Extensions of Support Theory

Support theory, introduced by Tversky and Koehler (1994), provides a unified descriptive account of subjective probability judgment. It departs from extensional models by making event descriptions (hypotheses) the primitives of judgment rather than the events themselves. This description-dependence means that alternative formulations of the same underlying event can systematically alter probability assessments. For instance, unpacking a category into its components tends to increase its perceived likelihood: Fischhoff, Slovic, and Lichtenstein (1978) found that when car mechanics evaluated causes of engine failure, the residual hypothesis “something other than the battery, fuel system, or engine” was judged more probable when broken down into specific subcauses (e.g., “starting system,” “ignition system”), even though the possibilities were already known. Similarly, Tversky and Kahneman (1983) showed that people give higher frequency estimates for words ending with ing than for words with n in the sixth position, despite the latter being a superset, because the ing description is easier to search in memory. Johnson et al. (1993) found that consumers were willing to pay more for insurance covering hospitalization for “any disease or accident” than for “any reason.” These failures of extensionality arise from two sources: explicit descriptions compensate for memory limitations by cueing relevant instances, and different descriptions shift the salience of outcome features, changing their weight in judgment even without new evidence.

Central to the theory is the construct of support, an intermediate representation of the strength of evidence for a hypothesis. A probability judgment is modeled as the balance of support between a focal hypothesis ( A ) and an alternative ( B ) under the assumption that exactly one is true:

[ P(A, B) = \frac{s(A)}{s(A) + s(B)} ]

Support exhibits two patterns of subadditivity that capture the effects of description on judgment. Implicit subadditivity states that the support for a packed description is less than that for an explicit disjunction of its components: ( s(A) \le s(A_1 \lor A_2) ). For example, the support for “natural disaster” is typically lower than for “fire, flood, hurricane, tornado, lightning strike, severe thunderstorm, or any other natural disaster,” because the unpacked version explicitly retrieves more supportive instances. Explicit subadditivity holds that the support for an unpacked disjunction is less than or equal to the sum of the supports for its individual components: ( s(A_1 \lor A_2) \le s(A_1) + s(A_2) ), as people may spontaneously repack the components into a composite. These properties reflect the action of heuristics such as availability and anchoring, integrating them into a common framework.

Two recent developments have extended support theory into new domains: calibration and choice under uncertainty.

Support and Calibration

Pure support theory addresses the coherence of probability judgments but does not speak to their calibration—the correspondence between subjective and objective probabilities. To fill this gap, Brenner (1995) proposed a random support model that views support as a random variable that fluctuates across judgment occasions. The model adopts a signal-detection framework in which separate distributions represent the evidence strength for correct and incorrect hypotheses (e.g., support for rain on rainy versus dry days). Unlike traditional signal-detection models, however, it omits response thresholds and instead maps support directly into probability using the support-theoretic mapping ( P(A, B) = s(A)/[s(A) + s(B)] ).

This parsimonious formulation captures key aspects of calibration data with two or three psychologically meaningful parameters. For a judged hypothesis, the parameters represent the judge’s discrimination ability (the separation between evidence distributions for true and false instances), bias toward the focal hypothesis (asymmetric support accrual independent of the truth), and extremity (tendency to produce probabilities near 0% or 100%). The model closely reproduces calibration curves observed in standard two-alternative tasks as well as in zero- and one-alternative tasks that use full-range probability scales. Koehler, Brenner, and Griffin (Chapter 39, this volume) applied the random support model to estimate patterns of miscalibration among domain experts, illustrating its potential for diagnosing and correcting judgment errors in applied settings.

Support and Decision Making

Beliefs about uncertainty shape choices, and support theory has been incorporated into a belief-based account of decision making under uncertainty (Fox & Tversky, 1998; Tversky & Fox, 1995; Wu & Gonzalez, 1999). In this framework, people first judge the probabilities of the events on which payoffs are contingent, consistent with support theory, and then integrate those subjective probabilities into a choice via the decision-weighting function of prospect theory.

A key empirical finding is bounded subadditivity in choices: events have disproportionately greater impact when they turn impossibility into possibility or possibility into certainty than when they shift probabilities within the intermediate range. Consequently, unpacking an uncertain prospect into subprospects increases the sum of its certainty equivalents. For example, Fox et al. (1996) presented professional options traders with an uncertain prospect paying $150 if Microsoft’s stock price closed below $94. The certainty equivalent of this prospect was less than the combined certainty equivalents of prospects paying $150 if the price closed below $88 and if it closed between $88 and $94. This pattern directly mirrors subadditivity in probability judgments; indeed, the same study found that probability judgments for these events exhibited exactly the unpacking effect predicted by support theory. The two-stage model, using support-based probability assessments as inputs, accurately predicts choices among uncertain prospects, and Fox (1999) further demonstrated that such choices can be reconstructed from direct ratings of support.

Applied research confirms that unpacking influences real-world decisions. Ayton (1997) analyzed bookmakers’ odds on soccer matches and found that the implied probability of an outcome like “England beats Switzerland” rose when the outcome was unpacked into specific half-time leaders or final scores. Comparable effects have been observed in insurance purchasing (Johnson et al., 1993) and medical diagnosis (Redelmeier et al., 1995). These studies underscore that description-dependent probability judgments, as formalized by support theory, have predictable consequences for decisions under uncertainty. The features of hypotheses and evidence explored here are suggestive rather than exhaustive; further investigation may deepen the integration of support theory with broader topics in social and cognitive psychology.