How the Ellsberg Paradox Impacts Your Investing Strategy

Properly evaluating uncertain outcomes is an important skill.

By SHARE
Jason Hull
Jason Hull

I’m a very impatient commuter. When I hit a traffic jam or a long light, I’m pretty likely to take a turn and go an alternate route, even if I know doing so will take longer. I’d rather do that than be blocked by the unknown.

Humans are hard-wired to avoid ambiguity wherever possible, and this tendency to shy away from ambiguities in decision-making is called the Ellsberg Paradox. The example, which Daniel Ellsberg (of the Pentagon Papers fame), used to demonstrate the paradox involves an urn and red, black, and yellow balls. There are 30 red balls, and an unknown number of black and yellow balls, which sum up to 60, meaning there are 90 total balls in the urn. You’re faced with two series of gambles:

  • Gamble A: You win $100 if you draw a red ball from the urn OR Gamble B: $100 if you draw a black ball, and
  • Gamble C: $100 if you draw a red or yellow ball OR Gamble D: $100 if you draw a black or yellow ball.
  • Which two gambles did you choose?

    A pair of dice on a casino table

    iStockPhoto

    If you’re like most people, you chose Gamble A and Gamble D. However, this is counterintuitive. If you chose Gamble A, then you believed that there were more red balls than black balls, which should mean that, according to your beliefs, Gamble C would be the higher likelihood gamble.

    Yet, in the cases of Gamble A and Gamble D, we’re going with known quantities—One in three balls for Gamble A and two in three balls for Gamble D—rather than trying to parse out the wide range of possibilities for Gambles B and C.

    How does this affect us in our investing lives?

    • We go for defaults. Whether it’s the default 2-percent investment that your employer puts on the 401(k) enrollment form or the default asset allocation that the 401(k) provider recommends, we tend to stick with whatever default is chosen for us. While Cass Sunstein argues that this creates an opportunity for well-intentioned overriding of defaults and inaction, it does not exonerate us of the responsibility to think through our choices.
    • We stick with what is tried and true. Since it’s the limbic system which is driving the train for our choices, we tend to use analogies to simplify the decision-making process. You’re more likely to choose a State Farm mutual fund over a Vanguard fund if you have your insurance with State Farm and have never heard of Vanguard.
    • We become too risk-averse. Even as we get older, we need to continue to put money to work in investments to give us a chance to beat inflation; however, the answer that “feels” safest to us is to invest solely in income-producing investments for fear of losing the principal. We’re choosing a known return—the income stream—over an ambiguous return – that of equities—even if the former choice will erode our buying power over time.
    • What can we do to help ourselves deal with the Ellsberg Paradox and embrace ambiguity in our investments?

      • Work to become more numerate. Research shows individuals and couples who were better at math tended to be in better financial conditions than those who were not.
      • Force yourself to think about outcomes. We tend to avoid the ambiguous outcomes because we do not want to have to think about them. Our limbic system wants the quick and easy solution, which is why you like Gambles A and D. Even if you only think about worst case, best case, and most likely outcome, you’re giving yourself more information with which to make decisions.
      • The next time I drive up to a long line of stopped cars, I’m going to fight the urge to give in to the Ellsberg Paradox and not take an alternative route. If you don’t see any more articles from me, it's because I'm probably still stuck in traffic!

        Jason Hull is a candidate for the CFP(R) Board's certification, is a Series 65 securities license holder, and owns Hull Financial Planning.