15:40: "On average, we are average, and not excellent, and typically it's even worse. So typically we are sort of mediocre, and I think that's absolutely fine, and I think we should embrace that, and not feel ashamed about that, and actually enjoy it." What an unusual way to wrap up a conclusion to a presentation
8:03: "So in the perspective of emsembles, what happens is that, the mathematics, in taking the average there, overemphasizes these rare exceptions... Over time, actually, everyone will lose... In this game, everyone will lose... but in the aggregate, they win... We are not used to that, this is something that is counter intuitive, and we keep making this mistake when we do statistics, when we think abut random events."
Very good talk , I notice too many have that kind of videogame thinking with life, operating as if they get to replay a level but it ain't like that at all.
One coin-toss: 1.5 vs. .60. Two coin tosses: 2.25 vs. .9 vs. .36. Three coin tosses: 3.38 vs. 1.35 vs. .54 vs. .216. Four coin tosses: 5.06 vs. 2.03 vs. .81 vs. .324 vs. .130 The clear negative trend should be visible. I left out the probabilities of each result. Middle numbers are more likely than the extreme numbers. The negative trend is visible upon flip of two coins: head and tail combine to form a loss. Tails 60%, heads 150% would be more accurate than tails gain 50%, heads lose 40%.
Great talk. I especially enjoyed the closing remarks. We really do, as societies, look down on mediocrity -- while at the same time, the average acheivements of any society will inescapably be mediocre. ...and no matter how obvious that is, I've never even thought of it.
The ruinous outcomes in the coin toss example aren’t from ergodicity or sequence of returns or anything relating to the difference between extending a time series to smooth outcomes vs using a Monte Carlo and generating alternate futures. It’s simpler than that. The coin toss represents a binomial distribution. Hence, the cumulative return for any two consecutive tosses is just the Geometric Mean of the returns of the two possible outcomes (1.5 and 0.6), which comes out to ~0.95. Take 0.95 to a high enough power and of course you’ll run out of money!! That’s not ergodic, that’s just an apparently asymmetric positive arrangement actually being a negative one.
But he's right in applying that model to our economics. If the coin toss was heads: +50%, tails: -50%, you would have an 0.87 mean. It seems everyone loses. But if you sum every player's wealth, including the outliers that get billionaires, you'll see that in the end you still have all the money you started with.
@@user-om7jp2zi4v Oh, no disagreement on the application. I think Ole is a pioneer and ergodic assumptions are a huge issue in classical economics. I was making the narrower point that the expectancy for a binomial distribution is not the arithmetic mean of the two outcomes. Hence, the coin toss, as presented, is not a positive expected value game. Having said that, I absolutely agree that applying lessons of non-ergodicity to our economic models is an important advancement.
@@Gra1te7 That’s the arithmetic mean. To see periodized returns you need to use a geometric mean. A simple example will help. Suppose you have the following five period series of returns: +50%, +50%, -100%, +50%, +50%. What’s the periodized return? The arithmetic mean is +20%. But that’s nonsense - you had a -100% period! You got wiped out. Geometric mean properly accounts for this. In finance you’ll often see it called an “annualized” return or a “Compound Annual Growth Rate” (CAGR). It’s only because people don’t understand this that they suppose the expected value for the coin toss is the arithmetic mean of the binary outcomes. It isn’t. It’s the geometric mean. Now, ergodic assumptions are still a real problem in economics and markets, it’s just that the coin toss problem gives us a poor demonstration of that.
@@sethhersch Thanks Seth, my mistake! 2 years resulting in 0.9 (1.5 x 0.6) gives SQRT(0.9) annualised. Isn't his point though that the few compounding at 150% every year bring the average up - the downside is bounded so the decreases get smaller, but the upside is not - it's just a skewed distribution.
Fascinating look at randomness, as I've been using it to describe our shared reality. I see that each of our personal universes are indeed almost always going to end in loss, as we die. We know this. It's part of life. But average all of our life stories together, and we get an ever increasing balanced, diverse, creative, collaborative ecosystem that evolves over time. Entropy is evolution/life progressing through time by adding more and more options to what it does, and on average, getting more impressive as the Story of Us.
Peters Non-ergodicity is still slightly different from the post-Keynesian non-ergodicity. The growth rate is ergodic is still some sort of assumption and you will never be able to prove that it is truely ergodic in real world both epistemologically and ontologically. However, it provides a new perspective of undertanding ergodicity and its relevance with time.
There's something I don't understand here. The experiment is iid, so in fact the time avg and the ensemble avg should be the same in the limit. What am I missing?
