Rational regret

Suppose that you have a career choice to make:

  1. There is a “safe bet” available to you, which will yield a discounted lifetime income of $1,000,000.
  2. 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.

Update History:

  • 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: “superamazing super-amazing“; “overconfidence is ones own abilities”

33 Responses to “Rational regret”

  1. Christian Peel writes:

    I’m not sure how many people are “rational”. I guess many are just looking for an option that’s good enough, or satisficing. For a very great many, $1M is enough.

  2. Peter K. writes:

    What Anthony Atkinson once said struck me as true. (He’s the British economist who created inequality studies and worked with Piketty) He suggesest, more equal society will be better and more conducive for entrepeneurs than an unequal one which gives outsized rewards as inducements.

    It makes sense that in a more equal, social democratic society people are freer to risk and fail. A person on the fence may decide to go for it. A friend or family member may decide not to talk them out of it or will lend them a little investment money.

    What does Warstler think? I bet he disagrees!

  3. Peter K. writes:

    What Anthony Atkinson once said struck me as true. (He’s the British economist who created inequality studies and worked with Piketty) He suggested that more equal society will be better and more conducive for entrepeneurs than an unequal one which gives outsized rewards as inducements.

    It makes sense that in a more equal, social democratic society people are freer to risk and fail. A person on the fence may decide to go for it. A friend or family member may decide not to talk them out of it or will lend them a little investment money.

    What does Warstler think? I bet he disagrees!

  4. Peter K. writes:

    Sorry about the repeat. Think about the psychology of the Great Depression. You had a the “Greatest Generation” who became very miserly and risk-averse after experiencing disaster. Then the Boomers reacted against that and embraced the unsustainable casino culture created by the “silent generation.”

  5. Dial Tone writes:
  6. Steve Roth writes:

    Seems to me it’s about the choice sets that we as a community make available to people through our institutions, rules, laws, and contractual constructs.

    If we create a society where more choices are low-probability/high return, and reduce the number that are high-probability/okay return, people can still choose. (Freedom!)

    Freedom is about having good choice sets available. “I really regret that I couldn’t make a low-risk choice that had high odds of a decent minimum return; there just weren’t many (any) of those on offer. I had to swing for the wall. Not surprisingly given the odds, I struck out.”

    Even the best batters only get on base one time out of three. Now imagine each batter got a single at-bat. If they get on base, would you call that skill, “merit”? Or largely luck?

    Do we want to structure our choice sets like that? Do we all want to be playing major league baseball, or would a big game of T-ball be nicer?

  7. Peter K. writes:

    @5 Dial Tone, France too. I believe Waldmann had a link.

  8. No one does a better job of showing that the assumptions of economics gives the economist only one rational response to public policy questions:

    Policy maker: Mr. Economist, what would you advise in this situation that will impact the lives of my constituents.
    Economist: If I am rational, I must decline to answer. It has been proven that I have nothing to say about what is actually important to people living their lives.
    Policy maker: C’mon, I’ll make you famous.
    Economist: Hmmm.

  9. PG writes:

    I don’t think option 2 is the best.

    Expected values are fine when we can iterate the game.

    But here is the one and only life.

    To make it more obvious, we can increase the $100M and
    decrease its probability, and vice-versa to the $200k,
    maintaining the expected value larger than option 1.
    Suddenly you realize that you are gambling your life in
    a lottery game…

    How about the diminishing returns of money? Dosn’t that
    change the expected utility?

    option 1: really nice life, with spare money to enter new “games”
    Option 2: more money than you really need, with smallish probability
    or… a mediocre middle class life, possibly nice but really limited,
    with large probability.

    I order option 1, thanks :)

  10. Brett writes:

    Eh, regret isn’t permanent. While most of the population choosing Option #2 would feel remorse for a period of the time for the Road Not Taken, they’d probably get over it with their nice $200,000/year stipend and move on to other stuff.

  11. Steve Randy Waldman writes:

    One of the (many) great things about commenters is they expose the distance between what a less-than-wonderful writer means to express and what a reasonable person would understand.

    The payoffs above are expressed as discounted lifetime incomes, but I think several of you have (reasonably and conventionally) interpreted “lifetime income” to mean an annual amount. That’s not what I mean though, and the word “discounted” was an inside-baseball kind of cue.

