2.0 Updates:

CSC394 / IS376: Rational Choice with Uncertain Futures

Elliott

Drawn from: Robyn, M. Dawes, "Rational Choice in an Uncertain World." (1988).

Rational Choice:

  1. ...is based on current assets. Sunk costs are not included in any rational calculation about the future.
  2. ... is based on the possible consequences of the choice.
  3. ...requires that when the consequences are uncertain, their likelihood is evaluated according to the rules of probability.
Expected value is the return expected times the probability of getting that return.

Utility value is filtered through the eyes of individuals, and relative to their independent circumstances.

Sunk costs:

Sunk Costs and the Tennessee-Tombigbee Waterway.

"To terminate a project in which $1.1 billion has been invested represents an unconcionable mishandling of taxpayers' dollars." Senator Jeremiah Denton, November 4, 1981.

"Completing Tennessee-Tombigbee WAterway Proejct is not a waste of taxpayers' dollars. TErminating the prjoect at this late stage of development would, however, represent a serious waste of funds already invested." Senator James Sasser, November 4th, 1981. 


Do we abandon the project?


		 CurrentExpenditure	RemainingCost		Return

Original:          $0			1 billion	    1.5 billion

Checkpoint one:	    1.2 billion		1.2 billion         1 billion

Checkpoint two:     1.2 billion		1   billion	    1.5 billion
The current expenditure is now irrelevant (the Honorable Senators notwithstanding). The only thing that rationally matters is the remaining costs and what the return will be. The original calculation, and checkpoint two favor continuing the project. Checkpoint one (which is what was true when the senators spoke) favors abandoning the project instead of losing another $200 million.
Your boss asks your opinion on the following situation: 1. The company spent $500K on project M so far. There is a 33.3 percent chance that M will not be worth anything in the market, and a 66.7 percent chance that it will be worth $1 million. It will cost $330K dollars to complete the project. If this is the only information you have to go on, should you recommend that the company continue with the project? If yes, why? If no, why? If the correct answer turns out to be the opposite of the one you otherwise know to be true, what further information can you then infer to be true?
Money
ONE 
You get $200.

Option A. I give you another $100
Option B. I flip a fair coin. If it lands heads you get another $200, but if
it lands tails, you get nothing.
TWO 

You get $400.

Option C. You give me back $100
Option D. I flip a fair coin. If it lands heads you give me back $200,
          but if it lands tails you can keep all your money.
Commentary. All choices are equivalent with respect to expected value, but while options A and C require "you" to walk away with $300, this is never possible with options B and D. This allows for different utility values to be assessed between A/C and B/D.

For example, if one really needed $300, and nothing less, than the Utility of $300 is much higher than the utility value of $200, and roughly equivalent to the utility value of $400. In this case options A and C are prescribed. Similarly, if one desperately needed $400, then the utility of having half a chance of getting it (options B and D) is much higher than the utility of having no chance of getting it (options A and C).

Choices A and C, and B and D, are equivalent with respect to expected value and utility value. They are, however, framed differently. This probably explains that for any body of human subjects roughly half will be inconsistent with respect to the utility value (whatever it might be) of risk-taking and risk-adverse behavior in this example.

The general rule is that people have their own preferences when it comes to being risk-taking, and risk adverse, with respect to gaining resources and independently with respect to losing resources. Another general rule is that people will tend to be risk-taking when it comes to retaining resources more than when it comes to getting additional resources.

Example: Small, but serviceable house in O.K. neighborhood. Big house of dreams in perfect neighborhood. Professor M can cheat on research and earn lots of money, but if found out will be thrown out of the university, and disgraced. Three children. Spouse and kids depend on Professor M for all family income.

Scenario One: The professor lives in the small house with family. A colleague suggests they cheat on research, make the big money, and can move into the house of dreams. Will professor M take the risk?

Scenario Two: The professor lives in the big house in the perfect neighborhood with family. Fortunes have been reversed and they are facing having to move to the small house, out of the perfect neighborhood. A colleague suggests that they cheat on research, make big money, and the professor can stay. Will professor M take the risk?

Most people would be more understanding of Professor M in the second case because they understand that the panic of "losing everything" might drive a person to do something they otherwise would not do. However, logically, in both cases the big house comes with the risk of disgrace, and the small house does not. Both scenarios are (roughly) equivalent with respect to utility value.

PLAGUE
All city and village councils across the county must make the following community decision. A plague is coming to the United States and it is known that, on average, one out of three people will die from it. There is a vaccine, but the vaccine is absolutely regular in the number of people it will kill, also one in three people. The plague will either strike everyone in any particular village, kiling them, or pass over the village altogether with no victims. The vaccine makes no distiction from one village to another. Death from plague or vaccine has identical symptoms.

600 people live in your village.

THREE 
Option A. Give the vaccine. It is an absolute certainty that 200
people will die.

Option B. Do not give the vaccine. There is one chance in three
that all 600 in the village will be killed by the plague.
FOUR 
Option C. Do not give the vaccine. In this case there are two chances
in three that all 600 people will be saved.

Option D. Give the vaccine. It is an absolute certainty that 400
people will be saved.
Commentary. The expected value of all choices is the same. 2/3 of the people will live, and 1/3 will die, on average. There may be utility value differences for any particular village. E.g., If preserving some descendents of the village at all costs is a priority, than taking the vaccine would be indicated. If avoiding mass death at all costs is a priority then not taking the vaccine would be a priority.

Option A and B are framed as death and dying. Option C and D are framed as saving lives.

Framing: There are many different ways to frame problems in ways to affect choice. For example, one study showed that (a) people tend to scan choices left to right (in the US and UK), and (b) the last option presented tends to have precedence. The clothes example, where clothes on the right are preferred, may have been discussed.

Advertising makes much use of framing effects.

" Satisficing." There are costs associated with choosing. Sometimes it is appropriate (and also often done when not appropriate) to chose the first available acceptable option.