I think it has to do with the direction in which the limit is taken. The ensemble average is the limit taken as the number of trajectories goes to infinity whereas the time average is taken for a single path as time goes to infinity.
This is an interesting exercise to me because you can effectively design games that create more winners, on average, than as you say, many losers and exceptional winners. Reality is near-impossible to model accurately with a game, of course. You can probably still get close enough where it’s applicable.
This is definitely still a bit over my head but I don't understand how this game can have a negative payoff. If heads increases money by 50% and tails decreases by 40% then even if you flipped tails every time it would asymptotically be reduced to zero (40% of a small number is a still smaller positive number).
Just imagine the simplest two distributions, up and down: 100 +50% =150, 150-40%=90 and down and up: 100-40%=60, 60+50%=90. in both cases you have less.
Yes that is one dimension of the argument, but he questions what happens to our decision making once we extrapolate it through time, as much economic data is. Economic data is presented as continuous through time, so all our decisions based on it is inherently time sensitive. Over time, we might find one country's GDP to be increasing due to the effect of a few people as opposed to the average person, and take the country to be doing well. However, we would have missed the chance to address this issue as we are relying on time, and thereby worsening it. Peters is basically saying: there is a problem, and we need to act now or worsen it by not acting at all.
Peters is a very engaging speaker and seems to have admirable intentions in applying his ideas. but his conclusions are invalid. what happens in repetitions of the game by different individuals versus what happens to repetitions for a single individual across time is reasonably well understood. the kelly criterion he references is a very old paper with many updates and well out of date. while i am a fan of dr peters erudition, skip this talk. he simply does not understand the statistical foundations of his conclusions. my own published research in this area may be helpful for those who have interest in the mathematical-statistical issues he raises.
15:40: "On average, we are average, and not excellent, and typically it's even worse. So typically we are sort of mediocre, and I think that's absolutely fine, and I think we should embrace that, and not feel ashamed about that, and actually enjoy it."
What an unusual way to wrap up a conclusion to a presentation
but also an awesome way!
is this the motto of goodenough college?
8:03: "So in the perspective of emsembles, what happens is that, the mathematics, in taking the average there, overemphasizes these rare exceptions... Over time, actually, everyone will lose... In this game, everyone will lose... but in the aggregate, they win... We are not used to that, this is something that is counter intuitive, and we keep making this mistake when we do statistics, when we think abut random events."
The implications of what he is saying really change my perspectives about life.
How?
Very good talk , I notice too many have that kind of videogame thinking with life, operating as if they get to replay a level but it ain't like that at all.
One coin-toss: 1.5 vs. .60.
Two coin tosses: 2.25 vs. .9 vs. .36.
Three coin tosses: 3.38 vs. 1.35 vs. .54 vs. .216.
Four coin tosses: 5.06 vs. 2.03 vs. .81 vs. .324 vs. .130
The clear negative trend should be visible. I left out the probabilities of each result. Middle numbers are more likely than the extreme numbers. The negative trend is visible upon flip of two coins: head and tail combine to form a loss.
Tails 60%, heads 150% would be more accurate than tails gain 50%, heads lose 40%.
Thanks for this comment John. Helped me to understand concept from this lecture. Cheers.
"Chance is a more fundamental conception than causality."~Max Born
Great talk. I especially enjoyed the closing remarks. We really do, as societies, look down on mediocrity -- while at the same time, the average acheivements of any society will inescapably be mediocre.
...and no matter how obvious that is, I've never even thought of it.
The ruinous outcomes in the coin toss example aren’t from ergodicity or sequence of returns or anything relating to the difference between extending a time series to smooth outcomes vs using a Monte Carlo and generating alternate futures. It’s simpler than that. The coin toss represents a binomial distribution. Hence, the cumulative return for any two consecutive tosses is just the Geometric Mean of the returns of the two possible outcomes (1.5 and 0.6), which comes out to ~0.95. Take 0.95 to a high enough power and of course you’ll run out of money!! That’s not ergodic, that’s just an apparently asymmetric positive arrangement actually being a negative one.
But he's right in applying that model to our economics. If the coin toss was heads: +50%, tails: -50%, you would have an 0.87 mean. It seems everyone loses. But if you sum every player's wealth, including the outliers that get billionaires, you'll see that in the end you still have all the money you started with.
@@user-om7jp2zi4v Oh, no disagreement on the application. I think Ole is a pioneer and ergodic assumptions are a huge issue in classical economics. I was making the narrower point that the expectancy for a binomial distribution is not the arithmetic mean of the two outcomes. Hence, the coin toss, as presented, is not a positive expected value game. Having said that, I absolutely agree that applying lessons of non-ergodicity to our economic models is an important advancement.
