Suppose that you have a career choice to make:
- There is a “safe bet” available to you, which will yield a discounted lifetime income of $1,000,000.
- Alternatively, there is a risky bet, which will yield a discounted lifetime income of $100,000,000 with 10% probability, or a $200,000 lifetime income with 90% probability.
The expected value of Option 1 is $1,000,000. The expected value of Option 2 is (0.1 × $100,000,000) + (0.9 × $200,000) = $10,180,000. For a rational, risk-neutral agent, Option 2 is the right choice by a long-shot.
A sufficiently risk-averse agent, of course, would choose Option 1. But given these numbers, you’d have to be really risk-averse. For most people, taking the chance is the rational choice here.
Update: By “discounted lifetime income”, I mean the present value of all future income, not an annual amount. At a discount rate of 5%, Option 1 translates to a fixed payment of about $55K/year over a 50 year horizon, Option 2 “happy” becomes $5.5 million per year, Option 2 “sad” becomes about $11K per year. The absolute numbers don’t matter to the argument, but if you interpreted the “safe bet” as $1M per year, it is too easy to imagine yourself just opting out of the rat race. The choice here is intended to be between (1) a safe but thrifty middle class income or (2) a risky shot at great wealth that leaves one on a really tight budget if it fails. Don’t take the absolute numbers too seriously.
Suppose a lot of people face decisions like this, and suppose they behave perfectly rationally. They all go for Option 2. For 90% of the punters, the ex ante wise choice will turn out to have been an ex post mistake. A bloodless rational economic agent might just accept that get on with things, consoling herself that she had made the right decision, she would do the same again, that her lived poverty is offset by the exorbitant wealth of a twin in an alternate universe where the contingencies worked out differently.
An actual human, however, would probably experience regret.
Most of us do not perceive of our life histories as mere throws of the dice, even if we acknowledge a very strong role for chance. Most of us, if we have tried some unlikely career and failed, will either blame ourselves or blame others. We will look to decisions we have taken and wonder “if only”. If only I hadn’t screwed up that one opportunity, if only that producer had agreed to listen to my tape, if only I’d stuck with the sensible, safe career that was once before me rather than taking an unlikely shot at a dream.
Everybody behaves perfectly rationally in our little parable. But the composition of smart choices ensures that 90% of our agents will end up unhappy, poor, and full of regret, while 10% live a high life. Everyone will have done the right thing, but in doing so they will have created a depressed and depressing society.
You might argue that, once we introduce the possibility of painful regret, Option 2 is not the rational choice after all. But whatever (finite) negative value you want to attach to regret, there is some level of risky payoff that renders taking a chance rational under any conventional utility function. You might argue that outsized opportunities must be exhaustible, so it’s implausible that everyone could try the risky route without the probability of success collapsing. Sure, but if you add a bit of heterogeneity you get a more complex model in which those who are least likely to succeed drop out, increasing the probability of success until the marginal agent is indifferent and everyone more confident rationally goes for the gold. This is potentially a large group, if the number of opportunities and expected payoff differentials are large. 90% of the population may not be immiserated by regret, but a fraction still will be.
It is perhaps counterintuitive that the size of that sad fraction will be proportionate the the number of unlikely outsize opportunities available. More opportunities mean more regret. If there is only one super-amazing gig, maybe only the top few potential contestants will compete for it, leaving as regretters only a tiny sliver of our society. But if there are very many amazing opportunities, lots of people will compete for them, increasing the poorer, sadder, wiser fraction of our hypothetical population.
Note that so far, we’ve presumed perfect information about individual capabilities and the stochastic distribution of outcomes. If we bring in error and behavioral bias — overconfidence is ones abilities, or overestimating the odds of succeeding due to the salience and prominence of “winners” — then it’s easy to imagine even more regret. But we don’t need to go there. Perfectly rational agents making perfectly good decisions will lead to a depressing society full of sadsacks, if there are a lot of great careers with long odds of success and serious opportunity cost to pursuing those careers rather than taking a safer route.
It’s become cliché to say that we’re becoming a “winner take all” society, or to claim that technological change means a relatively small population can leverage extraordinary skills at scale and so produce more efficiently than under older, labor-intensive production processes. If we are shifting from a flattish economy with very many moderately-paid managers to a new economy with fewer (but still many) stratospherically paid “supermanagers“, then we should expect a growing population of rational regretters where before people mostly landed in predictable places.
Focusing on true “supermanagers” suggests this would only be a phenomenon at the very top, a bunch of mopey master-of-the-universe wannabes surrounding a cadre of lucky winners. But if the distribution of outcomes is fractal or “scale invariant“, you might get the same game played across the whole distribution, where the not-masters-of-the-universe mope alongside the not-tenure-track-literature-PhDs, who mope alongside failed restauranteurs and the people who didn’t land that job tending the robots in the factory despite an expensive stint at technical college. The overall prevalence of regret would be a function of the steepness of the distribution of outcomes, and the uncertainty surrounding where one lands if one chooses ambition relative to the position the same individual would achieve if she opted for a safe course. It’s very comfortable for me to point out that a flatter, more equal distribution of outcomes would reduce the prevalence of depressed rational regretters. It is less comfortable, but not unintuitive, to point out that diminished potential mobility would also reduce the prevalence of rational regretters. If we don’t like that, we could hope for a society where the distribution of potential mobility is asymmetrical and right-skewed: If the “lose” branch of Option 2 is no worse than Option 1, then there’s never any reason to regret trying. But what we hope for might not be what we are able to achieve.
I could turn this into a rant against inequality, but I do plenty of that and I want a break. Putting aside big, normative questions, I think rational regret is a real issue, hard to deal with at both a micro- and macro- level. Should a person who dreams of being a literature professor go into debt to pursue that dream? It’s odd but true that the right answer to that question might imply misery as the overwhelmingly probable outcome. When we act as advice givers, we are especially compromised. We’ll love our friend or family member just as much if he takes a safe gig as if he’s a hotshot professor, but we’ll feel his pain and regret — and have to put up with his nasty moods — if he tries and fails. Many of us are much more conservative in the advice we give to others than in the calculations we perform for ourselves. That may reflect a very plain agency problem. At a macro level, I do worry that we are evolving into a society where many, many people will experience painful regret in self-perception — and also judgments of failure in others’ eyes — for making choices that ex ante were quite reasonable and wise, but that simply didn’t work out.
- 29-Oct-2014, 12:45 a.m. PDT: Added bold update section clarifying the meaning of “discounted lifetime income”.
- 29-Oct-2014, 1:05 a.m. PDT: Updated the figures in the update to use a 5% rather than 3% discount rate.
- 29-Oct-2014, 1:25 a.m. PDT: “
superamazingsuper-amazing“; “overconfidence is ones ownabilities”