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Comment by juskrey | Hacker News Reader

Many words about how economics is like physics, hence Peters makes a terrible insults to generations of respectful academics. And not a single word about how they are still missing the ruin problem, and how ergodicity is a dead simple and exact answer to it

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Economics is not like physics at all. It's a social science, rooted in many social assumptions and compromises and power relationships between human beings and groups. Most attempts to negate this are just tortuous ways to justify the current power structure.

There is a small nugget that is as hard as physics. Namely the tools can be analyzed in their theoretical performance.

But economics is deeply tied to politics. What type of economy you have is entirely dependent on current leadership. It's the government that sets the basic foundation and rules upon which the economy is built. Some governments decided to go to either extreme. Communism or capitalism. There is a price equilibrium, assuming one is allowed to exist, which is dependent on your government, but where exactly it lies is also entirely dependent on the laws the government set.

If the government bans garbage disposal in rivers then it would be completely unreasonable to insist that the equilibrium price should stay the same.

By this same logic if there is an inherent injustice or imbalance it exists in the laws the government created.

One prominent example would be the central bank flooding the market in a way that benefits existing asset holders, one could have done the exact opposite as well or maybe even done a little of both. It's not a question of which is the right action, the question is "What kind of economy do you want?" and the central bank has spoken.

Precisely. "What kind of economy do you want?" is a political question, that has no definite, scientific answer. And more restrictive economic questions, very often, also are political questions that should be democratically debated and decided, but are instead presented as "scientific" in nature, with the pretension that "we should do as our experts said" (whose experts exactly?).

The main article doesn't seem to refer to "the ruin problem" either. What is that?

Ole should repeat it on more occasions, since this is what it's all about: economic unit is not an average of the same imaginary economic units following different paths, some of which can end in a bankruptcy. Instead single bankruptcy will end the whole process, this is a ruin problem. That is economic unit is an average on its own timeline, not space.

  #!/usr/bin/python3
  import random
  #100 people start with $100
  balances=[100]*100
  #They take 10000 bets with an _expected_ return of 1.25x.
  # ... so they should end up with ~1.2e1000 at the end...
  for i in range(10000):
    balances=[0 if x<=0 else random.choice([x*2,x//2]) for x in balances]
  #Yet all or almost all are bankrupt:
  print(len([x for x in balances if x<=0]))

> # ... so they should end up with ~1.2e1000 at the end...

Who has ever claimed this? Also, people end up with zero because you are doing integer division in your code (ie the simplified expected return is wrong). Here are my results with 100 bets, and 10000 bet takers. The average return is also on the upward trend, but not really close since CLT doesn't really apply to this distribution:

    >>> sum(balances)/1000000
    24546192.840913434
    >>> print(len([x for x in balances if x<=100]))
    5426
    >>> print(len([x for x in balances if x>=100]))
    5381
    >>> print(len([x for x in balances if x>100]))
    4574

Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers.

You can show ruin without any flooring division:

  #!/usr/bin/sage
  import random
  balances=[Rational(100)]*100
  for i in range(10000):
    balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances]
  #Yet all or almost all are bankrupt:
  print(len([x for x in balances if x<=0]))

The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it.

One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing.

And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.

But that's factored in EUT anyway: you simplify the compound lottery and it turns out you have a huge probability of hitting zero. You might ask whether people will take the bet, and that's where the utility comes in. Enough risk averseness, and noone will take a return of a million dollars with a 1% chance of happening at a price of 100%

This article linked above covers it well, highly recommended: https://taylorpearson.me/ergodicity/

In a pithy form, it's the fact that in the long run we are all dead.

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