Issue 1/2 Vol. 39 1997

Combining linguistic probabilities

WALLSTEN, T., BUDESCU, D., TSAO C.

The first part of this article summarizes and justifies two background assumptions and five principles (Budescu & Wallsten, 1995) regarding how people process qualitative probability expressions. Part 2 reviews earlier research showing that when people receive qualitative expressions from two independent judges regarding the probability of an aleatory event, they tend to combine them by averaging. Part 3 extends this research to ask how people combine the qualitative opinions of two judges regarding statements of fact. The conclusion is that they tend to average the two opinions, but unlike in the aleatory case, then take somewhat more extreme values as their own opinion. Part 4 provides an explanation, based on normative considerations, for the discrepancy between how humans treat judgments about aleatory events and about factual statements.

Generally, when we ask experts or other people for information or judgments relevant to decisions that we have to make, they respond in qualitative rather than quantitative ways. Because linguistic probabilities such as likely, rather doubtful, and very certain are so commonly used, considerable research has been directed to questions of how people understand and process them in the service of judgment and decision making. (See Budescu & Wallsten, 1995, for a recent comprehensive review.) Issues that have been investigated include individual differences in location, precision, and nuance of phrase meanings; effects of context and communication direction on inferred meanings; and effects on decision quality of verbal versus numerical probabilities. Almost all of this research has focused on expressions taken one at a time, despite the fact that one commonly seeks opinions about an issue from two or more other people. For example, we decide on a course of medical treatment after consulting our family physician and one or more specialists about the chances of success and side effects; an executive launches a new product on the advice of a bevy of market researchers regarding its viability; a military or governmental decision maker operates following input from numerous experts; and we select a movie to watch after checking with friends and reviewers. This paper is concerned with how people combine, or integrate, verbal probabilities from two independent judges about the chances that an event will occur or that a statement is true. An analogous problem arises in any domain within which linguistic qualifiers are used to denote approximate numerical values. Without much trouble, the ideas developed here can be extended to them as well but we will not do so here.

This paper is organized as follows. As a general framework, we first present and justify two background assumptions and five principles regarding how individual linguistic probabilities are understood and processed. That section draws heavily from the recent Budescu and Wallsten (1995) chapter. Next we indicate how principles regarding the combination of phrases fit into such a framework and propose one that has evolved from our research. The following section summarizes the earlier research and presents a new study from which the principle flows. Finally, we conclude by relating the principle to a wide range of other tasks in which it has also been established and by considering its possible normative implications.

Keywords: subjective probability, linguistic probability, combining judgments, judgment

Short Title: Wallsten, T. et al. (1997) PsyBeit 1-2:27

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