When random people give money to random other people (2017)
quomodocumque.wordpress.com
quomodocumque.wordpress.com
And a blog post here: https://www.decisionsciencenews.com/?p=6221
- I don't see why it's important to this person that N people start with a total of N^2 dollars. It would seem more natural to have N people and M dollars.
- The piece says this:
> in the long run every possible state is equally likely; we are just as likely to see $9,901 in one person’s hands and everybody else with $1 as we are to see exact equidistribution again.
As stated, this is quite wrong. We're 100 times more likely to see $9,901 in one person's hands and everybody else with $1 than we are to see everybody with $100, because there are 100 different people who might have $9,901 to satisfy that description of the state. It isn't really clear whether the author understands this or not.
The problem states that everyone shares dollar on the clock tick - that means the node of the game graph has out-degree of smth like 99^100, not 100? (or maybe ~comb(199,100) with bizarre distribution if you dislike multi-edges)
And the whole idea of "undirected graphs have easy stationary distribution, so our almost-stationary one has almost-that" isn't grounded in anything but a hunch... (and having >30% of "bad" nodes doesn't seem all that much "almost" to me)
Some of the conclusions might be similar since random processes often have a certain regularity where exact details don't matter.
But basically every formula in the article is completely incorrect.
1. The specific people that are currently rich will become richer.
2. The people that are rich at any given instant in the future will be richer than the people that are rich at the current instant.
"The rich are getting richer" almost always means #2, but it depends on the context. #1 may be more interesting to individuals competing for wealth, or for an assessment of individual mobility, but #2 is much more relevant when describing the aggregate conditions of a society. For example, the Gini Coefficient depends on #2, not #1.
I don't think it's a stretch to say it's dishonest to presume the first meaning.
> 1. The specific people that are currently rich will become richer.
> 2. The people that are rich at any given instant in the future will be richer than the people that are rich at the current instant.
> "The rich are getting richer" almost always means #2, but it depends on the context. #1 may be more interesting to individuals competing for wealth, or for an assessment of individual mobility, but #2 is much more relevant when describing the aggregate conditions of a society. For example, the Gini Coefficient depends on #2, not #1.
> I don't think it's a stretch to say it's dishonest to presume the first meaning.
When I see people say "the rich are getting richer" - say, about tax cuts for high-income earners or businesses - it's always been definition 1. In the case of tax cuts, the action is expected to make the specific current rich people get richer. Or, when used as a more general idiom about the way of the world, that having money gives you a huge advantage in terms of making more money that means the gap is likely to widen over time.
Some other places interpreting the idiom that way:
https://www.phrases.org.uk/meanings/the-rich-get-richer-and-... "the inevitability of the literal truth that, the richer you are the more relatively rich you become and, for the poor, vice-versa"
https://en.wikipedia.org/wiki/The_rich_get_richer_and_the_po... "Shelley remarked that the promoters of utility had exemplified the saying, "To him that hath, more shall be given; and from him that hath not, the little that he hath shall be taken away. The rich have become richer, and the poor have become poorer; and the vessel of the State is driven between the Scylla and Charybdis of anarchy and despotism."[1] It describes a positive feedback loop (a corresponding negative feedback loop would be e.g. progressive tax)."
So it's hardly dishonest to assume the first meaning. Where are examples in common discourse of it frequently meaning the latter?
https://github.com/norvig/pytudes/blob/main/ipynb/Economics....
(The expectation of |H - T|, that is; the expectation of (H - T) is 0.)
(1) H is asymptotically normally distributed with mean N/2 and variance N/4 (central limit theorem)
(2) So H - T = H - (N - H) = 2H - N is ~normally distributed with mean 0 and variance N, or st.dev. sigma = sqrt(N)
(3) So |H-T| is "half-normal" (https://en.wikipedia.org/wiki/Half-normal_distribution). This has mean sigma * sqrt(2/pi) or approximately 0.8 sqrt(N).
This can be checked with a quick simulation. For example in R I run 1000 simulations with N = 10000 with the one-liner
mean(abs(2*rbinom(1000, 10000, 0.5)-10000))
The mean square of H-T will be approximately N, though (basically we can ignore the absolute value when computing the variance).
In fact, it's exactly N. H is Binomial(N, 1/2) which has variance N/4. H - T = 2H - N has variance N/4 * 2^2 = N, and mean 0, so its mean square is N.
However, the idea that “the mean distribution (the uniform, in this case)” needs to be near the N-th step one is what is statistically wrong, that is why I turned to the coin example.
