When random people give money to random other people (2017)
quomodocumque.wordpress.com124 points by munificent 3 days ago
124 points by munificent 3 days ago
There's a nice interactive simulation here: https://joshworth.com/jpw/does-this-simulation-explain-why-l...
And a blog post here: https://www.decisionsciencenews.com/?p=6221
The first time I saw a model like this, I assumed that randomness would eventually balance things out. But that is not what happened. The rules were completely fair, yet the system still ended up producing significant inequality.
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?
I also assumed randomness would balance things out, but "balance things out" means maximum entropy distribution.
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".
Ooo. Very cool. You just set off a storm of interesting connections for me. Assuming some ergodic process for distributing wealth then the asymptotic expectation for wealth inequality reduces to looking at random integer partitions.
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!
The Pareto distribution (and indeed other heavy-tailed distributions) come out of self-reinforcing processes, where each additional amount of something increases the probability of even more of that thing. (This is what it means for a distribution tail to be subexponential.)
In our capitalist system, wealth begets more wealth, thus heavy tails.
But I think the catch is that while the model preserves inequality it doesn't guarantee to preserve wealth for any individual player.
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!
Exactly.
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.
Two thoughts:
- 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.
I don't want to comment of philosophy part, but isn't math part flawed?
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)
Yes you are completely right. All the analysis is done for a game where one randomly chosen person with money gives one other randomly chosen person one dollar at each time step.
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.
Discussion (555 points, 2017, 241 comments) https://news.ycombinator.com/item?id=14729400
I remember that discussion because of the comment [1] pointing out that the rich people don't stay rich forever - the distribution may be skewed but that doesn't mean that the richer get richer.
Only if no interest is accrued on assets. When interest is introduced, there is no longer shuffling.
Nonsense. There is a big difference between the implications of the following claims:
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.
> Nonsense. There is a big difference between the implications of the following claims:
> 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?
This is explored in more depth in one of Peter Norvig's pytude notebooks:
https://github.com/norvig/pytudes/blob/main/ipynb/Economics....
Essentially similar to “after N throws of a coin, what will the difference be between heads and tails?”. It will most likely be away from 0, and probably large.
If you keep flipping a coin you get heads or tails every time. There's no streak-breaking limit where you stop counting consecutive heads after some point. But here a streak can run into a loss-limiting wall "for this turn, you have $0, so you can't give any more away." That boundary - unless you allow infinite negative balances - breaks the first-glance intuition. As people hit 0, the amount of dollars that are redistributed on the next turn goes down. So the richest will still be losing their dollar a turn, but are less likely to gain a dollar. Which will have the most significant effect on people nearly-broke, since they will still lose, but gain less frequently.
OK, interesting take which I had not realized: the problem is also different because there is a limited amount of cash, I now realize.
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!
Isn't the expectation sqrt(N)?
(The expectation of |H - T|, that is; the expectation of (H - T) is 0.)
I think it is so (I seem to recall it and the example from Feller's book).
It's definitely on the order of sqrt(N). But it's a bit smaller than sqrt(N) typically:
(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.
"inequality of wealth rapidly appears and then persists (though each individual person bobs up and down from rich to poor."
Does still sound fair to me.
This is only when no other effects/processes are accounted for. If every participant keeps their current funds in an account with the same interest rate, then the distribution permanently skews so that there is no longer bobbing. The rich stay rich. See this more detailed simulation linked in another comment: https://joshworth.com/jpw/does-this-simulation-explain-why-l...
The paper this is based on [1] does a good job of spelling out:
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...
Does a fair system mean everyone is equal all the time, or everyone has the same chance of being poor or wealthy?
Wouldn’t this be a cool game someone could build with crypto where all players will randomly give a unit of coin to other people every 5 minutes or so until some people get really rich?
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.
okey but the burning question now is: how much more fair it becomes when the richer participants give specifically to poorest participants, instead of random one?
The system is fair. While the distribution is non-uniform, over a long enough time span, all participants will appear at every place in the distribution.
This more detailed simulation shows the impact of UBI, interest, etc. Unsurprisingly it is much more balanced with UBI and even more extremely skewed with interest accruing. https://joshworth.com/jpw/does-this-simulation-explain-why-l...
