Why eventually, every single person on earth except for 1 person/family/group will have below the "average" net worth (not clickbait, maths explained)

[Seth Walsh]

Multiplicative randomness continuously separates trajectories, and arithmetic averages increasingly become descriptions of the extreme right tail rather than descriptions of ordinary people.
In wealth dynamics, the mean becomes more and more prosperous while becoming less and less representative of almost anyone actually living inside the system.
This explains individual economic decay as ensemble statistics look "better".

The first graph is the most important. At the beginning, about half the population is below the expected wealth level. As the multiplicative process runs, that proportion rises.
Why?


Because the distribution is not merely moving. It is stretching.


Imagine everyone begins here:



Time 0

●●●●●●●●●●●●●●●●●●●●
roughly equal



Then everyone receives independent percentage gains and losses.


After some time:



Later

●●●●●●●●●●●●●●● ●● ● ●
poor / ordinary rich very rich



Much later:



Much later

●●●●●●●●●●●●●●●●●●●●●●●●● ● ● ●
almost everyone extreme tail



The huge conceptual point is that wealth is multiplicative.


Suppose two people both get lucky.


One currently has €10.


One currently has €10 million.


A 20% positive shock gives the first person €2.


It gives the second person €2 million.


So once trajectories separate, subsequent percentage changes occur on radically different bases.


The distribution therefore keeps broadening.


And because wealth cannot symmetrically extend below zero in this simple model, the broadening becomes extraordinarily skewed in ordinary euro terms.


In log-wealth space, the distribution looks much more like a symmetric bell.


But when you transform back into actual wealth, the right-hand tail gets stretched enormously.


That is the central geometry:



LOG WEALTH

/\
/ \
/ \
_______/____________\_______

fairly symmetric



becomes something like:



ACTUAL WEALTH

███████████████████▇▆▅▄▃▂▂▁▁▁▁.........................tiny tail
but tail values are ENORMOUS



Most people occupy the dense mass on the left.


Very few people occupy the far-right tail.


But the far-right values become so enormous that they dominate the arithmetic average.


And that brings us to the third graphic.


I deliberately made the simplest possible toy economy.


There are 100 people.


Ninety-nine people each own €1.


One person owns €9,901.


Total wealth is €10,000.


Average wealth is therefore €100.


So:



99 people: €1
1 person: €9,901
-------------------
average: €100



Ninety-nine percent of people are below average.


There is nothing mathematically strange about that.


“Average” does not mean “middle.”


It means:

Add everyone's wealth together and divide by the number of people.

One extreme person can move that number almost arbitrarily far away from what nearly everyone possesses.


This is exactly why the sentence:

“The average person has X”

can be badly misleading when the distribution is extremely skewed.


The mean isn't lying.


You're asking it a question it wasn't designed to answer.


Now look at the second graphic above.


That gets even closer to Peters.


The upper line is expected, ensemble-average wealth.


The lower line is typical wealth.


They start together.


Then one goes up and the other goes down.


How can average wealth increase while the ordinary trajectory gets poorer?


Because rare trajectories become so enormous that they more than compensate for enormous numbers of mediocre trajectories.


Imagine one million people.


999,999 people each end up around €1.


One extraordinary trajectory reaches €1 trillion.


The total wealth is dominated by that one trajectory.


So the average can be around €1 million even though almost nobody has remotely close to €1 million.


That's the trick.


Now make the process continue.


The right tail gets wider.


The rare winners get rarer relative to the whole population, but their values become exponentially more extreme.


So you get the apparently paradoxical result:

The probability of being anywhere near the expectation gets smaller even while the expectation itself keeps growing.

 

[Zygomati𝖼]

Multiplicative randomness continuously separates trajectories, and arithmetic averages increasingly become descriptions of the extreme right tail rather than descriptions of ordinary people.
In wealth dynamics, the mean becomes more and more prosperous while becoming less and less representative of almost anyone actually living inside the system.
This explains individual economic decay as ensemble statistics look "better".
View attachment 5650236
View attachment 5650237
View attachment 5650238
The first graph is the most important. At the beginning, about half the population is below the expected wealth level. As the multiplicative process runs, that proportion rises.
Why?


Because the distribution is not merely moving. It is stretching.


Imagine everyone begins here:



Time 0

●●●●●●●●●●●●●●●●●●●●
roughly equal



Then everyone receives independent percentage gains and losses.


After some time:



Later

●●●●●●●●●●●●●●● ●● ● ●
poor / ordinary rich very rich



Much later:



Much later

●●●●●●●●●●●●●●●●●●●●●●●●● ● ● ●
almost everyone extreme tail



The huge conceptual point is that wealth is multiplicative.


Suppose two people both get lucky.


One currently has €10.


One currently has €10 million.


A 20% positive shock gives the first person €2.


It gives the second person €2 million.


So once trajectories separate, subsequent percentage changes occur on radically different bases.


The distribution therefore keeps broadening.


And because wealth cannot symmetrically extend below zero in this simple model, the broadening becomes extraordinarily skewed in ordinary euro terms.


In log-wealth space, the distribution looks much more like a symmetric bell.


But when you transform back into actual wealth, the right-hand tail gets stretched enormously.


