Wednesday, December 1, 2010

Prospect Theory

Prospect Theory is an explanation of choosing among alternatives [aka "prospects"] under conditions of risk.  Amos Tversky and David Kahneman are credited with the original thinking and coined the term "prospect theory".

Prospect Theory postulates several decision making phenomenon,  a couple of which were discussed in the first posting.  Here are two more:

The Isolation Effect
If there is a common element to both choices in a decision, decision makers often ignore it, isolating the common element from the decision process.  For instance, if there is a bonus or incentive tied to outcomes, for which there is a choice of methods, the bonus is ignored in most cases.

Here's another application: a choice may have some common elements that affect the order in which risks are considered; the ordering may isolate a sure-thing, or bury it in a probabilistic choice.

Consider these two figures taken from Tversky and Kahneman's paper.  In the first figure, two probabilistic choices are given, and they are independent of each other.  The decision is between $750 in one choice and $800 in the other.  The decision making is pretty straight forward: take the $800.

In the second figure, choice is a two step process.  In the first step, the $3000 is given as a certainty with a choice to choose the other path that has an EV of $3200.  This decision must be made before the consequences are combined with the chance of $0.  

The decision outcome [at the square box] is either sure thing $3000  or expected value $3200.  But, there is then a probabilistic activity that weights this decision such that at the far left chance node the prospect is either ($0, $750) or ($0, $800). 

So, the EV of the prospect is the same in both figures. However, in Figure 2 the second tree has the 'certainty' advantage over the first tree with the choice that is available to pick the sure-thing $3000 at the decision node.



The Value Function

Quoting Tversky and Kahneman: "An essential feature of the ..... theory is that the carriers of value are changes in wealth or welfare, rather than final states.  ...... Strictly speaking, value should be treated as a function in two arguments: the asset position that serves as reference point, and the magnitude of the change (positive or negative) from that reference point. "

The point here is that the authors postulate that every prospect has to be weighted with a factor that represents this value idea.  The weightings do not have to sum to 1.0 since they are not probabilities; they are utility assignments of value.  Weightings give rise to the apparent violations of rational decision making; they account for overweighting certainty; taking risks to avoid losses and avoiding risks to protect gains; and ignoring small probabilities, among other sins.

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