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 preceding 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 (= 0.5 × $30,000), assuming that the Wye company has as much chance of going bankrupt as of staying in business.
The problem with the rule of insufficient reason is that it may seem arbi- trary to assume that unknown probabilities are equal. Often we suspect that the probabilities of various outcomes are not equal, even while we do not know what the probabilities are. Moreover, the rule of insufficient reason yields different results when the options are described differently. We can distinguish four possibilities: Wye goes bankrupt, Wye stays the same size, Wye increases in size, and Wye decreases in size but stays in business. If we do not have any reason to see any of these outcomes as more likely than any other, then the rule of insufficient reason tells us to assign them equal proba- bilities. On that assumption, and if you will keep your job as long as Wye stays in business, then you have only one chance in four of losing your job; so your expected income in the job at Wye is now $22,500 (= 3⁄4 × $30,000). Thus, if we stick with the rule of insufficient reason, the expected value of the job at Wye and whether you should take that job seem to depend on how the options are divided.