: investigating the effects of display format and specificity, in the journal Human Factors.
Kahneman and Tverky's famous Prospect Theory has taught us that people can be highly idiosyncratic in their reasoning about probability (see e.g. this web page for an informal introduction). An interesting question, which has not been addressed yet to the best of my knowledge, is wheather vague expressions can sometimes reduce (or increase) our idiosyncrasy. There is a need for more experimental research in this area, which has great practical relevance for applications in which quantitative information needs to be understood by non-experts.
2. The logic of vagueness. After the publication of Not Exactly, I came across an excellent recent monograph on the logic and philosophy of vagueness which (like my chapters 8 and 9) defends degrees of truth: Vagueness and Degrees of Truth . The book proposes a novel approach to vagueness, known as fuzzy plurivaluationism. Nicholas Smith's book focusses squarely on the meaning of vague expressions, and contains little discussion of the question why vagueness can be useful.
3. Relevance Theory. The question why vague expressions are as frequent as they are (see chapter 11 of Not Exactly) has drawn considerable attention of game theorists and philosophers in recent years. What I didn't know is that linguists had written insightfully about this question as well, witness the following article: Interactive aspects of vagueness in conversation , in Journal of Pragmatics 35, of 2003. The paper focusses on vague additives, such as ``almost'', ``kind of'', ``quite'', and ``a bit''. It contains a relevance-theoretic analysis of a corpus of casual conversations between university students. For instance, someone says ``would you think she's almost forty'', followed by ``she's thirty eight''. The authors ask why the vague expression almost forty is used, given that the speaker knows the person is 38 years old. Jucker and colleagues write the following about this: ``Forty is an age laden with symbolic and predominantly negative meaning in American culture. Thus to describe a person as almost forty is to explicitly connect that person's age with a culturally significant reference point. The implications from this are clearer than those that would be drawn from the age itself.'' The paper draws on the 1994 book Vague Language, by Joanna Channell, which I had not come across before, and which offers a classification of vague additives (approximators, downtoners, shields, etc.)
4. Reading and querying graphs. Quantitative information is often conveyed through graphs. Graphs have their strong points of course (as in the proverbial picture worth a thousand words), but they have their weaknesses as well.
They are not so good so if you're blind, for example. Also, graphs are difficult to query by computer (just ask Google for graphs that show a steep drop in unemployment). Here's a paper representing a new line of work that aims to address both problems,
allowing (essentially) queries saying "In which months was there a steep drop in unemployment
but an increase in sales?" :
Modeling and Querying Graphical Representations of Statistical Data, by Dumontier, Ferres and Villanueva-Rosales (2009), in the journal Web semantics: science, services, and agents on the world wide web.
Vagueness -- what counts as a steep drop, for example? -- is often the key issue in such queries.
Back to main page for Not Exactly: in Praise of Vagueness