Elasticity of Belief

To evaluate research on attitudes like racial bias we need to know at least two things. First, just how important is, say, a distaste for margarine vs. butter, or a preference for African-Americans over whites, to individual X? Does X really care or is he just ticking a box to be polite? Archie Bunker may show a test bias against African Americans, yet he may be perfectly willing to vote for one or have his daughter marry one. Beliefs have a strength which is measured only imperfectly by surveys.

But beliefs also have a second property I will call elasticity. Elasticity is a familiar concept to economists. The simple law of supply and demand dictates that a small increase in price will (usually) cause a small decrease in demand. Elasticity is just the ratio of the small change in demand to the small change in: price, both expressed as ratios:

E= (∆Q/Q)/(∆P/P)

Where Q is the quantity of a good and P is its price. If price elasticity is great, then a small change in price will cause a large change in quantity bought, in demand.

Demand depends on the value, the utility, of a good. In most cases, utility is related to amount of good in a negatively-accelerated way, growing fast at first then reaching an asymptote (maximum). The value of each little ΔQ usually declines with value of Q: large at first (one slice of pizza) and decreasing as the amount consumed increases (the 10th slice). So price elasticity will be large if the stock of the good is small but smaller as the stock increases.

The same seems to be true of beliefs. There seems to be a parallel between amount of a good and amount of knowledge about something; and also a parallel between degree of belief and price. If you own very little of something desirable, you will be willing to pay a lot for a small increment: marginal utility, and price elasticity, will be high. Conversely, if you already own a lot, an increment will be much less attractive and you will not want to pay much for it.

Similarly, if you know very little about something, then a small addition to your stock may cause a large change in your belief. Conversely, if you already know a lot, a small increment in your knowledge is likely to have little effect. In other words, a bigot is not a bigot is not a bigot. A person who is bigoted because of hearsay and casual acquaintance is likely to be much more impressed by personal experience with the object of his bigotry than someone who has acquired his belief through an emotional personal history. In the words of a tendentious witticism: “A conservative is a liberal who has been mugged by experience”.

Thus we should not be too surprised at a recent report[1] that more information, whether positive or negative, reduces racial discrimination:

Recent research has found widespread discrimination by [Airbnb] hosts against guests of certain races in online marketplaces.... We conducted two randomized field experiments among 1,256 hosts on Airbnb by creating fictitious guest accounts and sending accommodation requests to them… requests from guests with distinctively African American names are 19 percentage points less likely to be accepted than those with distinctively White names. However, a public review [whether positive or negative] posted on a guest's page mitigates discrimination: …the acceptance rates of guest accounts with distinctively White and African American names are statistically indistinguishable. Our finding is consistent with statistical discrimination: when lacking perfect information, hosts infer the quality of a guest by race and make rental decisions based on the average predicted quality of each racial group; when enough information is shared, hosts do not need to infer guests' quality from their race, and discrimination is eliminated.

In other words, the modest racial bias Airbnb landlords showed at first was very elastic; it could be dissipated by almost any credible information, whether positive or negative. Unfortunately, attitudinal elasticity is not measured by standard opinion surveys.