Simpler Models of Rational Decision

Making

• Rational Choice Theory requires us to assign probabilities and numerical values to all possible outcomes and choose the action with the highest expected value.

• We now consider a couple of models that do not require such detailed information. We may think of these as special cases of the RCT model.

The Case Where No Probabilities Are

Needed• In some decisions we know

very well what the outcome of each option will be. The dilemma is to determine which outcome is of highest value.

• This situation is called decision making with certainty.

• From a formal point of view, this is a case of RCT where there is only one outcome for each action and it has a probability of one.

An Example of Decision Making with Certainty

• Many shopping decisions are this nature.

• Should I buy a 24-pack of cola in cans for $6 or four 6-packs of cola in bottles for $3 each?

• The cans option is cheaper, but I prefer the taste of cola in bottles and it would be a little nicer to offer drinks in bottles to my friends.

• Here the only issue is balancing money against aesthetics. I know exactly what I’m getting with each option.

Tips for Comparing and Combining Values

• The cola case involved only two value comparisons, cost and style. Other cases can be much more complex. When buying a house, one may need to consider the cost, distance from work, number of bedrooms, size of yard, quality of the local schools, whether it has a good place to set up a studio or workshop, etc.

Ben Franklin’s Advice

• “[M]y way is to divide a sheet of papers into two columns, writing over the one pro, and over the other con.

• I endeavor to estimate their respective weights; and when I find two, one on each side that are equal, I strike them both out.

• If I find a reason pro equal to two reasons con, I strike out all three.

• And though the weight of reasons cannot be taken with the precision of algebraic quantities, yet when each is thus considered, separately and comparatively, I think I can judge better.”

The Case where Probabilities are Needed

but Missing• Here we know that there is

more than one possible outcome to an option but we are totally uncertain as to how probable the possible consequences are.

• This is called decision making with complete uncertainty or decision making under ignorance.

• [Note that we are only ignorant of the probabilities.]

Example of Decision Making with Missing

Probabilities• Traveling in Central Europe you go to a

small restaurant which has only two choices for lunch. With some difficulty these are described to you as “Borscht” and “Tagessuppe”.

• You know you dislike borscht (a beet soup) quite a lot. But you have no idea what the soup of the day would be like. It could be much worse than borscht; it could be much better.

• You have no idea at all how probable each outcome would be - but you’re hungry and these are your only options.

Analysis of Soup Case

Choose

Borscht

Nearly

inedible

Choose

Taggessuppe

Makes

you

wretch

Quite O.K.

nice

Adding Values

• By assumption, the probability of detesting the borscht is one and we have no idea how likely we are to like the Taggessuppe.

• It is easy to rank order the outcomes: if we’re lucky, the soup of the day will be better than borscht; if we’re not, it will be worse.

• There are two strategies at this point: we could gamble or play-it-safe.

• Which strategy we use will depend on our personality - and perhaps on just how unsatisfactory we find the borscht option.

Rank Orderings of Soup Outcomes

Choose

Borscht

Nearly

Inedible

[3rd]

Choose

Taggessuppe

Makes

you

Wretch

[4th]

Quite O.K.

Nice

[1st] [2nd]

Do We Actually Sneak in Probabilities?

• Some philosophers doubt that we ever choose without any appeal to probabilities.

• If we gambled in the soup case, we seem to have assumed that the probability of wretched soup was not very close to one.

• If we played it safe, we were tacitly assuming that the probability of getting a good soup was not almost one.

Treating the Soup Case as a Problem of

Maximizing Expected Value

• Suppose we assign equal probabilities to the outcomes.

• If we now assign measures to the values of the outcomes (instead of just rank ordering them), we can now calculate the expected value of the two options and compare them.

• When we already have rankings, some people like to assign zero to the worst, 100 to the best and then set the in-between values.

Measures of Value of Soup Outcomes

Choose

Borscht

Nearly

Inedible

[10]

Choose

Taggessuppe

Makes

you

Wretch

[0]

Quite O.K.

Nice

[100] [60]