But yes, thanks for pointing out the differences!
Does still sound fair to me.
The instantaneous distribution of money among the agents of a system should not be confused with the distribution of wealth. The latter also includes material wealth, which is not conserved, and thus may have a different (e.g. power-law) distribution.
The simulation might be a good model of how money distribution works, but it doesn't reflect how wealth distribution works. The simulation only works because money can neither be created nor distroyed (in the simulation, at least). Wealth can be so we shouldn't expect the simulation to predict its behavior.
[1]: https://physics.umd.edu/~yakovenk/papers/EPJB-17-723-2000.pd...
To keep it fair the game must run for a fixed amount of time before people are allowed to withdraw their money. Then a new round begins.
Then why wouldn't I just stop working? Why bother working at all if I'm guaranteed to be subsidized by other people?
And if you wanna express yourself creatively or just do nothing for a while, that's fine by me too! I'm sure you'd get bored after a while and want to make yourself useful again, so I don't think you should starve in the meantime.
You have hobbies and personal relationships to give your life meaning, you pay to be allowed to do that not the other way around.
And why don't you want to turn that around?
You want the incentive to get rich and then have that incentive fall off as you acquire more wealth.
The list of enormously valuable privately developed technologies goes on and on- in fact, almost all technologies. Many of these developed in the 1800s and early 1900s when there was very little government spending on research/etc. For example, oil, railways, cars, etc.
Even in cases where government research did help, often the practical realization takes a lot of money!
P.S. Companies are not necessarily collectives. It depends on the ownership structure.
Did you know that their entire aviation industry was based on technology copied from a B-29 bomber that made forced landing in Russia?
Yes, but people like examples. There are plenty more. N Korea, for example. China, when they had collective farms. It goes on and on, to the point were I can't find any examples of successful collective farms.
> It was an incompetently managed and corrupt state
Nobody has ever managed to create one otherwise. State run economies are always a mess.
Consider all the innovations that come from Bell Labs, Xerox, Kodak, Boeing, Microsoft, Amazon, Apple, Google, Nvidia, RCA, US Steel, Ford, General Electric, industrialized agriculture, Dow Chemical, and on and on and on.
Every modern economy is a mixed economy where you have some private funding and collective funding, some collective ownership and some private ownership. Countries that try to embrace either extreme of all private or all public end up collapsing. Arguing between either extreme like it's some moral dilemma is kinda pointless.
The thing that works is a little of both. It's actually kinda funny, when someone argues for extremely wealthy individuals pushing the country forward by making unilateral economic decisions you end up arguing for a form of central planning. But massive wealth consolidation isn't doing anything for you when the rest of us are fighting over the scraps.
This is the "fixed pie" view of the economy, i.e. if someone has more, that means others have less. That may be true of socialism, but in free markets it is not true at all.
Wealthy people create wealth, they do not "consolidate" it.
If I go to Home Depot, buy some wood, make a table and sell it to you I created wealth, I didn't take it from you. If you planted an apple tree, harvested apples and traded them for the table, you didn't take wealth from me - you created the wealth.
PS. I don't think it's a coincidence that both of your examples of creating wealth are typical "poor people" jobs. Obnoxiously wealthy people rarely create anything because they can simply pay someone else to do it, usually for a fraction of the value of their output.
That's the Labor Theory of Value perspective. What actually happens in those cases is the particular jobs being done are not that productive. Consider if you could pay someone $10 to do $100 worth of work. Inevitably, your competitor sees you making this easy money, and entices your worker away for $11. Then you entice him back for $12. Then Fred entices him away for $13. See where this is going? The wages go up until it is barely profitable to employ the person.
> Obnoxiously wealthy people rarely create anything
What they do is conceive of it, finance it, and manage it. Those are critical wealth-producing activities. Start a company yourself, and this will quickly become apparent.
> is rarely distributed among those who actually do the work
Scores of millions of destitute people immigrated to America in the 19th century and moved up into the middle class and beyond.
Also, free markets do not "distribute" wealth. Again, that is the fixed pie viewpoint. The actors in free markets create wealth.
> Predatory pricing,
I.e. offering lower prices. Nothing wrong with that.
> regulatory capture
That's a problem with government, not free markets.
> and buying out competition
Nothing wrong with that, either. Lots of conglomerates become so complicated they collapse, and new competitors always spring up.
