I'm sure you're familiar with the 80/20 rule.

It's said that 80% of the effects come from 20% of the causes, and so upon application to Meritocracy, 80% of wealth is generated by 20% of the people.

This principle is used from business to sports to health and safety, to optimise all walks of life for the best possible outcome.

With application to wealth, you can approximate what this looks like yourself by modelling a population with the poorest person's wealth as some base number raised to the first power (1), (and multiplying that by some coefficient if you want to normalise the total to 100% of the total wealth of the population), the second poorest person's wealth as the same base number raised to the second power (2), (normalised by that same coefficient), and so on the larger the population you want to consider.

It turns out that the larger the population, the base number and coefficient tend towards particular values that reveal a constant ratio of wealth between the richest and poorest individuals whose wealth follows a Pareto distribution.

The base number holds for smaller populations, though the smaller the population, the more the ratio tends towards a population of 1 where 1 person has 100% of the wealth - so larger populations are more informative.

If you're spreadsheet savvy, try this yourself.

As your base number, raise the number 2200 to the power of (1 divided by the total population) e.g. 2200^0.1 for a population of 10 (to get a total of about 2.16)

As your coefficient for a population of 10 you want a number close to 0.0244.

Raise this base number to the power of 1, and mulitply by this coefficient to get the poorest person with just over 0.05% of the wealth.

Do the same to the power of 2, multiply by the coefficient to get the next poorest person with about 2.16 times the wealth of the poorest person.

The richest person has just over 54% of the wealth, which is just over 1000 times the wealth of the poorest person.

If you've worked out all the values in between, you'll see the 80/20 rule is close to holding, though the exact 80/20 ratio isn't exactly followed by an exact geometric progression.

Try it on larger and larger populations and you'll realise that the richest person tends towards having 2200 times more wealth than the poorest person.

The percentage of the total wealth owned by the richest person tends towards 770 divided by the population size.

The percentage of the total wealth owned by the poorest person tends towards 0.35 divided by the population size.

I decided to have a look at what this would look like applied to the world population:

There's currently over 7.7 billion people in the world, and it's estimated that world wealth in all its forms amounts to about $1 quadrillion.

Following the same approximation of the Pareto Principle:

The richest person should have *$1 million across all forms of wealth (including debt, real estate and derivatives), and

The poorest person should have just under *$455 across all the same forms of wealth.

Ha!

Go on, work it out for yourself.

Does the wealth of the real world follow the Pareto distribution? Not even close!

But let's consider just the world's money supply, which totals nearly $90 trillion:

The richest person in the world should have *$90,000 in coins, banknotes, accounts, savings and deposits. This includes *$37,000 in just coins, banknotes and in their bank.

The poorest person in the world should have *$41 in the same forms of money. This includes *$17 in readily available money.

Pff.

Obviously this widely utilised principle for optimisation must be best applied to everything but wealth...

edit: I have put a * next to numbers I miscalculated due to forgetting to divide percentages by 100.