A stereotype has been defined as a “fixed general image or set of characteristics that a lot of people believe represent a particular type of person or thing.” https://www.collinsdictionary.com/english/stereotype    Or, as “something conforming to a fixed or general pattern; especially : a standardized mental picture that is held in common by members of a group and that represents an oversimplified opinion, prejudiced attitude, or uncritical judgment.” https://www.merriam-webster.com/dictionary/stereotype  The implication is that the use of stereotypes in making decisions concerning populations or individual members of these populations is improper and should be avoided. [See for example, https://www.reference.com/world-view/stereotypes-harmful-dadca8d95b0fc67c or https://www.aauw.org/2014/08/13/why-stereotypes-are-bad] Yet stereotypes have long been and continue to be used to make decisions.

Focusing primarily on a simple summary measure, the following examines whether stereotypes can be used to make rational decisions and if so, under what circumstances. The essay considers both populations and individuals, taking into account that decision making requires information and that developing information is not costless. It is assumed that the information itself is accurate.

Stereotypes are summary measures. They may be very complex and consider an array of many characteristics. Examples would include an index of several factors such as a credit score—essentially a weighted average—or even a proprietary brand name and the quality it represents. Or stereotypes can be very simple and consider only one characteristic.

A very simple, perhaps the simplest, summary measure or stereotype for any particular population is its population mean with respect to one particular characteristic. A population mean provides a centrist measure of the location of the distribution of population members with respect to this characteristic. The variance of this population provides a measure as to how dispersed the individual members of the population are around its mean. Both measures provide significant information about the population. But distributions with large variances may provide only limited information about individual population members, creating a “fog of uncertainty.”

When making decisions about all members of a population taken as a whole, knowledge of the mean alone may be enough to make rational decisions irrespective of the variance. For example, consider auto insurance pricing where all or virtually all population members are required to carry insurance.  By setting a premium equal to the average, or expected, claim value per population member (plus administrative costs) insurance companies can provide risk sharing to all members of a population without taking into account variation among population members. This occurs because a characteristic of the mean is that the sum of all deviations from it, both plus and minus, will net to zero. [Harold W. Guthrie, Statistical Methods in Economics, Richard D. Irwin, Inc., Homewood Illinois, 1966. p. 34.] That is, those with less than average claims exactly offset those with greater than average claims.

But, what about making decisions that concern specific members of a population, not the entire population? Will relying on summary measures yield accurate decisions? Here the dispersion of the individuals around the mean, measured by the variance, comes into play. If the variance is small, a population summary measure can be expected to yield a relatively close approximation to each individual’s characteristic value. As the variance increases in size, however, the ability of a summary measure to predict the characteristic value of any particular individual will decline, as large variances have the potential to yield numerous, large errors with their associated costs Can rational decisions continue to be made in such situations?

Unlike the auto insurance example above where coverage is nearly universal and specific companies have large numbers of policy holders, most decisionmakers do not make decisions concerning most members of a population. Rather, their focus is on a subset of its members. For example, potential employers may hire a few members from a population or they may hire many members from it, but they do not hire everyone. In effect, each decisionmaker draws a random sample of a given size from the population when he or she makes new hires.

The distribution of the means of all the possible samples—subsets—of this size around the population mean (our summary measure) is known as the sampling distribution of the means. Its dispersion is measured by the population standard deviation divided by the square root of the sample size, or standard error. It will be larger when there is greater variation in the population but it also becomes smaller as the sample size increases. As a result, the accuracy of using any particular mean summary measure with any given level of variation depends on the frequency with which decisions are made. That is, the more decisions made the greater the sample size will be.

Some entities make decisions only infrequently. As a result, basing decisions on a summary measure such as a mean where there is significant variation in the population may not result in good outcomes for the infrequent decisionmaker. This situation arises because there are not enough decisions to make it likely that there will be enough good and bad outcomes to offset each other.  With higher population variances, the infrequent decisionmaker must choose between continuing to accept the risks and costs of a potentially bad outcome, abstain from making decisions altogether using the summary measure, or adopt a different approach. Unlike frequent decision makers discussed below, there are limited incentives for infrequent decision makers to incur the costs to develop improved measures because they cannot spread the costs across enough decisions to make it worthwhile.

