What is a good decision?

Suppose I come to you and offer to play the following game. I toss a fair coin. If it comes down heads, I give you £5; but if it comes down tails, you give me £10.

This is not a favourable gamble for you: the expectation is that I will win £2.50 — in other words, if we play this game n times, I will win a total amount that, as n increases, approaches £2.50 x n.

But suppose you just think, what the heck, let’s do it, and as it happens the coin comes down heads. You win £5 and walk away.

Now: when you decided to play, did you make a good decision?

13 responses to “What is a good decision?

  1. The outcome of a bet neither validates nor invalidates the choice to make it. The answer to your question depends on issues like whether the punter understood the odds, and the possibly subjective value he placed on the possible outcomes.

  2. Daniel Do Binau

    The answer is simple:

    At the time, no. In retrospect, yes.

    We can add that since the general time machine shortage of today’s society means we generally do not have the luxury of retrospect when having to make decisions, the first answer is the most relevant one.

    Similary, any purchase of any lottery ticket is in general a bad decision – but looking back at the purchase of a winning one, most people would be inclined to repeat their “mistake” if given the opportunity.

  3. araybold, perhaps I should have been more specific about the subjective values of the outcomes. For these purposes, they are identical to the objective values.

  4. I would say “no”. But sometimes a bad decision can have a net positive outcome. For example: staying out late and drinking enough to have a mad hangover the next day is a bad decision. But the memories may be worth it (:

  5. The answer has to be “no”. A bad decision with a lucky outcome was still a bad decision. It’s a typical fallacy (or cognitive bias) to judge the correctness of a decision based on information that could not have been known at the time.

  6. It’s a typical fallacy (or cognitive bias) to judge the correctness of a decision based on information that could not have been known at the time.

    I agree with this but, if you want to go all the way with it, what matters isn’t the decision, per se, but the decision-making process. We aren’t given a lot to go on in Mike’s description, “But suppose you just think, what the heck, let’s do it.” One could imagine various ways to arrive at that decision. If the thought process was, “I know the odds are against me, but I feel lucky right now.” That is clearly a bad decision. If the thought process was, “I don’t know the odds and don’t care.” That’s also a bad decision.

    If, however, I thought, “Mike seems like a nice guy, I don’t mind giving him £10” that’s a perfectly reasonable decision. Or, “I’m willing to pay £2.5 (on average) for the entertainment value of watching Mike flip a coin.” That would be an odd decision but a completely defensible one. Or if I’m thinking, “while he’s flipping the coin and talking with me he’ll be distracted and my accomplice can steal his wallet” that could also be a good decision.

  7. All good points, NickS, but a bit tangential to what I was aiming for :-)

  8. I stand by my reply regardless of where the punter’s values are on the objective/subjective spectrum. If, by objective, you mean that the punter’s sole interest was gaining money, and his value function for money was linear over the range of outcomes, then it was not a good bet and he was just lucky.

    It would be an error in analysis to decide what the punter’s values were after the event. I mention this because your punter apparently thinks “what the heck”, which is not a mindset associated with purely rational thought. Of course, he may have an objective (as described above) goal, but calculated the odds incorrectly as even: that would also be a bad bet. Perhaps the most interesting case would be if he genuinely did not know how to calculate the odds, and did not have someone he trusted to tell him. Such situations have existed for everyone (e.g. trading options prior to Black-Scholes) and no doubt still exist. In those cases, we still have subjective valuations: for example, a chance might be a good one to take if the downside is bearable (not that much worse than the the do-nothing case) and the upside is highly desirable. Such situations arise in areas as diverse as sports and medicine.

    Going back to my main point, that the outcome does not count in deciding if a bet was a good decision: intuitively, we feel that it does, and that error can have very serious consequences. NASA continued to fly its space shuttles after it was found that foam sometimes fell off the external tank and hit the orbiter. As the CAIB established, the mindset was that it had happened before without serious consequences, so ‘keep on flying’ was a good decision. For a while, it worked…

  9. Define ‘good decision’.

  10. That is rather what I am trying to get you to do.

  11. The idea of a good decision is so extrinsically loaded that the probabilities and payoffs can be dwarfed by other values. For example: Was the bet part of a charity fund raiser? Was the bet the first step in a long con? Were you trying to impress the young lady with you that you were spending freely that night? Was it part of a running joke between us? Were you trying to reassure a third party that you were a serious player? Was it part of a fraternity/sorority house prank? Was it part of a more complex betting strategy?

    I remember one journalist offering a betting strategy for renting space at a roulette table, the idea was that one would lose money, but one could stay at the table absorbing the atmosphere and listening in on conversations.

    The obvious Bayesian answer is that the decision was a bad one a prior, but a good one a posteriori. The difference being the knowledge that you won the bet. Of course, not all of us are Bayesians.

  12. This is why the word “good”, unqualified, is so often useless. You made a good-in-actual-outcome decision. You made a bad-in-expected-outcome decision. You may (see e.g. kaleberg’s comment above) have made a good-in-expected-outcome decision, measured in terms of things other than money that you cared more about. (Or you might conceivably have had private information that made the probabilities what we think they are — e.g., if you are somehow controlling the result of the coin flips.)

    But once we know all that sort of information, there is no *further fact* about whether your decision is a “good” one or not. When you nail that down, all you’re doing is choosing one of many possible notions of “goodness” to use on this particular occasion.

    (Perhaps the question is shorthand for “how should I make decisions in the future?” — one possible policy being to choose things with good expected outcomes, one being to choose things that actually work out well. Of course the latter would be great but it isn’t actually a policy you have any way of following. Or you could choose things that resemble past ones that had good expected outcomes, or things that resemble past one that had good actual outcomes; which works better will depend on how much data you have, how good your probability estimates actually were, etc.)

  13. I think we often conflate “good decision” and “good outcome” when we probably shouldn’t. It’s perfectly possible for a good decision to result in a bad outcome sometimes, or a bad decision to result in a good outcome sometimes. We have a tendency to go back and redefine the decision based on the actual outcome (eg. “It turned out to be a good decision, because xyz happened…”). I would say a good decision is a decision that aligns the available information about the conditions and expected outcomes with your values the best. If for whatever reason you ignore information or decide against your values, I would call that a bad decision, regardless of whether or not it turned out well.

    If I have to choose between option 1 and 2, and have information A, B, and C, and based on A, B, and C, my values dictate option 1, then picking option 1 is a good decision. If at a later point in time I find out information D, and the set of A, B, C, and D would have resulted in the good decision being option 2, I would posit that that doesn’t retroactively make my decision for option 1 a bad decision. Option 1 was still a good decision given the information I had. I might be willing to call the decision to make a decision before information D was know a bad decision, though. The decision to choose now rather than later is a separate decision from the decision about what I choose.

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