The basic arithmetic in this paper isn't even sound. The coin toss example obviously guarantees that even if heads and tails are of exactly equal probability you would lose wealth over time.
Wealth(c) = current wealth
Heads: Wealth(c+1) = 1.5 Wealth(c)
Tails: Wealth(c+1) = 0.6 Wealth(c)
if you win once and lose once you end up with 0.9 (10% less) wealth. Over time, assuming equal numbers of heads and tails your wealth tends to zero. Only an idiot would take this gamble, even without any fee to play.
Garbage.
ONE SOUL AT A TIME
Originally Posted by DannoOriginally Posted by resolve
The paper itself misues the example. It creates a strawman 'expected outcome' to try and make it's bloviated explaination of the true outcome it monte-carlos seem erudite. The expected outcome they give is obviously nonsense to anybody with GCSE/Highschool level algebra. The blue line in the graph is simply wrong. The expected outcome of this gamble after 1000 rounds is 0.9^500 * the starting wealth (i.e. you lose almost all of your wealth). The blue line should go down on the log scale, not up. This renders all their waffle about ergodicity a moot point.
The reason why economics cannot predict things with such precision is simply that it deals with systems much too complex and chaotic to perform controlled experiments on, or to know all the initial conditions of.
Last edited by Cullion; 5th December 19 at 05:33 PM.
ONE SOUL AT A TIME
Originally Posted by DannoOriginally Posted by resolve
Thats sentence doesnt even make sense.
The blue line isnt on a log scale & the derivatve of it is in fact going down.The expected outcome they give is obviously nonsense to anybody with GCSE/Highschool level algebra. The blue line in the graph is simply wrong. The expected outcome of this gamble after 1000 rounds is 0.9^500 * the starting wealth (i.e. you lose almost all of your wealth). The blue line should go down on the log scale, not up.
Which is why the ergodic hypothesis has never worked out in economic models.The reason why economics cannot predict things with such precision is simply that it deals with systems much too complex and chaotic to perform controlled experiments on, or to know all the initial conditions of.
"Thats sentence doesnt even make sense."
It's perfectly simple. They set up a false expectation to make their prediction seem surprising and interesting when it isn't.
"The blue line isnt on a log scale & the derivatve of it is in fact going down."
The absolute value should go down on a log scale because it should be a graph of 0.9^(x/2)
Last edited by Cullion; 6th December 19 at 10:15 AM.
ONE SOUL AT A TIME
Originally Posted by DannoOriginally Posted by resolve
Oh dear go back & read the paper properly. Its a graph of u(x) = ln x & nowhere is it said that it was graphed on a 'log scale' because that would make the blue line straight.
WTF are they teaching you?
Your last post is completely irrelevant to my point. Their line of expected values is incorrect.
Here's the graph. It's using logarithmic y axis.
The expectation values are wrong. We *wouldn't* expect the wealth of a player to increase over time, just with simple secondary school algebra. No monte carlo simulation is required to tell that is an incorrect expectation. See above.The example gamble is given in equation (2). The expectation value, 〈x〉, (blue line) is the average over an infinite ensemble, but it doesn’t reflect what happens over time
We would expect the blue line to be a plot of 0.9^(number of rounds/2), which would have a negative slope plotted on this graph, or approach zero plotted on linear axes.
Last edited by Cullion; 6th December 19 at 12:51 PM.
ONE SOUL AT A TIME
Originally Posted by DannoOriginally Posted by resolve