    What I mean is the “present value” of all the money you will ever make, computed by “discounting” future payments to the present.

    I’ve added an italicized “update” to the text, converting “discounted lifetime incomes” into annual amounts.

  12. Harald K writes:

    It’s all nice and well that you emphasize that it’s a discounted lifetime income, but Christian Peel’s satisficing objection still holds. We’re looking to “win” the game, with a win condition partially chosen by ourselves, but also dictated by our environment. We are not looking to maximize our score.

    When faced with a one off choice like this, I think satisficing is the more reasonable thing to do, and I think that’s what most of us actually do.

    I think that the people who take big risks in these lifetime one-off situations, are driven not by ambition, but by a kind of necessity. In my experience, there isn’t all that much regret. But this may be a consequence of living in a welfare state, where failing to make the career you aimed for very rarely means your kids will grow up in misery.

  13. Ian Lee writes:

    It’s become cliché to say

    You think “cliché” is an adjective.

  14. reason writes:

    Great post – here is another one that makes a related point:

    PG @9 Lifetime income does not mean annual income.

  15. Nick Rowe writes:

    So why do lots of people buy lottery tickets, despite buying lottery tickets having a negative expected payoff? People who buy lottery tickets have a revealed preference for increased inequality of outcomes, and are even prepared to pay positive amounts for increased inequality of outcomes.

  16. dilbert dogbert writes:

    Nice mathy hypothetical example but in the real world the probability of a payoff
    on that 10mil bet would be very close to zero not 0.1. Most folks would choose #1.
    Liars lie and cheaters cheat sort of thing.

  17. stone writes:

    Nick Rowe @15, people buy lottery tickets because they feel loosing a tiny amount of money each week is something that won’t make any difference and is worth it to chase “the dream”.

    Does anyone who has just won the lottery (or is rich some other way) then wager it ALL as a one off purchase of loads of lottery tickets? I’ve never heard of anyone doing that. That would be more akin to genuinely choosing a winner takes all style life plan.
    Gambling addicts do fritter away fortunes but a one off rational choice is something else.

  18. stone writes:

    In a similar vein, Ole Peters gives a great example of how if everyone were to take a punt at something that gave an equal chance of a 50% gain or 40% loss, then as a population it would be good. BUT if anyone were to repeatedly make such a bet, they would be virtually certain to loose essentially everything:

    That is perhaps a bit like real life. The innovations that transform all of our lives when they work out are perhaps like a series of bets that all pay off. The problem is that although those are sensible bets, its an awful risk for any individual.

  19. Steve,
    The “career choice” you present at opening is a choice between a spot near the middle of a Normal curve and a spot near one of the tails. Obviously, this Normal curve is not symmetrical…

    The shape of that curve describes the economic environment.

    I’m probably off-topic again, but your words reminded me of these words:

    For if effective demand is deficient, not only is the public scandal of wasted resources intolerable, but the individual enterpriser who seeks to bring these resources into action is operating with the odds loaded against him. The game of hazard which he plays is furnished with many zeros, so that the players as a whole will lose if they have the energy and hope to deal all the cards. Hitherto the increment of the world’s wealth has fallen short of the aggregate of positive individual savings; and the difference has been made up by the losses of those whose courage and initiative have not been supplemented by exceptional skill or unusual good fortune. But if effective demand is adequate, average skill and average good fortune will be enough.

  20. George Bing writes:

    this is instructive and useful site that is examining with “different type of writing service ” with its commonsense. Much appreciated for this course of action. I have a site of composing administration, you may visit simply click here writing essay tips

  21. George Bing writes:

    It is instructive and useful site that is examining with “different type of writing service ” with its commonsense. Much appreciated for this course of action. I have a site of composing administration, you may visit simply click here writing essay tips

  22. stone writes:

    Nick Rowe @15, adding to what I wrote @17, often the same people who buy lottery tickets also choose to buy insurance. Typically people bias towards wanting a slim chance of striking lucky and also want to avoid the risk of things going really bad. That even shows up in the prices of financial options doesn’t it. Market prices for put and call options show that people want a small chance of a fortunate windfall (even at an overall cost) but want to protect against a small chance of calamity (even at an overall cost). They want a convex not a concave payoff profile.

