### Healthcare consumers aren't rational

10/21/2013 03:01:00 PM
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 Intransitive preferences can be problematic in healthcare.
Previously on Separating Hyperplanes, I used a study published in Trends in Endocrinology and Metabolism to disprove the economic theory of rationality as it applies to artificial sweeteners. Actually there is a rather persistent literature in Health Economics about the prevalence of irrational choice patterns in health behaviors, and the soon-to-be latest installment in this line will be published in the Journal of Health Economics.
The new research highlights a particular type of irrationality called "preference reversal."

Let's start on some background on what economists mean by "rational." In principle, the economic choice theory can be applied to any choices individuals make, not just traditionally "economic" choices. So just consider a scenario where you must make a choice. There could be an infinite number of possibilities (note, "possible" doesn't mean "affordable"--many "possibilities" will be beyond an individual's ability to obtain but he will nevertheless have defined preferences over them), but lets use the letters $A$, $B$, $C$ to represent any arbitrary three of those possible choices. We will use the symbol $\succeq$ to indicate preference--that is, $A\succeq B$ would mean that the individual either prefers $A$ to $B$, or is indifferent between the two. Economic rationality, then, means that a consumer's choice pattern when presented with this scenario will be
1. complete: either $A\succeq B$ or $B\succeq A$ (or both), and
2. transitive: if $A\succeq B$ and $B\succeq C$, then $A\succeq C$.
Note that these definitions differ from the street definition of "rational," which is generally understood to mean "don't do stupid crap." In fact, a person who consistently chooses to do stupid crap is just as rational as a person who makes sane choices, from the economist's perspective

Preference reversal is an example where condition (2) does not hold. The classic example of preference reversal is where an individual is presented with choices over two wagers. One wager has a low probability of winning a large reward, and the other wager has a high probability of winning a small reward. The subjects are then presented with two kinds of choices involving these wagers: in one case they are asked to bid a monetary amount on each wager, and in the other case they are asked to choose between the two wagers.

As it turns out, medicine is a field where customers are routinely presented with exactly those kinds of choices. Patients are forced to choose between treatment options with varying chances of success, and to decide how much they are willing to pay for each. This paper examines these cases and finds the same kind of preference reversal as has been found elsewhere: patients generally choose the high probability/low reward option, but are willing to pay more for the low probability/high reward option.

This implicitly reveals preferences over three choice possibilities. Let $A$ be the amount of money that the individual is willing to pay for the low probability/high reward option, let $B$ be the low probability/high reward option, and let $C$ be the high probability/low reward option. Thus we have that $B\succeq A$ simply by definition of willingness-to-pay. This paper documents that in healthcare, we have $A\succeq C$ because patients aren't willing to pay as much for the high-probability/low-reward treatment, but not $B\succeq C$ because patients choose the high-probability/low-reward treatment over the alternative treatment.  Thus, patients' healthcare choices are irrational.

The paper does not go this far, but a possible implication of this is that this explains part of why healthcare is so expensive, for it is well known that intransitive preferences are exploitable. In particular, a cunning doctor could start by charging a price $A$ for treatment $B$. Then, because the patient would rather have treatment $C$, the doctor could charge a little extra to switch to treatment $C$. In principle, the individual would actually then be willing to pay a termination fee to halt treatment, since at this point the full cost of the treatment exceeds his willingness to pay for $C$. That brings us back to $A$, where the doctor could start the whole process over again. Repeat until other behavioral notions of "fairness" and reputation step in to halt the spiral.