Basics of Rational Choice Theory

• For each option, list all the possible alternative outcomes.

• To each outcome, assign a numerical probability and a numerical value representing its desirability.

• Calculate the expected value for each option.

• Choose the option with the highest expected value.

Calculating the Expected Value of an Option

• For that option, sum the values of each possible outcome, weighted by the probability that that outcome will occur.

• This sum represents the benefit that one can expect on average to obtain if one were to choose that option.

• The term expect here is similar to what we mean when we speak of life expectancy.

Requirements on Probability Assignments

• Rational Choice Theory itself puts only formal constraints on the probabilities. We only require that they not violate the probability calculus.

• Sometimes people speak of such probabilities as being subjective or personal.

• They need not correspond to actually observed frequencies as long as they are internally coherent.

Example of Coherent, But Non-Objective Probability Assignments

• Suppose Jones mistakenly believes that the probability of drawing a face card (A,K,Q,J) from a standard bridge deck is one-third.

• RCT per se does not criticize this assessment as long as Jones also believes that the probability of drawing a non-face card is two-thirds.

Requirements on Evaluations Assigned to Outcomes

• Again, RCT puts only minimal formal constraints on the assignment of measures of personal value.

• For example, preferences must be transitive, consistent and comparable.

• But RCT per se does not care how bizarre or immoral one’s tastes are.

Other Non-Issues in RCT

• Rational Choice Theory also puts only formal constraints on how one defines the decision situation.

• The options considered must be taken to be mutually exclusive.

• The outcomes listed must be both mutually exclusive and exhaustive.

• RCT does not care about how correctly one has identified the outcomes of the various options as long as they are internally coherent.

Three Senses of Rationality

• RCT attempts to lay down the formal characteristics of what is sometimes called instrumental rationality.

• It does not talk about whether the contents of our beliefs are rational, including beliefs about probabilities.

• Neither does it attempt to answer questions about which desires or goals are rational ones for humans to pursue.

Uses of Rational Choice Theory

• RCT serves as a “logic of decision”. It doesn’t tell you what your beliefs or probabilities or values should be.

• But it does tell you useful things about what they cannot be.

• This permits us to critique and analyze our own decision making.

Example of the Flying Parents

• Suppose parents of small children have to go on a trip and are wondering whether they should fly together or fly separately.

• They assume that the children are more apt to become orphans if they fly in the same plane.

• But it is more convenient and pleasant to fly together. What is the rational choice for them to make?

Setting up the Matrix

• The first step in any such problem is to lay out the alternative options and then the possible outcomes of each option.

• In this case there are two simple options: fly separately or fly together.

• (We assume there is no other alternative - such as driving.)

Outcomes for the “Fly Together” Option with Probabilities

Outcomes for the “Fly Separately” Option with Probabilities

Outcomes for the “Fly Separately” Option with Probabilities

Outcomes for the “Fly Together” Option with Values

Exploring the Choice

• We can first do some algebraic manipulations of the equations for the two expected values to see if any simplifications or approximations can be made.

• We can then insert plausible values for p, x, y, and z to find out which option is the most reasonable one to choose.