That is the central geometry:



LOG WEALTH

/\
/ \
/ \
_______/____________\_______

fairly symmetric



becomes something like:



ACTUAL WEALTH

███████████████████▇▆▅▄▃▂▂▁▁▁▁.........................tiny tail
but tail values are ENORMOUS



Most people occupy the dense mass on the left.


Very few people occupy the far-right tail.


But the far-right values become so enormous that they dominate the arithmetic average.


And that brings us to the third graphic.


I deliberately made the simplest possible toy economy.


There are 100 people.


Ninety-nine people each own €1.


One person owns €9,901.


Total wealth is €10,000.


Average wealth is therefore €100.


So:



99 people: €1
1 person: €9,901
-------------------
average: €100



Ninety-nine percent of people are below average.


There is nothing mathematically strange about that.


“Average” does not mean “middle.”


It means:




One extreme person can move that number almost arbitrarily far away from what nearly everyone possesses.


This is exactly why the sentence:




can be badly misleading when the distribution is extremely skewed.


The mean isn't lying.


You're asking it a question it wasn't designed to answer.


Now look at the second graphic above.


That gets even closer to Peters.


The upper line is expected, ensemble-average wealth.


The lower line is typical wealth.


They start together.


Then one goes up and the other goes down.


How can average wealth increase while the ordinary trajectory gets poorer?


Because rare trajectories become so enormous that they more than compensate for enormous numbers of mediocre trajectories.


Imagine one million people.


999,999 people each end up around €1.


One extraordinary trajectory reaches €1 trillion.


The total wealth is dominated by that one trajectory.


So the average can be around €1 million even though almost nobody has remotely close to €1 million.


That's the trick.


Now make the process continue.


The right tail gets wider.


The rare winners get rarer relative to the whole population, but their values become exponentially more extreme.


So you get the apparently paradoxical result:

It is multiplicative, it doesn’t shift the pile, it stretches it. In log wealth the thing still looks like a bell. Exponentiate back into euros and the right tail goes insane. The arithmetic average is then a tail statistic. It is not a description of a person.

That’s why “average wealth went up” can be true while almost everyone’s path is worse. A few trajectories get so large they pull the ensemble mean with them. The ordinary path is closer to the median, or to exp(E[log W]), and that can fall even while E[W] rises. Nothing paradoxical if you stop treating “average” as “normal.”

The 99 people with €1 and one person with €9,901 is just the cartoon of that. Mean = €100. Almost nobody has €100. The mean isn’t lying. You asked it for a middle and it gave you a total divided by n.

 

[Seth Walsh]

Yeah. Mean vs typical. That’s the whole trick.

The process is multiplicative, so it doesn’t shift the pile. It stretches it. In log wealth the thing still looks like a bell. Exponentiate back into euros and the right tail goes insane. The arithmetic average is then a tail statistic. It is not a description of a person.

That’s why “average wealth went up” can be true while almost everyone’s path is worse. A few trajectories get so large they pull the ensemble mean with them. The ordinary path is closer to the median, or to exp(E[log W]), and that can fall even while E[W] rises. Nothing paradoxical if you stop treating “average” as “normal.”

The 99 people with €1 and one person with €9,901 is just the cartoon of that. Mean = €100. Almost nobody has €100. The mean isn’t lying. You asked it for a middle and it gave you a total divided by n.

One caveat so this doesn’t turn into a morality play: this is the geometry of a pure multiplicative model (no wages, no floor, no tax, no bankruptcy). Real life is mixed: additive income plus multiplicative returns, so it doesn’t prove everyone is decaying. It does prove you cannot read a mean as a life.

The useful sentence is yours: the mean gets more prosperous by becoming less representative.

Thank you, ChatGPT

The motive of this thread is to distrust ensemble average statistics as explanations. So if you see "here's the median and mean household income".

You can see the mean is higher. Okay so more than half the "participants" fall below the mean.

But try breaking that down even further. Obviously most household wealth will be condensed in families who have fully owned homes with fully paid of mortgages. The multiplicative dynamics determine that future wealth will flow to them, too.

So people should ask. "Household wealth"? Does that include only people who own a fully paid off home. Or the prior, including those who own the home but are still paying the mortgage. Does it include or exclude "households" who are renting? If it includes renters, then obviously you get a group who will end up clustered at the very left tail of the wealth distribution within the "household wealth" statistic itself. Because time and multiplicative dynamics work as a wealth condensation system that puts more wealth into the hands of outright ownership.

 

[Seth Walsh]

Thank you, ChatGPT

The motive of this thread is to distrust ensemble average statistics as explanations. So if you see "here's the median and mean household income".

You can see the mean is higher. Okay so more than half the "participants" fall below the mean.

But try breaking that down even further. Obviously most household wealth will be condensed in families who have fully owned homes with fully paid of mortgages. The multiplicative dynamics determine that future wealth will flow to them, too.

So people should ask. "Household wealth"? Does that include only people who own a fully paid off home. Or the prior, including those who own the home but are still paying the mortgage. Does it include or exclude "households" who are renting? If it includes renters, then obviously you get a group who will end up clustered at the very left tail of the wealth distribution within the "household wealth" statistic itself. Because time and multiplicative dynamics work as a wealth condensation system that puts more wealth into the hands of outright ownership.

This is why I don't shut the fuck up about social class.