Prospect theory: A three-way conversation

For the past six weeks, Jeff Harrison (of MoneyLaw and Class Bias in Higher Education fame, among many other things) and I have had an extended e-mail exchange about prospect theory. It all started with Jeff's use of prospect theory to evaluate law school policy and faculty behavior. I chipped in some thoughts of my own. Jeff then decided to go to the ultimate authority on prospect theory: Daniel Kahneman. With the acquiescence of all involved, I thought I would share choice portions of our three-way conversation on prospect theory with the author of Thinking Fast and Slow. Enjoy.

Read the rest of this post . . . .

---

From Jeff Harrison to Jim Chen:

Jim: I have a question that I should know the answer to since I have talked about and written about prospect theory for years. . . . One of the teachings of PT, or so I have seen it described, is that when the same choices are framed in a negative or positive way, people change their answers. An example is the epidemic hypothetical. People are willing take a chance when the choice is framed as a loss.

On the other hand, when considering a possible movement to a higher level of wealth they value the gain more than they value avoiding the loss. . . .

So what is the message of prospect theory? Is it that negatively framed choices are less attractive or is it that a movement to a risky more negative position is to be guarded against more than a movement to a risky more positive position is pursued? Does this even make sense?

From Jim Chen to Jeff Harrison:

Hi Jeff,

Here are three ways of expressing the principle in ways that I understand:

1. Losing hurts more than winning feels good. (We'll leave for another day the idea that there is a site called wife.org and that it contains information like this.)
2. "Threat of loss, not hope of gain, is the essence of economic coercion." United States v. Butler, 297 U.S. 1, 82 (1936).
3. Daniel Kahneman, Thinking Fast and Slow.

I hope this helps.

From Jeff Harrison to Jim Chen:

Thanks Jim, It's just that I read an article that put it all in terms of framing and I always felt that it was the more like these definitions. I have the book and it seems consistent with that too.

I felt framing was more generally associated with preference reversals as a form of irrationality.

From Jim Chen to Jeff Harrison:

Now I see where the shoddy rhetoric of others led you into confusion.

I'd start with Wikipedia's very helpful discussion of the use of "framing" in the social sciences:

Perhaps because of their use across the social sciences, frames have been defined and used in many disparate ways. Entman called framing "a scattered conceptualization" and "a fractured paradigm" that "is often defined casually, with much left to an assumed tacit understanding of the reader."

I think you used it the right way in your MoneyLaw post. The upshot is that there is a systematic asymmetry in preference for gains versus fear of losses.

For my part, I do think that you and the "confusing" sort are on to something else. There are circumstances where people irrationally gamble huge amounts on ridiculous long shots. We've seen it in faculty hiring. The same effect can be observed at any racetrack or lottery ticket counter — people make actuarially lousy bets in the hopes of a huge win. Never mind Powerball — it took me years to figure out why anyone would ever assemble an exacta, trifecta, or superfecta bet when straight-up betting paid off so much more reliably, and more in line with actual evaluation of equine performance.

Let's go beyond gambling. There are very serious real world consequences to this sort of asymmetry. Despite a decade plus of zero gains, not to mention spectacular examples of awful failure (Harvard 2008, anyone?), institutional investors, including university foundations and public employee pension systems, are doubling down on the "Yale model" of portfolio management touted by David Swensen. On its own, the illiquidity of the resulting portfolio should be enough to discourage its adoption. Then there is the inherent trap of the advisor's incentives to lie about performance, since (s)he alone knows what's really happening (if anyone does, which is yet another problem). Oh, let me mention performance again. It isn't there, hasn't been there, and is unlikely ever to show up.

In short, there are situations where individuals, from gamblers to investors, systematically prefer mysterious but possibly outsized gains, notwithstanding obvious and undeniable evidence of almost guaranteed loss. I do think there is a way to reconcile this preference for mark-to-mystery or mark-to-make-believe with prospect theory. But that's enough musing on behavioral finance (or at least on financial behavior) for one morning.

From Jeff Harrison to Jim Chen:

I think I can express my question about prospect theory a bit more coherently . . . .

My simplest explanation for my students is that people dislike losses more than the like gains of the same amount. In that form it’s like the diminishing marginal utility of money. So there must be more going on.

Then I see the statement that it means people are risk averse with respect to gains and risk preferring when faced with losses. The typical examples of gains are a certain amount as opposed to an expected amount that is higher. Depending on the amounts, of course, they prefer the certain amount. The reverse is true for losses – rather than suffer a certain loss, they will opt for an expected loss that may be higher.

What I cannot square this last statement with is the purchase of insurance. Over my lifetime, I may pay with certainty $30,000 in car insurance knowing full well that my expected loss over that period is less. Yet, I opt for the certain loss because I am risk averse.

OK, so how does that mean we are risk seeking when it comes to losses?

From Jim Chen to Jeff Harrison:

You're referring to a side application of prospect theory called the reflection effect.

The distorting effect of human evaluations of probability, and the asymmetrical alignment of those evaluations based on whether a gain or a loss is at stake, can be expressed through the reflection effect. Being willing to gamble on a 20% loss of 100 rather than pay a known, certain premium of 20 does in fact suggest greater risk-seeking with respect to losses. This is in tension with core prospect theory, which posits that individuals weigh losses more heavily than they credit gains. Hence the label "reflection effect."

Insurance purchases are consistent with what I'd call core prospect theory. I know that a $25,000 loss (say, needing to replace my car) would quite dramatically damage my ability to pay other bills and therefore could reduce my standard of living. So I agree to pay $500 a year for insurance, even though there is less than a 2 percent probability of that loss. The insurance company makes money because the expected loss is less than my premium. Prospect theory in that sense does explain insurance, and quite nicely.

The reflection effect, as I see it, is a "minor key" variation on the main melodic theme of prospect theory in B-flat major. Most people happily buy health insurance, because they understand that a single catastrophic illness or accident can erase life savings. The reflection effect explains those people who have material as opposed to (or perhaps in addition to) a reflexive ideological objection to the PPACA's individual mandate.

From Jeff Harrison to Daniel Kahneman:

Dear Professor Kahneman:

I hope you have time for a question about prospect theory. I have written about it and applied it in my own writings in the area of law and economics. Now I have come to think I actually do not understand it. Let me explain.

My simplest explanation for my students is that people dislike losses more than the like gains of the same amount. In that form it’s like the diminishing marginal utility of money. So there must be more going on.

Then I see the statement that it means people are risk averse with respect to gains and risk preferring when faced with losses. The typical examples of gains are a certain amount as opposed to an expected amount that is higher. Depending on the amounts, of course, they prefer the certain amount. The reverse is true for losses – rather than suffer a certain loss, they will opt for an expected loss that may be higher.

What I cannot square this last statement with is the purchase of insurance. Over my lifetime, I may pay with certainty $30,000 in car insurance knowing full well that my expected loss over that period is less. Yet, I opt for the certain loss because I am risk averse. . . .

From Daniel Kahneman to Jeff Harrison:

Your question is a very good one. Prospect theory explains the purchase of insurance (and of lotteries) by a misweighting of low probabilities. Giving too much weight to a low probability of a gain favors gambling and too much weight to an improbable loss favors insurance. Even more important, there is a framing effect: insurance is much more valued when presented as a purchase (presumably, of peace of mind) than when it is described as a choice between losses.