Assessing Joint Distributions with Isoprobability Contours

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Analogous to the three legs of a stool, the three fundamental bases for any decision are (1) The alternatives, or what we can do; (2) The information, or what we know; and (3) The preferences, or what we like. When faced with uncertainty, people may choose different alternatives based on their taste for risk and the information they have about that uncertain situation. This research focuses on the information element of the decision that is captured by joint probability distributions of several variables. Incorporating dependence is a fundamental step for making inferences about uncertain events or for learning when we receive new information, but eliciting a representative probability distribution is a task that requires care if one is to minimize the effects of cognitive and motivational biases. When eliciting joint probability distributions, we are faced with added difficulties such as conditioning the probability assessments on several variables or assessing dependence parameters between them. These requirements make the assessment of joint probability distributions a difficult task to perform in practice. The objectives of the proposed research are to develop and test a new method for constructing joint probability distributions of continuous random variables using isoprobability contours (contours of points with the same cumulative probability). We explore a new method for constructing isoprobability contours by eliciting pairwise preferences over binary gambles, without the need for numeric responses from the decision maker. This approach facilitates the joint probability assessment significantly. Once the isoprobability contours and at least one one-dimensional marginal probability distribution is determined, is it possible to construct the joint distribution of all the variables present. Thus, we also propose a new method for assessing dependence between the variables of the decision situation using isoprobability contours.