When is someone irrational?

I like reading books about mistakes people commonly make:  logical fallacies, bad mental shortcuts, tricks that advertisers use, and so forth.  It is obvious that our minds are not perfectly logical, and I like to be aware of my illogical inclinations so I can prepare for them.  Economists, psychologists, and mathematicians are among the people who write books on this sort of thing.

The economic angle gets a lot of attention these days because of the work of Daniel Kahneman, Nobel-prize winning economist who studied ways that people behave irrationally, allegedly contrary to economic principles.  I say "allegedly" because I believe that consumers are not expected to behave rationally according to an absolute standard of maximizing utility, because consumers define utility by their choices.  If I buy a cheap product that falls apart in a year rather than a somewhat more expensive product that will last for ten years, it may appear irrational to a neutral observer, but this is (in my opinion) not the case.

I don't want to dwell on this point, but I do want to bring up a particular example from the book I am currently reading, You Are Not So Smart by David McRaney.  He says that most people will prefer $50 today to $100 in a year, but will prefer $100 in six years to $50 in five years.  Allegedly this is an example of irrationality, since the cases are exactly the same.  They are, of course, not exactly the same, but I want to elaborate on why waiting may not be preferable.  Two of the reasons are explainable by economics, and one of them relates to the fundamental problem of addressing rationality among consumers.

The first reason for preferring a relatively small amount of money now to a larger amount in the future is the simple time value of money:  everyone prefers something today to the same thing in the future.  This is a well-known feature of preferences and requires little elaboration.  Moreover, the difference between today and a year from now is significantly greater in time preference that the difference between 5 and 6 years from now.

The second reason for preferring something now rather than later is the uncertainty factor.  Uncertainty is partly factored into time preference, but I am creating a separate group for it because it is highly dependent on circumstances and may not be immediately obvious in an abstract question about time preferences.  I don't have the book text in front of me to quote (it is an audio book), but basically the author phrases the situation as, "If I offer you $50 now or $100 in a year, which would you take?"  This is fine in principle, but it conceals the big question of who "I" and "you" are and what are the conditions of the offer.  If someone walks up to you in the street and presents this offer to you, you would rightly be sceptical whether you would ever see the $100 if you chose that option.  Who is this person, and is he really going to take the trouble to track you down in a year and give you the money?  (I'm leaving aside the serious problem that a person cannot be held legally responsible for failure to give a gift, so there is nothing binding in the promise anyway.)  You may, in fact, be sceptical why he wants to give you $50, and wonder if this isn't the beginning of some scam.  Assuming you could get over that concern, you would certainly have a lot more confidence in the $50 bill that he is dangling before you than in his promise that he will give you two such bills in a year if you can wait that long.  In the case of $50 in five years or $100 in six, both involve a promise of future delivery and therefore the fact that one is a year after the other is a much smaller concern.  Taking the $50 in five years reduces your uncertainty vis-a-vis the $100 option much less than having money in hand right now over waiting a year.

The third question is beyond economics to some extent, although it relates to Austrian economics and the subjectivity of value.  Let me change the scenario for a moment to the Stanford marshmallow experiment, which is similar in structure but easier to discuss in psychological terms.  Basically, a research study tested whether children could refrain from eating a small snack (such as a marshmallow) for 15 minutes with the promise of a second snack if they held out.  The children who were able to wait ended up having much more successful lives by most measures:  higher intelligence, lower body fat, and other things.

The implication, of course, is that the ability to exercise self-restraint is valuable in life; and, more directly, that any rational person would prefer two snacks in 15 minutes than one snack right away.  (The similarity to the money question should be clear.)  What I would like to emphasize is that waiting is as much a personal preference in economic terms as the child's choice of a marshmallow, cookie, or pretzel as the snack he was to receive.  Think of a puppy vs. an old dog.  The puppy is excited about everything, wagging his tail at every experience, but also becomes despondent the moment he is left alone.  The old dog does not get very excited about anything anymore; he likes his walk, but it's the same walk he has been taking for 10 years, so it is not a thrill.  On the other hand, being left alone is also not a disaster; he has been alone before and he is confident that this one, like the others, will end relatively soon.  He accepts his fate.

If we were to graph their emotional states, the two dogs might look like this:
graph of 3*sin(t), showing same x-intercepts, but three times the height
Puppy

graph of sine wave, from -2pi to +4pi
Dog

(These are obviously sine graphs from a math site; the point is the shape of the curves rather than the numbers.)

In other words, the puppy experiences higher highs and lower lows.  Humans have a similar pattern between children and adults; part of maturing is often considered to be avoiding emotional extremes.  However, differences of a similar sort appear between different humans of the same age, some of which is certainly biological in origin.

Who is to say which is better?  Humans seem to strive to moderate emotions, but we are also drawn to people with strong feelings.  And though the graphs show a perfect symmetry around the x-axis, there is no reason to believe that people necessarily have emotions that behave that way.  Likely some people have emotions that rarely, if ever, become positive, and other people are happy more often than not.

A person with a "steeper" emotional curve will have more trouble resisting the temptation to eat the snack, simply because it will give him more pleasure than it would to someone with a shallower emotional curve.  And since we all know from economics that any good has a decreasing marginal value, maybe he is right to eat the snack.  Perhaps having a second snack will add very little to his pleasure.  Perhaps the person with a shallow emotional curve is also right to wait:  not because the second snack is that much more valuable, but because the first one simply doesn't bring so much pleasure that it is worth it to consume it right away and forgo the second one in 15 minutes.

There is no way to choose objectively which emotional pattern is better.  People likely have little choice in any case, so it wouldn't make sense to say that people whose emotions stay closer to the x-axis are more "rational" than those who vary widely.  Being patient (not eating the snack) could be the result of better calculation and self-restraint, but it could also be the result of anhedonia.  The fact that people who exercise patience are more capable of studying and refraining from overeating in the future could signal great strength of will, or it could just be that they get less pleasure from life and therefore have an easier time doing the difficult things (like studying and eating healthier but less enjoyable food).


Whatever a person chooses -- eat the marshmallow or wait for a second one; take the $50 or wait for $100 -- has to be considered rational from his point of view.  There is no objective way to decide that one is more correct than the other.  Demand curves consist of aggregations of these sorts of choices.  The only thing the consumer has to do to be rational is to prefer paying less for the same product under the same circumstances.

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