As an example, skill and ability levels of recent college graduates vary significantly. The summary measure of having earned a degree is only a limited predictor of quality. Infrequent potential employers have the option of using this measure and risking a poor new hire, avoiding hiring altogether, or adopting a different approach such as recruiting only from premier, top-tier schools. The selection and training processes for people from these schools can be expected to produce graduates with higher and more uniform mean abilities. But hiring recruits with this pedigree quality measure may be more costly.

The situation can be expected to be different for frequent decisionmakers. Because they make numerous decisions—draw a larger sample—they can rely on summary measures with larger population variances and expect average outcomes to be close to the population mean much of the time as bad choices are offset by good ones. (The standard error of the larger sample size is smaller than for infrequent decisionmakers.)   In the example above, recruiters can hire college graduates with the anticipation that the ability levels of their new hires as a group will very likely approximate the mean of all graduates. They do not need to be preoccupied with getting bad apples because overall group performance is predictable and stable.

Although frequent decisionmakers can expect to make decisions with relatively stable overall outcomes based on summary measures, economic incentives may encourage them to improve their decision making by developing improved measures. Not only will improved measures allow the decisionmakers to select better members of the population, the costs of doing so can be spread across many decisions. An improved measure will give any particular decisionmaker a competitive advantage, at least until competitors are able to imitate the better measure or develop their own better measures.

Returning to the college graduate example, because some graduates of non-top tier schools are of similar quality to graduates of top-tier schools, an incentive exists for potential employers to develop measures to identify these better graduates. If this can be accomplished at an aggregate cost that is less than the premium salary margin that may have to be paid to top-tier-school graduates, firms can be expected to make the investment required to develop the more precise measure. In so doing, these firms can reduce their labor costs and may enjoy a competitive advantage. As noted, frequent decisionmakers will have a greater incentive to undertake such investments because development costs of a superior measure can be spread over a large number of new hires.

It should be acknowledged that making decisions based on a summary measure where there is significant population variation may not be fair to the individuals being evaluated. In the college graduate example, those individuals with desirable characteristics better than the mean will not be recognized as better while those with worse characteristics will be protected by the fog of uncertainty. To the extent that large population variances cause infrequent decisionmakers to abstain from making decisions altogether, all individuals may be potentially harmed.

If the alternative approach of hiring only from top tier schools is adopted, it may reduce the risk of poor hires but will also disadvantage higher quality candidates from second-tier schools. Should frequent decisionmakers adopt improved measures to identify better graduates from second-tier schools, these graduates likely will initially be underpaid. But their salaries can be expected to increase as other employers imitate and adopt these improved measures. Concurrently, less capable graduates of second-tier schools will no longer be shielded and can be expected to experience a relative decline in salaries.

Although infrequent decisionmakers have limited incentives to develop better measures, third parties may nonetheless do so. Especially in regard to high variance populations, the creation of improved summary measures, although too costly to be developed by individual decisionmakers, may still be undertaken by third parties if they can sell the measures to a sufficient number of consumers.

In the case of hiring, employment agencies often serve this function for infrequent decisionmakers. The agencies incur the costs of identifying the better members of a large variance population and spread this cost across placing numerous hires with smaller firms. Agencies can be compensated either by employers or job seekers or both.

With respect to consumer products, consider the marketing of used cars. The summary measure—stereotype—is that used cars are inferior. In fact, some are of very high quality.   Some car dealers have identified higher quality used cars and market them as “certified” merchandise guaranteed to meet certain standards. And the chain used car dealership CarMax has developed a reputation of offering better used vehicles with limited warranties.

In summary, decisionmakers can make rational decisions based on stereotypes under a wide variety of circumstances. Exceptions may occur when decisions are made infrequently or the decisionmaker would incur extensive losses should a poor outcome occur. In such cases decisions are either not made or a substitute, typically higher cost, approach adopted.

Decisions based on stereotypes also may not be considered fair to those individuals affected by the decisions. However, natural economic incentives exist to encourage development and adoption of better decision-making criteria. Indeed, a significant business opportunity exists for anyone who can develop improved selection measures where population variances are large. Although adopting better measures will in general improve decision outcomes for decisionmakers and for better than average members of stereotyped groups, inferior members of these groups can be expected to fare worse as they are no longer shielded by the fog of uncertainty.

Mr. Hoffer is a transportation economist, formerly with the Federal Aviation Administration.  Contact him at snhoffer@aol.com.  See the Contributors page for more about Mr. Hoffer.