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The infamous coin toss

ergodicityeconomics.com

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Re: The infamous coin toss

#161

Post by LeonB »

Swenrekcah wrote: post #145
LeonB wrote: post #140

Earlier quoted context omitted.

You asked two questions. Sorry if I answered the wrong one. I think when the person above suggested eating the rich you literally believed them and you’ve been on a misguided tear ever since. There’s little I can do to help you, but by god I’m glad I tried. Best wishes.

This isn’t an adverserial exchange my friend. I’m sorry if I got on your nerve with the “worldly and educated” jab, but you were (and have continued to be) quite condescending in your responses. Have a nice day :)

Um ok.

Backing up a little and answering your next question.

The naivety is that you say “I know vat is regressive but if it’s a low amount…”

Ok.

First thought I had here was:

What a middle class person considers a low amount of tax on a necessity is not the same as what a poor person considers a low amount of tax on a necessity.

At that point - just pondering that, which is only a preliminary consideration, I think - this person, I like them and I care for them but they are a bit naive. I’m not “adversarial” I’m just a bit sorry, thinking, this dude can’t see past their privilege. Fair enough. I make the same mistake multiple times per day. Genuinely.

But then I consider just how extraordinary the gap is, not between low and middle class people but between low+middle class people and “wealthy” people. Low and middle have very different opinions on the impact of 10c on a loaf of bread. But those opinions are utterly insignificant compared to the value a wealthy person places on that same 10c. Logarithmic difference.

There’s so much more to it -/ but yes just saying “vat is regressive but…” is to me a betrayal of a kind of (on the one hand) admirable level of optimism (I genuinely appreciate that) but also a naive/blinkered/privileged eye rolling “here we go again” level of ignorance that is Just. So. Exhausting.

Again - if all things were equal, if people were all starting from the same starting point - then we could “genuinely” engage in simplistic first principles discussions that treat all market participant as frictionless spheres in a vacuum etc — but we’re very far past that point… 10,000 plus years of civilisation beyond that.

Thank you for reading this far. Best wishes.

Re: The infamous coin toss

#162

Post by twobitshifter »

ano-ther wrote: post #143
rerdavies wrote: post #64

Huh. So I wrote the code, and ran the simulation. Now I get it. Investors: 100,000 Iterations: 100 Average worth after 100 iterations: $83.923 Average net worth increases. However the distribution of wealth is skewed dramatically. Winners: 13,704 (net worth of more than $1 at the end) Investors worth What That Guy was worth (the investor who made the most money): $1,171,830.00 He flipped 71 heads and 29 tails. Median…

> Average wealth increases; but average log(wealth) decreases What’s the mathematical rationale (or intuition) for looking at the log values? I don’t quite understand what they represent.

Log is useful for repeated trials, since it’s a way of looking at exponential growth. If you write out the formula for a repeated trial, you’ll get an exponential function. Log tells you the value of the exponent a in e^at.

Re: The infamous coin toss

#163

Post by bzax »

jakell wrote: post #33
bzax wrote: post #27

Earlier quoted context omitted.

I believe the entire point of the ergodicity question here is "If you apply this process n times, with n approaching infinity, obviously the result may depend on what point in the n-times iterated distribution you sample, but if you choose a volume of vanishingly small measure to exclude, can you make a single concrete statement about what the process is doing without taking an expected value over the different outco…

Great description of a framing I hadn’t considered before, thanks!

I should admit I'm being very generous to Peters here - I came to the conclusion that this is what he means only because the math of ergodicity (https://en.wikipedia.org/wiki/Ergodic_theory#Ergodic_theorem...) talks a lot about "except on a set of measure zero". He provides no explanation of how he moves from "the time average of values in a particular run of the process" (which is ergodicity) to "what does a typical process round do, with probability 1" (which is perhaps what someone computing a utility function cares about).

I asked a friend who is an econ professor "Why does this Peters guy explain this so poorly" and his response was more or less, yes, all of economics has been wondering that too since he first published his Nature Physics paper on this a decade ago.

Re: The infamous coin toss

#164

Post by LeonB »

robertlagrant wrote: post #146
LeonB wrote: post #144

Earlier quoted context omitted.

You’ve presented two options and there are many more than two. I don’t have to list them to point at that at face value it is obvious that the two options you listed are not the only options. Can you genuinely imagine no other options? Really? I am giving a true dichotomy here, either: 1. You believe there are precisely two options 2. You do not believe there are precisely two options. Which is it?

You don't have to list them to say that it's a not dichotomy, but you do if you want to demonstrate it's not a dichotomy. I don't know why you're spending 100s of words on the theory of dichotomy, instead of just providing a third option to show how it's not one. E.g. this could have gone: LeonB: what about businesses owned by many people? robertlagrant: ah, yes - what I was saying would put them in the "private owne…

Is that 1 or 2?

Re: The infamous coin toss

#165

Post by twobitshifter »

rerdavies wrote: post #64

Huh. So I wrote the code, and ran the simulation. Now I get it. Investors: 100,000 Iterations: 100 Average worth after 100 iterations: $83.923 Average net worth increases. However the distribution of wealth is skewed dramatically. Winners: 13,704 (net worth of more than $1 at the end) Investors worth What That Guy was worth (the investor who made the most money): $1,171,830.00 He flipped 71 heads and 29 tails. Median…

My somewhat controversial opinion is even if success were based on merit, this is still random chance since merit depends on one being born with ability in a supporting environment. Meritocracy can be social Darwinism.

