#time preference

This is an opinion editorial by Heliand, a Bitcoiner with a background in real estate and finance. In the realm of digital currencies, Bitcoin has emerged as a groundbreaking phenomenon, revolutionizing not only the financial landscape but also the way we perceive and interact with money. However, beyond its potential for economic empowerment, Bitcoin holds a deeper significance that transcends…

[Disclaimer for those unfamiliar with the topic: the “gambling” here is mostly a metaphor for other things, not literal gambling on coin flips. Describing it as gambling is just a simplified picture in order to make it easier to reason about the ideas involved. If you were to apply any of the stuff I’m talking about here at an actual casino, the answer it would give you would be “bet zero dollars” or “bet a negative number of dollars” (i.e. “be the casino and take the other side of the bet”). This whole topic is more applicable to prediction markets, not so much to casinos. ]

So, with the Kelly Criterion (the thing that says, if you are repeatedly betting on events, where you know the chance of the event happening, and also the ratio of what you get back in addition to what you risked if you win, what fraction of your current betting-money to bet each round, in order to maximize your long-run winnings)

so, the derivations for it that I’ve seen, seem to be based on the situation where each bet resolves before the time when you make the next bet.

But, what happens if they don’t?

What if there is a coin which has a result of heads with probability q each time it is flipped, and each round, you are given the option to bet on, not the result of the next flip, but the 5th flip after now, where your bet will pay out (or fail to pay out) when it is flipped. (when you win one of the tosses, you win (c+1)*x where x is the amount of money you spent to make the bet. So, you win back the x, and then c*x in addition to that.)

In such a situation, is the Kelly bet (bet (p - (1-p)/c) of your current money) really the thing that produces the fastest long-term growth?

I think probably not, because it doesn’t take into account the money that you might win between when you make the bet and when you will receive the money for it.

I think the correct amount to bet (assuming the goal of maximizing long-term growth) is a little bit more than that, with the precise amount depending on how much you have put into bets which haven’t resolved yet, but which will resolve before the bet you are currently making does. Or, more generally, depends on the probability distribution of how much money you will win (or otherwise receive) before the bet you are making is resolved.

If you know with certainty that before the bet resolves, that you will receive x, and your current wealth is w, and your utility is log(your wealth at the time that the bet resolves), then, effectively by taking into account the x that you will receive as part of your current wealth, the optimum bet would be (1 + (x/w)) multiplied by the Kelly bet.

I’ve thought a bit about how to handle the case where there is a probability distribution over different amounts you might receive before the new bet resolves, but I haven’t managed to work it all out yet.

I think the answer to this question should say something interesting about time preference.

Namely, if you are trying to make your long-term trajectory grow as quickly as possible over time (rather than over “number of rounds”), how does scaling the amount of time until you the bets are resolved, compare to scaling both [how often you can make a bet, and how long until bets resolve] together ?

The “maximize long-term trajectory” thing seems like it does a good job of motivating log-utility in wealth, but I think when adding in these considerations, the same goal should motivate something about time preference as well.

What is Time Preference?

Saifedean Ammous shared his chapter on time preference: https://twitter.com/saifedean/status/1441724730705420288?s=20 Time Preference, Chapter 13 of my forthcoming textbook, Principles of Economics, is now available for members of http://saifedean.com This is my most detailed discussion of time preference yet. Or you can watch this video if you don’t have the required patience yet:

Text from The Bitcoin Standard, written by Dr.Saifedean Ammous:

“Time preference refers to the ratio at which individuals value the present compared to the future. Because humans do not live eternally, death could come to us at any point in time, making the future uncertain. Time preference is positive for all humans (the present is always more valuable than the future).

Animals’ time preference is far higher than humans’, as they act to the satisfaction of their immediate instinctive impulses and have little conception of the future. Human beings’ lower time preference allows us to curb our instinctive and animalistic impulses, think of what is better for our future, and act rationally rather than impulsively. Whereas animals and humans can both hunt, humans differentiated themselves from animals by spending time developing tools for hunting. Only through a lower time preference can a human decide to take time away from hunting and dedicate that time to building a spear or fishing rod that cannot be eaten itself but can allow him to hunt more proficiently.

As humans reduce their time preference, they develop the scope for carrying out tasks over longer time horizons, and they develop the mental capacity to create goods not for immediate consumption but to produce future goods – capital goods.”

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