Consider, even without such a system, more people than you realize have enough to live on (and pass on for generations), but still work. A lot of rich people also didn't work for their wealth. People have worked their whole lives and not become rich. I'm not sure there's a connection.
The incentive is that you could potentially enjoy something briefly and that's the best deal you can get.
Many people might say that is a lower incentive than to being able to leave your family better off than they were, or in your more greedy interpretation, so that their children and their children can enjoy something less briefly than you were able to.
Humans are capable of and do, in fact, act on more than just one or two simplistic external levers. We have agency, understanding, and drive to have empathy and to create.
People don't naturally collaborate the way you see them in the developed world no.
The idea that people in the wild are uncivilised savages is old racist propaganda.
I suggest erring on the side of earnesty when replying. The discussions that come out of those threads tend to be more interesting.
I think you would be conscripted to fight whether you liked it or not, and inculcated with the belief that it's the right thing to do. Maybe even feeling shame are your unwillingness but forcing yourself to fit in anyway.
As some french guy said, probably: "De la contrainte nait la créativité"
The discrepancy comes from confusing money with wealth. You can take my $100 and then you will have $100. But if you take my business away from me, you will end up with very little. And so will everybody else that was benefitting from the business that I was running.
And the result you have is: the modern American economy, where most efforts go into derivative financial products and investing, rather than actual productive enterprise. Day-to-day goods and services get worse and more expensive while the stock market keeps going up.
> where most efforts go into derivative financial products
No evidence for "most".
> and investing
Yes, investing in productive enterprises.
Who do you think invested in Microsoft, Google, Amazon, Nvidia, Apple, etc?
You're looking at just the APY on savings accounts. Actually the rich make far more than that on interest-derived financial products through various forms of rent-seeking. Interest is the hidden tax baked into every transaction. Some studies found interest accounts for roughly half of end-user prices—12 percent on garbage collection, up to 77 percent on public housing.[1]
And as Musk warns: “If we don’t act, the entire government budget will be used just to pay interest — there won’t be money for anything. No, there won’t be money for Social Security, no Medicare, nothing. That’s where we’re headed.” [2]
In the late-stage capitalist West, most public and private money goes to servicing interest at some point in the food chain.
[1] https://base.socioeco.org/docs/margrit_kennedy.pdf
[2] https://economictimes.indiatimes.com/news/international/us/e...
The US would not be the wealthiest country in the world if its wealth was acquired through rent seeking.
It turns out that selfish incentives are far more effective than any others.
And if necessary, the creditor needs to be able to pass the loan on to someone else instead of $1 (since the loan itself in theory represents $1) anyway.
Each round the debtor should randomly either pay a loan or pay a random person.
The longer a debtor goes without paying loans, the more it hurts their credit score.
Credit score can be used to determine the probability of any creditors extending a loan to someone. Everyone’s credit score starts at roughly 50%.
That stuck with me. Sometimes, all it takes is time and a bit of randomness for imbalance to emerge on its own. Inequality does not always come from someone doing something wrong. It can simply be the long-term result of randomness playing out. So the real question is, once we understand that, what do we do with it?
Real life has feedback loops too that help preserve and grow the wealth of the rich so it is worse than the sim. It also has feedback loops the other way like tax. This makes tax very important!
With 100 people, there are only 100 configurations where one person has all of the money. But there is also only one single configuration where everyone has the same amount of money. There are a small number of configurations where everyone has almost the same amount of money.
The vast majority of the configuration space consists of configurations that on a macro level fall under the umbrella category "unequal". This is not because they are more likely states, but just because there are so many of the states we would label "unequal".
Blah blah, jargon. Mostly thinking out loud here.
Basically, you're making the astute observation that the majority of configurations fill all wealth brackets... I think? The maxentropy distribution involves maximizing over products of combinations, and I'm just gut feeling at the moment.
How does this jibe with the supposedly empirical observation that wealth tends to follow a Pareto distribution?
Very cool. Thanks for kicking off the this conceptual avalanche!
In our capitalist system, wealth begets more wealth, thus heavy tails.
For my part, I keep repeating (reposting) this refrain:
"Inequity is just math, not a moral statement. It's inevitable without some kind of proactive redistribution."
(Any feedback on my phrasing? I always appreciate better word smithing.)
It takes a long time for these kinds or counterintuitive notions to percolate thru society. But eventually they stick.
FWIW, Scott Galloway is really good at honing and refining his talking points over time.
It's called taxing the first to keep the second on welfare benefits.