Mathematically correct but psychologically wrong

The snowball strategy says to pay off your smallest debt first, then the next smallest, and so on until you’re out of debt.

When I first heard of this I thought it was silly. Clearly the optimal strategy is to pay off the debt with the highest interest rate first. That assessment is mathematically correct, but psychologically wrong. The snowball strategy provides a sense of accomplishment and encouragement by reducing the number of debts as soon as possible. Ideally someone would be able to pay off at least one debt before their determination to get out of debt wanes.

My point here isn’t to give financial advice. I bring up the snowball strategy because it is an example of a problem with an obvious but naive solution. If someone is overwhelmed by debt, they need encouragement more than a mathematically optimal strategy. However, the snowball strategy may not be psychologically optimal for everyone. This further illustrates the idea that optimal real-life strategies are more complicated than mathematical models.

Many things that don’t look optimal are in fact optimal once you take the necessary constraints into account. For example, software that seems poorly designed may in fact have been brilliantly designed when you consider its economic and historical constraints. (This may even be the norm. Nobody complains about how badly obscure software was designed. We complain about software that has been successful enough to criticize.)

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15 thoughts on “Mathematically correct but psychologically wrong

  1. This is like the “mental relativity” effects, and why prices are always x.95 or x.99. Our mind just adjusts the price to the lower bound… Psychologically correct, mathematically (or financially) incorrect. But as a mathematician, I hope that you are not in deep enough debt to need a snowball effect and can instead work with a mathematically better model :)


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  2. Part of the problem is software usually doesn’t contain these constraints so no outsider can possibly know why software is what it has become.

  3. I’m reminded of something Bjarne Stroustrup, designer of C++, once said: “There are two kinds of programming languages: the ones everybody complains about, and the ones nobody uses.”

  4. I know the point wasn’t to give financial advice but this post makes me wonder if “debt consolidation” services actually try to use your monthly payment in a mathematically optimal way. I would hope the answer is yes but the part of me that has seen corporate greed is pessimistic.

  5. Debt consolidation could be a good idea mathematically and psychologically. You may be able to reduce both the number of loans and the interest rate at the same time.

  6. I wasn’t aware from that quote from Stroustrup. It is kind of similar… Along with Wayne Chang’s comment: consider the current flow of readers from Digg to Reddit: a flow towards simplicity.

    @John: Debt consolidation would be perfect (mathematically, economically and psychologically) if the interest rate they offered was not as high as currently offer. But of course, a lot of people needing debt consolidation may end up not paying, and the company has to enable some money recouping system.



  7. @Ruben, @John: My pessimistic side was saying that debt consolidation companies probably do not work optimally in a mathematical sense. Instead they may compromise between mathematical optimality and getting the longest, most profitable payment system out of you before you decide that it’s not worth it.

  8. Rob: I do something similar, particularly when I’m feeling overwhelmed with my to do list. Knocking out a few little things makes me more willing to tackle the bigger ones.

  9. Mathematical strategy would have been equivalent to psychological strategy had we been rational, fully-logical beings. As Dan Ariel points out in two book, we are predictably irrational.

  10. Dan Ariely’s publisher probably chose to use “irrational” in the title of his book to be provocative. In my opinion, “irrational” should be used to indicate an error in logic and not just taking into account factors that are difficult to model mathematically.

    If someone says “I owe Sam $10 and I owe Jill $7. Therefore I’m $5 in debt.” they are being irrational. But if someone says “My plan for eliminating my debt will take into account my understanding of human nature” then I would say they are being rational.

  11. Actually, the snowball strategy IS the mathematically optimal way to go if one takes into account a mathematical variable for the psychological factor to calculate an “Effective Debt”:

    Monetary debt = M
    Effective debt = M – P(n)

    where P(n) = psychological inclination as a function of n number of accounts with a balance; note P(n)=0 only for androids or people w/ no emotions

    In this case, P(n) increases with decreasing n. For a person with n=10 credit cards, say P(n) = -10,000

    If M = $30,000 and P(10)= -10,000,
    Effective debt = $40,000

    …Getting rid of two accounts by paying them off (even if they owed say $1,000 on each account) has an additional psychological benefit in that now P(n) = P(8) = -8,000

    Effective debt (of 8 accounts) = $26,000

    But as a counterexample, if the same $2,000 was targeted toward accounts with the highest interest rate without actually resulting in any reduced # of accounts, P(n) would still be equal to P(10) = 10,000


    Effective debt (of 10 accounts) = $28,000

    That’s how you incorporate psychology into mathematics and allow the math to do its thing!


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