Everyone starts with the same money in this thought experiment. How do you define richer and poorer with that in mind?
What incentive is there to work to become rich if you have to give it away anyway?
This argument reminds me of theists asking, "without a god, what is there to keep you from being amoral and running around killing people?"
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.
Right but the natural state of humanity without real social norms and meta norms is to just form small, violent, relatively unproductive tribes. Civilization doesn't scale without rules.
Of whose natural humanity? Areyou naturally violent and unproductive without coercion? I'm not.
Of course we are (maybe not you as an individual but whatever)
As some french guy said, probably: "De la contrainte nait la créativité"
I build things, just not things anyone else wants. Other people absolutely do seem to have violent tendencies without coercion.
People don't naturally collaborate the way you see them in the developed world no.
You say people don't collaborate yet cite no source, so I can only assume you mean you wouldn't be collablrative. I can assure you I would be collaborative.
The idea that people in the wild are uncivilised savages is old racist propaganda.
You wouldn't exist because part of what makes you who you are is the society you've lived in and its social norms. If you had been born into a tribal society, you'd be tribal - or dead if you refused to cooperate with its culture.
Right but what says that culture would be violent and unproductive, rather than kind and productive? That's what I don't get. Runs counter to what I think is my nature and tbose around me, so I'd expect a position that has considered more evidence from your end.
Is this a serious comment? It hits all the bases.
All my comments are serious in matter. Some are whimsical in tone. Many are wrong in fact.
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 there is a bit stronger version of your argument: The wealth that I have is intrinsically tied to me personally: It's a business that I'm running, an idea I'm pursuing, etc. Taking it away from me destroys it.
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.
This is a compelling argument but there is an upper limit of how much wealth can be intrinsically tied to a person. When we start talking about 8, 9, 10, 11, even 12 figures it's really hard to argue that the value of the wealth would diminish if it was distributed among more people. If anything I would expect people with more modest amounts of wealth to be more motivated to manage it (rather than hiring someone else to do it, at which point there is no intrinsic personal connection).
What incentive is there to work if you are going to die anyway?
The incentive is that you could potentially enjoy something briefly and that's the best deal you can get.
>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.
Many more people are single and don't plan on having a family. And for those who have .. tax is always lower than 100%. You won't leave your family worse off by earning more money, regardless of the specific level of the tax.
A little bit of inequality is good as an incentive as you describe. A large amount of inequality devolves an economy into being pseudo-centrally-planned as nearly all the wealth is allocated by a small group of super wealthy individuals.
You want the incentive to get rich and then have that incentive fall off as you acquire more wealth.
We already have a pretty steeply progressive income tax. Part of the problem with schemes like this is that the wealthy have the resources to dodge them so it mostly just creates problems for the productive middle class.
You can't do great things without a large amount of money. Preventing people from accumulating large amounts of money means you cannot have things like SpaceX. By limiting wealthy people, you put a cap on your own standard of living.
Most great things that require a large amount of money are funded mostly by collectives (historically the state and church, more recently companies) rather than wealthy people. SpaceX has certainly done some cool stuff (even before it started being funded by taxpayer money through government contracts), but I think the value of all of these billionaire-funded endeavors are a rounding error in comparison to all the infrastructure, science, education and healthcare that has been collectively funded. By limiting excessively wealthy people you give money a better chance to be allocated well.
You might find it interesting to know that in the mid 1800s, in the UK, during a 10-year period, private investment in railways totaled 40% of GDP- an average of 4% per year. For comparison, the Apollo program was <0.5% of GDP.
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.
If you were correct, the Soviet Union would have dominated the world. Instead, they copied technology from the west. They did have some innovations, but not many.
Did you know that their entire aviation industry was based on technology copied from a B-29 bomber that made forced landing in Russia?
I don't see how the failure of Soviet Union is supposed to disprove my argument – correlation does not imply causation. It was an incompetently managed and corrupt state. Collectively funding infrastructure projects and science is not something that only happened in the USSR, it was (and is) the norm everywhere. Consider all the innovations that spawned from (D)ARPA and NASA research projects for example. Taxpayer money through government contracts drives the entire military-industrial complex.
> correlation does not imply causation
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.
But then you get to list every invention that was funded by taxpayer dollars and well.. you end up with two very long lists.
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.