  23. RK writes:

    People in real life have no way of knowing the discounted value of their choices. Do you think Gates, Zuckerberg, Jobs, etc thought about the discounted value of their ventures before they started? Heck no. I live in Silicon Valley and have worked in startups. There is a saying in the valley that if you are doing startups for the money, you are doing it wrong. There is no way to predict how a startup would go. The only right reason to do a startup is because you believe in an idea and believe it worth your while to leave a (possibly a very well paying) job to pursue it.

    If a startup is to fail, it will fail pretty quickly — within 3-5 years. The fact that failure happens quickly is actually good for entrepreneurs. This allows them to learn their lessons and put that experience to beneficial use in their next jobs or ventures. In other words, even if a venture fails, its participants would gain something (mostly intangible skills) that they can re-use subsequently.

  24. reason writes:

    Nick @15,
    of course you know very well that people buy both Lottery tickets AND insurance (insurance is odd in a way – a sort of reverse lottery that reduces rather than increases inequality). Might have something to do with the asymmetry of reaction between losses and gains.

  25. reason writes:

    Oops Sorry I missed that Stone said essentially the same thing.

    But you are of course correct, people want to be able to dream, it is just the discounted value of that dream doesn’t have to be very high. That doesn’t mean that they would prefer to live in a less equal world, sometimes there is a disconnect between individual actions and social outcomes.

  26. reason writes:

    Stone @18
    By the way that stuff you link to is interesting. The link to Ole Peters left me frustrated though – he promises a lot, but it is not there to see. I want the detail (the math). Do you have links to it?

  27. Nick Rowe writes:

    Stone: like reason, I found the link to Ole Peters very unsatisfying. Maybe there’s more to it, but maybe there isn’t. But it seemed like hifalutin bafflegab to me.

    reason: yep, there’s a puzzle about why people (sometimes the same people) buy both lottery tickets and insurance. Maybe it can be explained by an S-shaped utility function, though that looks a little ad hoc.

    But my point was a simpler one. If Steve (and others) can use examples of risk-aversion, or regret-aversion, in arguing that inequality is a bad thing, then I (or anyone else) can use examples of risk-preference, or hope-preference (what’s the opposite of regret-aversion?), to argue that inequality is a good thing. The argument cuts both ways.

  28. stone writes:

    Reason@26, I think some of the maths is in http://rsta.royalsocietypublishing.org/content/369/1956/4913.full (My personal maths understanding though is sadly very limited)

    I guess both you and Nick Rowe@27 were much less impressed than me by the simple arithmetic fact that a crowd of people can collectively prosper by all throwing dice that give an equal chance of a 50% gain or a 40% loss BUT any individual will face certain ruin by repeatedly doing that (because 1.5×0.6=0.9<1). It only works out OK if the winners and losers rebalance between each other. I don't see that as hifalutin bafflegab, I see it as a very basic and under-appreciated reality.

  29. […] your life in their hands) The Ebola Vaccine, Traffic Congestion, and Global Warming Kill Me Now Rational regret An Introvert as President Shorter Reverse Frank Bruni Jim Crow returns: Millions of minority voters […]

  30. Nick Rowe writes:

    Stone: here’s a simpler example: suppose that every year there is a 1% risk that I will lose all my wealth. Then eventually, if I live long enough, I will lose all my wealth. Therefore, I should buy insurance. And the insurance company can pool my risk with other people’s risk, if our risks are independent. (Though I don’t understand how Nature can distinguish between my wealth and other people’s wealth.) No fancy math.

  31. MissTanni writes:

    this is news site and discuss with “Rational regret” thanks a lot for this. Now I am sharing a site to get all the service of writing service follow the link pay to write paper

  32. stone writes:

    Nick Rowe@30, you can’t sensibly offer private insurance against enterprize risk can you? To me this is all about how to ensure that people can take on board enterprise risk rather than simply keeping their savings/employment unproductively safe.
    If real life randomly dishes out success in rare huge dollops, then some kind of redistribution may be needed for enough people to make full use of their talents and property for everyones overall benefit.

  33. Joshua writes:

    I think the core analysis is missing exactly how great the human capacity for regret really is. Whatever you do in life, there will always be things not done. I would guess that this is similar to happiness for which we seem to have our own set-points that are resistant to change from external factors. The implication is that regret is not a factor that should be considered because it will be roughly equal in any financial outcome.