## Non-ergodicity and the arrow of time (wonkish)

30 Dec, 2013 at 22:57 | Posted in Statistics & Econometrics | 10 Comments

One of my favourite science videos from 2013 is Ole Peters presentation at Gresham College, showing why time irreversibility and non-ergodicity are such extremely important issues for understanding the deep fundamental flaws of mainstream neoclassical economics.

1. Coincidence, I posted this video the other day on my Facebook page with the same comment that you have now!

• Happy coincidence indeed — but at the same time reassuring to know that one isn’t alone in appreciation!
Happy New Year ðŸ™‚

2. Happy New Year and a little limerick by which to demonstrate your New Year’s bona fide to others

My New Year resolution is resolute
I will be kinder, gentler and more astute
I will listen to others without malice
Imbibing from them as from a golden chalice

3. Happy New Year and thanks for the inteersting blogs.

Happy New Year and thanks for the interesting blogs.

IMHO the talk starts with a straw man argument, i.e. it creates an artificial image to attack. The 50% gain as compared to a 40% loss is designed to get the intended result to set up the strawman. However, this is not an ensemble versus time perspective issue but a good old risk of ruin problem. Nobody in the right state of mind would risk 40% to gain 50% with a 50% success rate unless he has gone mad, I mean really mad. This is just ludicrous because the risk of ruin equation for coin toss which is well known gives us the necessary fraction of capital to risk for a given success rate in order to reach a wealth target before getting ruined. Thus, there is a closed form solution of this problem that avoids ruin.

In other words, if one risks a small fraction of the capital, for example 0.5%, to gain a multiple of that, let us say about 1.5% when there is a win, then there is enough time (actually it is not time but trials and the use of time here is peculiar because a computer can play this game instantly for all practical purposes) for the success rate of the coin toss to converge to 0.5 and then the positive expectation kicks in to accumulate wealth. Obviously, if the payoff ratio is only 1.25 (50%/40%) the probability of ruin is extremely high and this is more of an issue of playing the wrong game rather than an issue of expectation versus time perspective.

Therefore, anyone who is familiar with probability may elect to stop watching the video after about the 9 minute mark. One just cannot invent anything new out of old risk of ruin theory that Bernoulli himself, or even Kolmogorov did not know.

4. I would like to just add the result from risk of ruin analysis for the probability of reaching a target N of wealth before getting ruined for the trivial case of a fair coin toss (p = 0.5) and a payoff ratio of 1 (+1 gain, -1 loss) is just P = h/N, where h is the starting capital. The probability goes to zero as N gets very large naturally and thus the probability of ruin goes to 1. This is a known result that can be extended to a payout ratio greater than 1.

The above has nothing to do with positive expectation and this has been known for ages. Positive expectation applies only at the limit of large numbers and depending on starting capital and wealth target one can get ruined. The math can be found here: http://www.mathpages.com/home/kmath084/kmath084.htm

5. Thanks! Very interesting! Happy New Year!

6. So, based on Digi’s view, everybody in the audience at Gershom knew nothing about probability and continued to listen beyond nine minutes. What’s the probability of that? (he, he)

• P = 1, i.e.the certain event except in a set of measure 0, if you judge from the number of people that gather in thousands to hear politicians speak during elections, for example. It is called herd behavior. a form of cognitive bias. It is clear that the speaker sets up a strawman from start to then attack. Expectation makes sense only at the limit of large numbers. Nobody makes any bets based on expectation alone unless he has gone mad.

7. […] Empezamos el aÃ±o con una conferencia sobre el concepto de ergodicidad y su aplicaciÃ³n para el estudio de la evoluciÃ³n dinÃ¡mica de un sistema (ya sea una rentabilidad basada en un proceso probabilÃ­stico) o para aplicaciones mÃ¡s diversas. Es de 2012, pero lo vi el otro dÃ­a gracias al blog de Lars P. Syll. […]

• I only watched the first 9 minutes, but it did seem underwhelming. It is true that the expected money return is +5%, but rationality is conventionally taken to mean maximizing utility, for which log(money) is the usual proxy. In this case, this yields a negative expected utility. Thus the apparent difficult is dissolved by using the appropriate scale. The issues about time and ergodicity are very important, but I do not see how they come in to this example. (Maybe I should watch on?)

A common observation is that most businesses fail and so investors ought to expect their investments to fail. Yet (supposedly) the economy grows. Hence we ought to encourage businesses by protecting them from the worst consequences of failure.This common idea seems to be in line with the message of the talk, so I don’t see that it is at all novel. Unless we have forgotten what utility is?

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