## A Pareto Distribution of Wealth

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### A Pareto Distribution of Wealth

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.
Last edited by Silhouette on Thu Nov 07, 2019 5:24 pm, edited 1 time in total.

Silhouette
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### Re: A Pareto Distribution of Wealth

I'm "liking" this post, in the sense that people send likes to content including text messages.
Ecmandu
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### Re: A Pareto Distribution of Wealth

I gather those numbers do not iinclude the homeless population or near homeless , who are not factored in. But probably the gross medium is what determines the closest approximation ., or about .2%.
The standard deviation by that small a number would be of no measurable consequence.
However, the deviation caused by unethical and illegal profiteering, of included, may make a very big difference , of those immeasurable approximations , once they are qualified into the study
Or am I misunderstanding the objective behind producing a viable study.

Or are they factored in

Thanks, for anyone bothering my question for:

'However, one should not conflate the Pareto distribution with the Pareto Principle as the former only produces this result for a particular power value, {\displaystyle'

This information I gathered after asking the question, reduces the question to general accessible knowledge.

Therefore, my first thought was to withdraw the question, it becomes an interesting query, whether sensible questions may correspond to prior concerns.
The oft informality of immediate responses, tends toward 'sensible, yet already treaded upon inquiries.

Some questions of this type do hAve corresponding approaches, where procedures and formal rules of logic may present problems in their conflated , or, otherwise presented mode.

Thanks , anyway, if unduly concerned with it.
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### Re: A Pareto Distribution of Wealth

I had to correct 6 of the numbers I used in the opening post. The result only reinforces my point even further. In a world of 7.7 billion and all the wealth we have between us, an optimising distribution according to the Pareto Principle would have hardly any millionaires in the world if any at all.

Meno_ wrote:I gather those numbers do not iinclude the homeless population or near homeless , who are not factored in. But probably the gross medium is what determines the closest approximation ., or about .2%.
The standard deviation by that small a number would be of no measurable consequence.
However, the deviation caused by unethical and illegal profiteering, of included, may make a very big difference , of those immeasurable approximations , once they are qualified into the study
Or am I misunderstanding the objective behind producing a viable study.

Or are they factored in

If I'm understanding what you're saying, yes the numbers would be including everyone, even the homeless or near homeless.

The reason is that the numbers are starting from the theory of an entire population, whatever their living conditions, and comparing this to practice afterwards. I'm not looking at the real world first and subsequently modelling it theoretically, because as you will have gathered from my conclusion - the real world looks nothing like it uses the same Pareto Principle that is used to optimise so much else in life.

As I stated, the figure of $1 quadrillion includes money in all its forms, "including debt, real estate and derivatives". Since homes are included in real estate, homelessness would imply that all homes throughout the entire world were valued above the poorest person's wealth (in all forms including real estate) of$455. This doesn't seem hard to imagine for us in the West, but given that the estimated value of only the world's developed real estate is $217 trillion, of which 75% is housing, that yields$162 trillion worth of houses throughout the whole world, and a distribution of people in line with the Pareto Principle would have the richest person owning only $162,000 in housing but the poorest would still own$74 of housing. So whilst you won't find many houses in the West for 74 dollars (or even $162k for that fact), it may be the case that any number of people could own housing worth more than$74 but just not live there... - in which case there could be homelessness, but out of choice rather than poverty.

So it's hard to say homelessness or near homelessness would really be an issue for an optimising distribution of wealth in line with the Pareto Principle - especially if you believe the claim that Americans are richer than 99% of the rest of the world. This means they would collectively own about 7.4% of the world's homes if they followed the Pareto Principle, which is $12 trillion in total, or if you go by the fact that their population of 330 million is about 4.3% of the world, they would own$7 trillion between them all. Whether Americans were the top 1% or 4.3% in housing ownership, in both cases even the poorest American would still own around $150k or$116k in housing depending on each of these respective cases. But obviously there are plenty of other parts of the world with people in the top 1% or 4.3% of world wealth, so the numbers wouldn't be quite that high.

Today there's probably about 20 million millionaires in the world. With Pareto optimisation of wealth, that's 0.3% of the world who won't get to call themselves millionaires anymore. I'd have to know the graph of the world's actual distribution of wealth to see where they intersect, to work out how many more would lose out (in absolute number at least) if we were to instead have a distribution of wealth according to the Pareto Principle - though it wouldn't be a great many more. Of course, the "position" one currently has in the world leaderboard of wealth ownership wouldn't have to change in such a conversion, so relatively speaking nobody would lose out.

It's true that many people are too young or old, or dependent for some other reason on others having wealth when they have little to none themselves, but even allowing for this, the world is far far away from this optimising distribution used so widely in other aspects of life.

