EFFECTS WITH MULTIPLE CAUSES: EVALUATING ARGUMENTS USING THE SUBJECTIVE PROBABILITY MODEL.

• Author: Allen, Mike

The subjective probability model represents one of the few quantitative approaches that examines the impact of arguments on a person's beliefs (McGuire, 1960; Wyer, 1974; Wyer & Goldberg, 1970). The subjective probability model remains an accurate predictor of beliefs based on numerous investigations testing the veracity of the basic model (Hample 1977; 1978; 1979). The model retains a high degree of predictive accuracy despite tests using longer chains involving more complex arguments (Allen, 1987; Allen & Burrell, 1992; Allen & Kellermann, 1988).

The importance of the model lies in the ability to evaluate arguments and argumentative strategies. For example, the controversy in the academic debate community over high impact/low probability arguments within academic debate was tested using this model (Allen & Kellermann, 1988). The results indicated that judges who based decisions on such arguments acted rationally and with prudence when considering the available evidence. The evidence indicates that naive persons listening to such arguments judge them as possible and acceptable when provided the available evidence.

This paper examines another untested extension of the model. Consider an argument that says that some event C is caused by two events (A and B). The current data testing the subjective probability model considers a single causal sequence of one event leading to another. The mathematical logic of the model, based on the Total Probability Theorem, extends to the more complex case of argument where multiple events cause some single outcome. This experiment tests whether the model continues to maintain accuracy when considering such arguments. Further, this experiment provides a persuasive message on the topic and determines if the model accurately handles change generated as the result of a persuasive message.

SUBJECTIVE PROBABILITY MODEL

The subjective probability model explains the workings of a causal argument. Causal arguments suggest an explanation for the nature of cause and effect among elements of a system. The typical arguer will suggest that one event occurs and that event subsequently causes another event, which in turn causes another event, etc. The application of subjective probability model usually involves arguments about public policies where one event leads to another event. Consider the following example of a sequential argument: The North American Free Trade Agreement (Event A) caused corporations to relocate in Mexico for cheaper labor (Event B) and subsequently hundreds of thousands of persons became unemployed in the United States (Event C). This simple causal argument suggests that if event A occurs then event B takes place and ultimately event C. Such arguments are commonplace in the public forum where arguments about actions and the consequences of those actions form a constant part of the argumentative landscape.

The subjective probability model argues that the estimation of the occurrence of any event is equivalent to the sum of the probability of the occurrence of causal events multiplied by the probability that the causal events in fact result in the event under consideration. For a simple chain event where event A is said to cause event B the equation is:

P(B) = P(A)P(B/A) + P([sim]A)P(B/[sim]A)

This equation reads that the estimate of the probability of event B occurring is equivalent to the probability that event A will occur multiplied by the probability that event B will happen given event A added to the probability of A not occurring multiplied by the probability that if A does not occur B still takes place.

The subjective probability model is an application of the Total Probability Theorem (see Wyer & Goldberg, 1970 for a more complete explanation of the mathematical issues). The theorem states that given an event B and an exhaustive set of mutually exclusive events Ai, the probability of the event B is provided by:

P(B) = [sigma]P([A.sub.i])P(B/[A.sub.i]).

If the events causing B are simply a combination of two events (A and [sim]A) then the equation can be reduced to the previous equation for the subjective probability model. The following example helps to illustrate our test of the model.

Suppose a person asks what is the probability of peace if the United Nation's security forces catch all the outlaw warlords. The equation contains two sides: (a) the actual estimate of the consequent (event B) and (b) the estimate of the consequent (event B) based on the equation. If the model works then the two sides of the equation should be roughly equivalent. A person first estimates the belief in the probability of peace-P(B). The next estimate may consider the probability that the UN would capture all the warlords-P(A). The next estimate is the probability that there would be peace if the UN security forces catch all the outlaw warlords-P(B/A). These two probabilities are multiplied and added to the multiplied probabilities of: (a) the probability that the UN security forces will not catch the outlaw warlords-P([sim]A) and (b) the probability that there will be peace even though the UN security forces do not catch all the outlaw warlords-P(B/[sim]A). The estimation process requires that the individual provide an estimate for each of the probabilities.

Essentially, the argument considers the impact of how various conditions work to cause or estimate the belief in a particular consequence. Typically, arguments made by communicators are constructed to alter or change the belief in particular probabilities. An arguer may wish to argue that the UN security forces will catch all the warlords and provide evidence and reasoning about the effectiveness (or ineffectiveness) of the UN security forces, The utility of the model is that if a person wants to make an argument to increase (or decrease) the belief in event B, the knowledge of how a group or individual connects the causes of B to B assists in understanding messages. The probability of those causes of B occurring (also part of the model) permits an assessment of the estimate the largest potential for change. Thus, the model permits an arguer to target a message or messages in order to change a belief and increase the acceptability of a particular conclusion.

This...