Saturday, November 27, 2010

Prospect Theory: Decisions under Risk

Daniel Kahneman and Amos Tversky may be a project manager's best friends when it comes to understanding decision making under conditions of risk. 

Of course, they've written a lot good stuff over the years.....my favorite is "Judgement under uncertainty: Heuristics and biases".  You can find more about this paper in a posting about the key points at HerdingCats

The original prospect thinking
Tversky and Kahneman are the original thinkers behind prospect theory..  Their 1979 paper in Econometrica is perhaps the best original document, and it's entitled: "Prospect Theory: An analysis of decision under risk".  It's worth a read [about 28 pages] to see how it fits project management

What's a prospect?  What's the theory?
 A prospect is an opportunity--or possibility--to gain or lose something, that something usually measured in monetary terms.

Prospect theory addresses decision making when there is a choice between multiple prospects, and you have to choose one.

A prospect can be a probabilistic chance outcome, like the roll of dice, where there is no memory from one roll to the next. Or it can be a probabilistic outcome where there is context and other influences, or it can be a choice to accept a sure thing. 

A prospect choice can be between something deterministic and something probabilistic.

The big idea
So, here's the big idea: The theory predicts that for certain common conditions or combinations of choice, there will be violations of rational decision rules

Rational decision rules are those that say "decide according to the most advantgeous expected value [or the expected utility value]".  In other words, decide in favor of the maximum advantage [usually money] that is statistically predicted.

Violations driven by bias:
Prospect theory postulates that violations are driven by several biases:

  • Fear matters: Decision makers fear a loss of their current position [if it is not a loss] more than they are willing to risk on an uncertain opportunity.  Decision makers fear a sure loss more than a opportunity to recover [if it can avoid a sure loss] 
  • % matters: Decision makers assign more value to the "relative change in position" rather than the "end state of their position"
  • Starting point matters: The so-called "reference point" from which gain or loss is measured is all-important. The reference point can either be the actual present situation, or the situation to which the decision maker aspires. Depending on the reference point, the entire decision might be made differently.
  • Gain can be a loss: Even if a relative loss is an absolute gain, it affects decision making as though it is a loss
  • Small probabilities are ignored: if the probabilities of a gain or a loss are very, very small, they are often ignored in the choice.  The choice is made on the opportunity value rather than the expected value.
  • Certainty trumps opportunity: in  a choice between a certain payoff and a probabilistic payoff, even if statistically more generous, the bias is for the certain payoff.
  • Sequence matters: depending upon the order or sequence of a string of choices, even if the statistical outcome is invariant to the sequence, the decision may be made differently.

Quick example
Here's a quick example to get everyone on the page: The prospect is a choice [a decision] between receiving an amount for certain or taking a chance on receiving a larger amount.

Let's say the amount for certain is $4500, and the chance is an even bet on getting $10,000 or nothing. The expected value of the bet is $5,000.

In numerous experiments and empirical observations, it's been shown that most people will take the certain payout of $4,500 rather than risking the bet for more.

The Certainty Effect: Tversky and Kahneman call the effect described in the example the "Certainty effect". The probabilistic outcome is underweighted in the decision process; a lesser but certain outcome is given a greater weight.

The Reflection Effect: Now, change the situation from a gain to a loss: In the choice between a certain loss of $4,500 and an even bet on losing $10,000 or nothing, most people will choose the bet, again an expected value violation. In other words, the  preference....certain outcome vs probabilistic outcome...is changed by the circumstance of either holding onto what you have, or avoiding a loss.

These two effects are summarized in their words:

....people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses.

Other Effects:  There are two other effects described by prospect theory, but they are for Part II....coming soon!

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