I don't get this - mean of 1.5 + 0.6 = 2.1/2 = 1.05
@@Gra1te7 That’s the arithmetic mean. To see periodized returns you need to use a geometric mean. A simple example will help. Suppose you have the following five period series of returns: +50%, +50%, -100%, +50%, +50%. What’s the periodized return? The arithmetic mean is +20%. But that’s nonsense - you had a -100% period! You got wiped out. Geometric mean properly accounts for this. In finance you’ll often see it called an “annualized” return or a “Compound Annual Growth Rate” (CAGR).
It’s only because people don’t understand this that they suppose the expected value for the coin toss is the arithmetic mean of the binary outcomes. It isn’t. It’s the geometric mean.
Now, ergodic assumptions are still a real problem in economics and markets, it’s just that the coin toss problem gives us a poor demonstration of that.
@@sethhersch Thanks Seth, my mistake! 2 years resulting in 0.9 (1.5 x 0.6) gives SQRT(0.9) annualised. Isn't his point though that the few compounding at 150% every year bring the average up - the downside is bounded so the decreases get smaller, but the upside is not - it's just a skewed distribution.
Fascinating look at randomness, as I've been using it to describe our shared reality. I see that each of our personal universes are indeed almost always going to end in loss, as we die. We know this. It's part of life. But average all of our life stories together, and we get an ever increasing balanced, diverse, creative, collaborative ecosystem that evolves over time. Entropy is evolution/life progressing through time by adding more and more options to what it does, and on average, getting more impressive as the Story of Us.
Great talk and innovative ideas!
Dr. Peters argument is so important. Probably the reason why financial crises occur.
What does r thaler get wrong here?
Peters Non-ergodicity is still slightly different from the post-Keynesian non-ergodicity. The growth rate is ergodic is still some sort of assumption and you will never be able to prove that it is truely ergodic in real world both epistemologically and ontologically. However, it provides a new perspective of undertanding ergodicity and its relevance with time.
What if I have a strictly fixed time horizon? Then the randomness won't go away.
There's something I don't understand here.
The experiment is iid, so in fact the time avg and the ensemble avg should be the same in the limit. What am I missing?
I think it has to do with the direction in which the limit is taken. The ensemble average is the limit taken as the number of trajectories goes to infinity whereas the time average is taken for a single path as time goes to infinity.
Have you simulated games where over a long stretch of time, the average person wins?
This is an interesting exercise to me because you can effectively design games that create more winners, on average, than as you say, many losers and exceptional winners.
Reality is near-impossible to model accurately with a game, of course. You can probably still get close enough where it’s applicable.
This is definitely still a bit over my head but I don't understand how this game can have a negative payoff. If heads increases money by 50% and tails decreases by 40% then even if you flipped tails every time it would asymptotically be reduced to zero (40% of a small number is a still smaller positive number).
Just imagine the simplest two distributions, up and down: 100 +50% =150, 150-40%=90 and down and up: 100-40%=60, 60+50%=90. in both cases you have less.
1.5x 0.6 = 0.9 ... So there's a 10% fall after evry 1 head and 1 tail ... Eventually it will go to zero !!
@tzuspic20 SPAM post
Isn’t this just median vs mean with inequality showing a positively skewed graph? No need for the time stuff surely
Yes that is one dimension of the argument, but he questions what happens to our decision making once we extrapolate it through time, as much economic data is. Economic data is presented as continuous through time, so all our decisions based on it is inherently time sensitive. Over time, we might find one country's GDP to be increasing due to the effect of a few people as opposed to the average person, and take the country to be doing well. However, we would have missed the chance to address this issue as we are relying on time, and thereby worsening it. Peters is basically saying: there is a problem, and we need to act now or worsen it by not acting at all.
Peters is a very engaging speaker and seems to have admirable intentions in applying his ideas. but his conclusions are invalid. what happens in repetitions of the game by different individuals versus what happens to repetitions for a single individual across time is reasonably well understood. the kelly criterion he references is a very old paper with many updates and well out of date. while i am a fan of dr peters erudition, skip this talk. he simply does not understand the statistical foundations of his conclusions. my own published research in this area may be helpful for those who have interest in the mathematical-statistical issues he raises.
Can you please share your research? Thanks.
Hello! Have you tried the British Box Breakout (do a search on google)? Ive heard some great things about it and my work buddy got tons of pips.