The Language of Argument

2 6 9

D e c i s i o n s U n d e r I g n o r a n c e

As an example of partial ignorance, suppose that, just after graduating

from college, you are offered three jobs. First, the Exe Company offers

you a salary of $20,000. Exe is well established and secure. The next of-

fer comes from the Wye Company. Here the salary is $30,000, but Wye is

a new company, so it is less secure. You think that this new company will

probably do well, but you don’t know how likely it is to last or for how

long. Wye might go bankrupt, and then you will be left without a job. The

final offer comes from the Zee Company, which is as stable as Exe and of-

fers you a salary of $40,000 per year. These offers are summarized in the

following table:

Wye does not go bankrupt     Wye goes bankrupt

Take job at Exe $20,000  $20,000

Take job at Wye $30,000 $0

Take job at Zee $40,000 $40,000

Let’s assume that other factors (such as benefits, vacations, location, interest,

working conditions, bonuses, raises, and promotions) are all equally desir-

able in the three jobs. Which job should you take?

The answer is clear: Take the job from the Zee Company. This decision is

easy because you end up better off regardless of whether or not Wye goes

bankrupt, so it doesn’t matter how likely Wye’s bankruptcy is. Everyone

agrees that you should choose any option that is best whatever happens.

This is called the rule of dominance.

The problem with the rule of dominance is that it can’t help you make

choices when no option is better regardless of what happens. Suppose you

discover that the letter from the Zee Company is a forgery—part of a cruel

joke by your roommate. Now your only options are Exe and Wye. The job

with Wye will be better if Wye does not go bankrupt, but the job with Exe

will be better if Wye does go bankrupt. Neither job is better no matter what

happens, so the rule of dominance no longer applies.

To help you choose between Exe and Wye, you might look for a rational

way to assign probabilities despite your ignorance of which assignments

are correct. One approach of this kind uses the rule of insufficient reason:

When you have no reason to think that any outcome is more likely than

any other, assume that the outcomes are equally probable. This assumption

enables us to calculate expected monetary value or utility, as in the preced-

ing sections, and then we can choose the option with the highest expected

utility. In our example, this rule of insufficient reason favors the job at Exe,

because your expected income in that job is $20,000, whereas your expected

income in the job at Wye is only $15,000 ( 5 0.5 3 $30,000), assuming that

the Wye company has as much chance of going bankrupt as of staying in

business.

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