Re: The infamous coin toss

#166

Post by amelius »

AdamN wrote: post #86
drekipus wrote: post #76

Earlier quoted context omitted.

> increasing wealth concentration is an unavoidable consequence of capitalism My bad I thought you made a coin flip simulation, not a capitalism simulation. At what point do we stop wagging the finger at the ghost of capitalism and just say it's mathematics? You don't hear people crying for the upheaval of mathematics

People do say that. Usually the critique of (perfect) capitalism is that it (structurally and mathematically) skews towards increasing wealth for winners at the expense of the rest of the population and that this is inevitable. Then the response of advocates against this situation is to either commit to more structures to prevent that outcome towards diluted (non-perfect) capitalism or other social forms (socialism,…

> skews towards increasing wealth for winners at the expense of the rest of the population

The usual response against that is: what is wrong with being a winner? I did something right, let me have my well-deserved money.

The problem with someone getting well-deserved money is that the money starts working against everybody else, so essentially this money gives everybody else negative money.

Re: The infamous coin toss

#167

Post by robertlagrant »

LeonB wrote: post #164
robertlagrant wrote: post #146

Earlier quoted context omitted.

You don't have to list them to say that it's a not dichotomy, but you do if you want to demonstrate it's not a dichotomy. I don't know why you're spending 100s of words on the theory of dichotomy, instead of just providing a third option to show how it's not one. E.g. this could have gone: LeonB: what about businesses owned by many people? robertlagrant: ah, yes - what I was saying would put them in the "private owne…

Is that 1 or 2?

I don't know about options, but I was describing two main buckets you could classify things in, so...1ish?

The irony of you determinedly pinning me down, when I'm happy to converse, while you will do anything but answer what I was asking, is hopefully not lost on you.

Re: The infamous coin toss

#168

Post by cubefox »

n2d4 wrote: post #67
DarkNova6 wrote: post #63

Earlier quoted context omitted.

Confusing the equivalence of -50% and +50% is very common. In fact, many video games provide wrong bonuses based on this misunderstanding (Age of Empires 2 being a famous example). Even a simple calculation will show the truth: -40% = 0.6 +50% = 1.5 0.6 * 1.5 = 0.9 Conclusion: With every coin-toss you lose 10% of wealth on average.

While I agree, that conclusion is wrong because you forgot to look at the win-win and loss-loss cases. Even with two coin tosses, as in your example, you'll win on average: 1.5 * 1.5 = 2.25 0.6 * 1.5 = 0.9 1.5 * 0.6 = 0.9 0.6 * 0.6 = 0.36 => 1.1025x total It's counter-intuitive because even though you almost always lose, you still win (linear) wealth on average (but not median). The difference is that if you have unl…

You should maximize the geometric EV, not the (usual) arithmetic EV. In your average calculation you took the arithmetic mean, but the geometric mean is relevant.

(2.25 * 0.9 * 0.9 * 0.36)^(1/4)

=0.9

Which is below 1!

To test the geometric mean with the earlier example ("+100% is equivalent to -50%"):

(2.0 * 0.5)^(1/2)

=1, as expected.

Re: The infamous coin toss

#169

Post by cubefox »

n2d4 wrote: post #155
svnt wrote: post #119

Earlier quoted context omitted.

They are saying parent is correct that plus 50% and minus 50%, while appearing to be balanced, is a losing proposition for the individual. They are also saying parent is not correct in saying that it also loses on a population basis, showing that the average across a population is still winning.

Yes, that's what I meant. You probably don't want to take unnecessary risk by going +50%/-50% markets, but it's not for the reason the parent mentioned in the conclusion.

No the parent was right, I commented.

Re: The infamous coin toss

#170

Post by jncfhnb »

robertlagrant wrote: post #100
LeonB wrote: post #95

Earlier quoted context omitted.

Imagine if — on top of that - we let the undeserving rich invest their wealth in things such as: - owning media - lobbying the government - owning the means of production It could take that dire situation and make it drastically worse. I mean, in theory.

> owning media Who should own media? Private people, or the state? > lobbying the government If lobbying the government is effective, it's either because the lobbying was correcting a wrong, or the government is allowing itself to be corrupted. > owning the means of production The "means of production" was barely relevant when Marx found out what a factory was from his factory-owning mate. A plumber owns "the means o…

> The "means of production" was barely relevant when Marx found out what a factory was from his factory-owning mate. A plumber owns "the means of production" when he owns his own tools. It's far too low resolution a phrase to be useful, except for anyone who finds it useful to teach people to hate another group of people.

A plumber owns a fraction of the means of production so small it’s not worth mentioning. How much of the means of production is owned by megacorps? A sizeable amount.

How much of the means of production is owned by singular entities in the context of local economies? Sometimes over 90%.

At the end of the day if some guy owns a fabulous machine and will pay you a non living wage to press a button on it while he reaps the rewards you will grow resentful. Especially if the shittier prior machine required more skilled interactions and higher wages.

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