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?
kqr · 1h ago
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".
xelxebar · 2m ago
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!
bravesoul2 · 2h ago
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!
NooneAtAll3 · 3h ago
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)
k__ · 12h ago
"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.
cantaloupe · 11h ago
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...
munificent · 10h ago
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.
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.
autobodie · 12h ago
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.
majormajor · 11h ago
> 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://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?
pfortuny · 13h ago
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.
majormajor · 11h ago
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.
thaumasiotes · 12h ago
Isn't the expectation sqrt(N)?
(The expectation of |H - T|, that is; the expectation of (H - T) is 0.)
pfortuny · 11h ago
I think it is so (I seem to recall it and the example from Feller's book).
madcaptenor · 10h ago
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)
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?
munificent · 13h ago
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.
Everyone starts with the same money in this thought experiment. How do you define richer and poorer with that in mind?
msgodel · 13h ago
What incentive is there to work to become rich if you have to give it away anyway?
Nifty3929 · 10h ago
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.
andriamanitra · 1h ago
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).
dakr · 11h ago
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.
msgodel · 10h ago
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.
kqr · 10h ago
Of whose natural humanity? Areyou naturally violent and unproductive without coercion? I'm not.
msgodel · 9h ago
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.
kqr · 1h ago
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.
jaoane · 27m ago
Is this a serious comment? It hits all the bases.
JackSlateur · 8h ago
Of course we are (maybe not you as an individual but whatever)
As some french guy said, probably: "De la contrainte nait la créativité"
myflash13 · 10h ago
What incentive is there to work to create wealth if an interest-based system is rigged towards the already-wealthy?
WalterBright · 4h ago
Creating wealth for yourself is what matters. Other people having more than you is irrelevant.
dfxm12 · 12h ago
You can become rich enough that you can afford to give away a dollar to someone every second and still be rich. For some perspective, this full amount is about 33% of annual income of $100mm. The richest people make well more than this.
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.
Nifty3929 · 10h ago
Unfortunately, money is not stuff. Taking money from rich people and giving it to poor people doesn't create any additional stuff for those poor people to consume.
bongodongobob · 9h ago
Rich people generally don't make a goddamn thing.
WalterBright · 4h ago
Elon Musk
WalterBright · 4h ago
Not enough incentive is left for a sustainable society.
It turns out that selfish incentives are far more effective than any others.
scotty79 · 12h ago
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.
mhuffman · 11h ago
>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.
scotty79 · 10h ago
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.
Jimpulse · 13h ago
Initially, security. Then maybe a realization that you don't need all of your wealth to be secure.
parliament32 · 12h ago
> maybe a realization that you don't need all of your wealth to be secure
Then why wouldn't I just stop working? Why bother working at all if I'm guaranteed to be subsidized by other people?
input_sh · 12h ago
To give your life a purpose? To do something meaningful and fulfilling? To build something cool? To be able to afford additional, cooler things? To work on a common mission with likeminded people? To contribute something back to the system? To experience how things work in the background? To have a sense of ownership over your productive output?
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.
ncruces · 10h ago
I'm sure people who, idk, have to clean up office toilets, do it because it's meaningful and fulfilling.
msgodel · 11h ago
Oh yeah I forgot that's why I deal with insane corporate administrative bullshit to write bad software that solves problems only generated because of the scale of the internal social interactions: because it gives my life meaning.
You have hobbies and personal relationships to give your life meaning, you pay to be allowed to do that not the other way around.
darkwater · 10h ago
> 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?
msgodel · 13h ago
How does it provide security if you're giving it away? Why do you need it if not working for it means you're more likely to get it for free?
the_cat_kittles · 11h ago
what incentive is there for you to post this comment if it isnt going to make you rich?
Spivak · 12h ago
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.
msgodel · 11h ago
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.
WalterBright · 4h ago
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.
andriamanitra · 1h ago
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.
thaumasiotes · 12h ago
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.
wordglyph · 13h ago
Introduce credit so the people with zero can still give. Then I suspect it would be more even.
deadbabe · 6h ago
The credit would have to come from someone willing to loan out money.
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%.
deadbabe · 6h ago
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.
MichaelRo · 11h ago
>> When random people give money to random other people
It's called taxing the first to keep the second on welfare benefits.
rexpop · 10h ago
This is also an approximation of commercial exchange.
And a blog post here: https://www.decisionsciencenews.com/?p=6221
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?
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!
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!
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)
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...
[1] https://news.ycombinator.com/item?id=14729930
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?
(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
which returns 79.944.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.
https://github.com/norvig/pytudes/blob/main/ipynb/Economics....
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.
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.
As some french guy said, probably: "De la contrainte nait la créativité"
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.
It turns out that selfish incentives are far more effective than any others.
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.
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.
- 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.
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%.
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.
It's called taxing the first to keep the second on welfare benefits.