Just to remind you there are some anomalies and temporal discounting behavior. The first is preference reversals, flips and preference from one reward to another as time passes.

Preference reversals

Imagine two hypothetical decision-makers Elizabeth and Henry each of whom is about average in terms of their overall patience, they differ however and how they think about time. To Elizabeth the value of money decreases with a constant proportion over time hundred dollars now might keep 90% of its value over one month 90% of what’s left over over the second month 90% what’s left over the third month and so forth.

The first month is no different than the fourth month time is time is time. Elizabeth’s temporal discounting function for $100 would look like a smooth curve that starts high and then loses 10% of its current value each month. The mathematical term for such a curve is an exponential function. Henry approaches money differently. To him the present matters much more than the future.

So $100 now might only be worth about $75 after one month delay and only $60 after two months. But future times don’t matter as much to Henry, he doesn’t really care much about the difference between 11 months or 12 months or between 12 months and 13 months. Henry’s temporal discounting function for $100 would decline much more sharply than Elizabeth at first but then would flatten out thereafter.

The mathematical term for this curve is a hyperbolic function and there’s been an impressive amount of research trying to fit these and other curves to people’s temporal discount functions. While some details remain unsettled there is a consensus that temporal discounting should follow an exponential function but that it does follow a hyperbolic function in most settings.

To illustrate this consensus let’s consider the following choice which would you prefer $100 now or $105 dollars a week from now? Many people find this a pretty easy choice. They’d rather have the smaller but sooner $100. Now let’s change the dates. Which you prefer? $100 and 52 weeks, $105 and 53 weeks? This seems like a very easy choice to almost everyone they’d rather have the larger later $105.

These two situations only differ because of the passage of time, the second scenario just happens one year later than the first but people choose differently in the two situations, choosing the smaller sooner reward when it is near but the larger later reward when it is distant. Think about what that implies about people’s preferences.

Someone who prefers $105 in 53 weeks would have to wait and wait and wait for the reward to be delivered, then after a year had passed they would then be in exactly the situation of the first question and they now prefer to get the hundred dollars now instead of waiting another week. Their preferences would reverse just because the passage of time.

Intertemporal choices

Preference reversals like this imply that people discount rewards faster when they are near in time. Thus they aren’t consistent with the constant discounting of the next financial function but they are consistent with the rapid short-term discounting of a hyperbolic function. So we might want to be rational like Elizabeth but were really impulsive like Henry.

A second anomaly in intertemporal choices out of sequence effects. By itself temporal discounting applies and we should want to receive good outcomes as soon as possible. When they are most valuable to us and often that is true we’d rather have money now instead of later. We indulge with a slice of cake now even though will need to exercise more later. But there are specific situations in which we’d instead prefer to wait for a good outcome.

Suppose you’ve won gift certificates for dinners at three local restaurants you’re familiar with all three one is basically a no-frills English pub, it’s inexpensive has good food and drink but is more like comfort food than a fancy meal the second is a fanciest Italian restaurant in town a real splurge in all regards and the third is a casual French bistro it’s intermediate in price and quality clearly better than the pub but clearly worse than the fancy Italian restaurant.

Over the next three weekends you can dine at those three restaurants in any order you choose. Which do you pick for your first weekend, for your second and for your third? There’s obviously no right answer here and people may have personal reasons for picking these in any order, but people do show a strong general tendency for an ascending sequence of quality.