The Role of Probability in Discrimination Cases

An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination.

A company decides to hire 14 people. The applicant pool is large, and there are equal numbers of equally qualified women and men in the pool. To avoid claims of discrimination, the company decides to select the prospective employees at random.

Questions to consider:

1.  How big a difference between the numbers of men and women who are hired might occur just by chance?

2.  How likely is it that equal numbers of men and women are hired?

3.  How big a difference might suggest discrimination in hiring?

1. Repeat the hiring process 20 times. Each time record the number of men hired, the number of women hired, and the difference (use absolute value of the difference)

Run / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
# Men
# Women
Difference
Run / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20
# Men
# Women
Difference

2. What fraction of times in the 20 runs did the number of men equal the number of women?

3. What fraction of times in the 20 runs did the difference between the number of men and number of women equal 2 (8 men and 6 women or 6 men and 8 women)?

4. Fill in the fraction of times your differences had each of the following values.

Difference / 0 / 2 / 4 / 6 / 8 / 10 / 12 / 14
Fraction

5. Based on the data in 4, is it likely or unlikely that the difference would be 8 or more? Is it likely or unlikely that the difference would be 10 or more?

6. Suppose you didn’t know whether the hiring was fair or not, and suppose you saw that there was a large difference between the number of men and women, say 10 or 12. Then this might be explained in two ways. One, it could be due just to chance although a very slim chance, or two, it could be due to discrimination. What would the difference have to be to make you believe “beyond a reasonable doubt” that discrimination occurred in this hiring process? Use the table in 4 to help you make this decision.

7. In a real case, what additional information besides probability might a lawyer use to help prove or disprove discrimination?