7 ms·

When random people give money to random other people (2017)

125 points by munificent 1y ago

deleted 1y ago
[deleted]
munificent 1y ago
There's a nice interactive simulation here: https://joshworth.com/jpw/does-this-simulation-explain-why-life-is-unfair/ https://joshworth.com/jpw/does-this-simulation-explain-why-l... And a blog post here: https://www.decisionsciencenews.com/?p=6221 https://www.decisionsciencenews.com/?p=6221
gnabgib 1y ago
Discussion (555 points, 2017, 241 comments) https://news.ycombinator.com/item?id=14729400 https://news.ycombinator.com/item?id=14729400
- probably_wrong 1y ago
  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. [1] https://news.ycombinator.com/item?id=14729930 https://news.ycombinator.com/item?id=14729930
  - autobodie 1y 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 1y 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://www.phrases.org.uk/meanings/the-rich-get-richer-and-the-poor-get-poorer.html 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_poor_get_poorer 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?
  - cantaloupe 1y ago
    Only if no interest is accrued on assets. When interest is introduced, there is no longer shuffling.
dgan 1y ago
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 1y 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.
- msgodel 1y ago
  What incentive is there to work to become rich if you have to give it away anyway?
  - Jimpulse 1y ago
    Initially, security. Then maybe a realization that you don't need all of your wealth to be secure.
    - msgodel 1y 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?
    - parliament32 1y 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 1y 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.
pfortuny 1y 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.
- thaumasiotes 1y ago
  Isn't the expectation sqrt(N)? (The expectation of |H - T|, that is; the expectation of (H - T) is 0.)
  - pfortuny 1y ago
    I think it is so (I seem to recall it and the example from Feller's book).
    - madcaptenor 1y 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) (3) So |H-T| is "half-normal" (https://en.wikipedia.org/wiki/Half-normal_distribution 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)) 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.
- majormajor 1y 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.
wordglyph 1y ago
Introduce credit so the people with zero can still give. Then I suspect it would be more even.
- deadbabe 1y 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%.
k__ 1y 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 1y 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-life-is-unfair/ https://joshworth.com/jpw/does-this-simulation-explain-why-l...
- munificent 1y 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. [1]: https://physics.umd.edu/~yakovenk/papers/EPJB-17-723-2000.pdf https://physics.umd.edu/~yakovenk/papers/EPJB-17-723-2000.pd...
- reassess_blind 1y ago
  Does a fair system mean everyone is equal all the time, or everyone has the same chance of being poor or wealthy?
thaumasiotes 1y 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.
MichaelRo 1y ago
>> When random people give money to random other people It's called taxing the first to keep the second on welfare benefits.
- rexpop 1y ago
  This is also an approximation of commercial exchange.
deadbabe 1y 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.
- dreghgh 1y ago
  You've invented gambling.
staplung 1y ago
This is explored in more depth in one of Peter Norvig's pytude notebooks: https://github.com/norvig/pytudes/blob/main/ipynb/Economics.ipynb https://github.com/norvig/pytudes/blob/main/ipynb/Economics....
Noelia- 1y ago
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?
- bravesoul2 1y 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!
- kqr 1y 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 1y 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!
NooneAtAll3 1y 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)
- dreghgh 1y ago
  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.

125 points by munificent 1y ago

deleted 1y ago

[deleted]

There's a nice interactive simulation here: https://joshworth.com/jpw/does-this-simulation-explain-why-life-is-unfair/ https://joshworth.com/jpw/does-this-simulation-explain-why-l... And a blog post here: https://www.decisionsciencenews.com/?p=6221 https://www.decisionsciencenews.com/?p=6221

gnabgib 1y ago

Discussion (555 points, 2017, 241 comments) https://news.ycombinator.com/item?id=14729400 https://news.ycombinator.com/item?id=14729400

probably_wrong 1y ago
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. [1] https://news.ycombinator.com/item?id=14729930 https://news.ycombinator.com/item?id=14729930
- autobodie 1y 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 1y 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://www.phrases.org.uk/meanings/the-rich-get-richer-and-the-poor-get-poorer.html 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_poor_get_poorer 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?
- cantaloupe 1y ago
  Only if no interest is accrued on assets. When interest is introduced, there is no longer shuffling.

dgan 1y ago

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 1y 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.
msgodel 1y ago
What incentive is there to work to become rich if you have to give it away anyway?
- Jimpulse 1y ago
  Initially, security. Then maybe a realization that you don't need all of your wealth to be secure.
  - msgodel 1y 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?
  - parliament32 1y 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 1y 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.

pfortuny 1y 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.

thaumasiotes 1y ago
Isn't the expectation sqrt(N)? (The expectation of |H - T|, that is; the expectation of (H - T) is 0.)
- pfortuny 1y ago
  I think it is so (I seem to recall it and the example from Feller's book).
  - madcaptenor 1y 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) (3) So |H-T| is "half-normal" (https://en.wikipedia.org/wiki/Half-normal_distribution 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)) 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.
majormajor 1y 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.

wordglyph 1y ago

Introduce credit so the people with zero can still give. Then I suspect it would be more even.

deadbabe 1y 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%.

k__ 1y 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 1y 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-life-is-unfair/ https://joshworth.com/jpw/does-this-simulation-explain-why-l...
munificent 1y 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. [1]: https://physics.umd.edu/~yakovenk/papers/EPJB-17-723-2000.pdf https://physics.umd.edu/~yakovenk/papers/EPJB-17-723-2000.pd...
reassess_blind 1y ago
Does a fair system mean everyone is equal all the time, or everyone has the same chance of being poor or wealthy?

thaumasiotes 1y 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.

MichaelRo 1y ago

>> When random people give money to random other people It's called taxing the first to keep the second on welfare benefits.

rexpop 1y ago
This is also an approximation of commercial exchange.

deadbabe 1y 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.

dreghgh 1y ago
You've invented gambling.

staplung 1y ago

This is explored in more depth in one of Peter Norvig's pytude notebooks: https://github.com/norvig/pytudes/blob/main/ipynb/Economics.ipynb https://github.com/norvig/pytudes/blob/main/ipynb/Economics....

Noelia- 1y ago

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?

bravesoul2 1y 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!
kqr 1y 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 1y 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!

NooneAtAll3 1y 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)

dreghgh 1y ago
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.