Plausibility Theory

Plausibility Theory is that province of logic which describes and formalises the way we reason, or we think we ought to reason, about plausibility. In precisely the same sense, well-known deductive logic describes and formalises the way we reason about truth. There are many mathematical similarities between plausibility theory and the various probability theories that stroll and limp around. But its strength lies in its meaning and its interpretation; and on this account it is intimately related to Bayesian probability theory.

According to Collins & Michalski, "something is plausible if it is conceptually supported by prior knowledge". The Plausibility Theory of Wolfgang Spohn (1985-), Collins & Michalski (reasoning, 1989), Lemaire & Fayol (arithmetic problem solving, 1995), Connell & Keane (cognitive model of plausibility, 2002) provides new insights into decision-making with risks that can't be known. Plausibility is an ineluctable phenomenon of everyday life and ubiquitous. However, it was ignored in cognitive science for a long time, and treated only as an operational variable, rather than being explained or studied in itself. Until the arrival of the plausibility theory, the common theory which was used by scientists to explain and predict decision-making, was Bayesian statistics. Named for Thomas Bayes, an 18th-century English minister. Bayes developed rules for weighing the likelihood of different events and their expected outcomes. Bayesian statistics were popularized in the 1960s by Howard Raiffa for usage in business environments. According to Bayesian theory, managers make decisions, and managers should make decisions, based on a calculation of the probabilities of all the possible outcomes of a situation. By weighing the value of each outcome by the probability and summing the totals, Bayesian decision makers calculate "expected values" for a decision that must be taken. If the expected value is positive, then the decision should be accepted; if it is negative, it should be avoided. At first sight, this may seem like an orderly working method. However unfortunately, the Bayesian way of explaining decisions faces at least two phenomena that are difficult to explain:

• The appreciation of downside risk. People normally take a gamble at a 50% chance to earn $10 when they have to pay $5 if they have bad luck. But why generally they refuse to take the same gamble at a 50% chance if they can win $1.000.000 versus a potential loss of $500.000?
• How to deal with risks that can't be known. These kind of risks, that do not involve predictable odds, are typical for business situations! Why do managers prefer risks that are known, over risks that can not be known?

Both of these phenomena can be dealt with if the Bayesian calculation of "Expected Value" is replaced by the "Risk Threshold" of the Plausibility Theory. Like its predecessor, the Plausibility Theory assesses the range of possible outcomes, but focuses on the probability of hitting a threshold point - such as a net loss - relative to an acceptable risk. For example: a normally profitable decision is rejected if there is a higher than 2% risk of making a (major) loss. Clearly, plausibility can resolve both weaknesses of Bayesian thinking: the tendency of managers to avoid unacceptable downside risks, and the tendency of managers to avoid taking risks that can't be known. Typical examples of the application of plausibility theory are the new Basel II rules for capital allocation in the financial services industry.