Meno_ wrote:However, one should not conflate the Pareto distribution with the Pareto Principle as the former only produces this result for a particular power value

If you mean the Pareto Principle is only one form of Pareto distribution then yes, I could have been more specific about this in my opening post.

The title is addressing "a" Pareto Distribution of Wealth and I open speaking about the Pareto Principle, but yes, there's two instances when I didn't specify Pareto Distribution as one that follows the Pareto Principle.

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### Re: A Pareto Distribution of Wealth

The reason I posted that I liked this thread, wasn't just about money - sexual selection isn't Pareto normative either.
Ecmandu
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### Re: A Pareto Distribution of Wealth

In the interests of actually enacting this Pareto Distribution based on the Pareto Principle in the real world, it's useful to consider successful models of constrained quantifiable transactions that are used in other areas of life, by which people actively and willingly participate in abiding.

One such control, which is widely used to measure and confine values to a certain distribution in competitive pursuits like chess, football, board games and video games is the Elo rating system. This rating system allows people to "transact" according to their ability, such that winners and losers gain and lose their Elo rating in accordance with the Elo rating of the person they're dealing with. This means that participants trade away less of their Elo rating when losing to more able people and more when losing to less able people, and likewise they gain more Elo rating when winning against more able people and gain less when winning against less able people.

When applied to wealth, the same concept translates to a kind of "exchange rate" depending on the Elo rating of whoever is trading. In the same way as things work already, businesses maximise profits by selling less expensive products to poorer people in higher numbers as well as selling more expensive products to richer people, who are less in number. Using the principles of the Elo rating system, which is based around the Logistic function, the Pareto Principle can be adapted to function such that the poor pay less than the rich for the same trade but only the the extent that everyone's wealth remains in accordance with the 80/20 rule as a result.

I've adapted the Pareto model I laid out in the opening post to the afore-mentioned "logistic function", to cope with trading situations, in the following way:

The logistic function takes the form of f(x) = L/(1 + e^(-k(x-x0))), where L is the curve's maximum value, k is the logistic growth rate (steepness of the curve) and x0 is the midpoint of the curve.

When matching this form specifically to the Pareto Principle, L takes the value of around 49 divided by 3 times the population, k takes the value of 7.7 divided by the population, and the midpoint x0 is half of the population.

Using these particular values transforms the exponential curve of the Pareto Principle (which is the same as the model I outlined in the opening post when excluding the "+1" in the denominator) to a sigmoid (S-shaped) curve once the "+1" added to the denominator. If I'm working it out correctly, the richest person is only paying about 50 times (more precisely the square root of 2200) more for the same item as the poorest person, even though they're 2200 times as rich - assuming things are distributed within the 80/20 rule as I laid out in the opening post. However to transition from what we have now to a Pareto Principle distribution of wealth, it might be necessary to increase that proportion, at least to accelerate the transition. This depends on what the current world wealth distribution is.

The positive consequences of this are that every person remains proportionally richer than those they were richer than before in accordance with Meritocracy - as you have to continue to earn to maintain richness - only wealth inequality is constrained to an optimised Pareto distribution of wealth without compromising the decentralised market model - instead of allowing inequality to spiral far outside the 80/20 rule like it has been.
Possible negative consequences of this are that, without certain adjustments, it's possible that the richer may resort to refraining from hiring or trading with the poorer to avoid losing out from the more significant exchange rate between more greatly differing levels of wealth:

1) Assuming rich people earned their richness, they're costing companies more in wage expenses or drawings etc. so it's already an incentive to employ cheaper people who are thereby less rich from earning less wages, which may still offset the larger costs for richer companies to employ poorer people, however no such problem will present itself to poorer companies - meaning new businesses get a natural boon and businesses that are large get penalised to the extent that they approach monopoly.
2) Selling to one poorer person earns less revenue than selling to one richer person, but it's already the case that there many more poor people than rich people, and numbers of smaller sales can make up for smaller numbers of larger sales, although the reduction in profit may make previously viable production and service provision no longer viable. However this slack can be picked up by newer and poorer businesses who don't lose out to selling to poor people, and gain from taking money off the hands of the rich - enabling the constraint within the optimised Pareto distribution behind this model.

In the possible case that these two potentially negative considerations are more detrimental than beneficial, it may be advisable to restrict the exchange rate system only to non-business transactions and only partly or not at all to business entities (including sole traders) who can prove their transactions relate to business. However this may not be necessary upon full consideration of the game theory of the Pareto model that I'm proposing.

The model actually introduces an incentive for richer and successful people to spend their wealth instead of hoard it, in order to make the most cost-effective use of the exchange rate system, alongside the incentive get recognised as being able to achieve a high Elo rating, and to be seen as significant contributors to the less wealthy. Current usage of the Elo rating system sees no less fierce and innovative competition at the top levels. There's no danger of people stopping trading once they've achieved a high rating, unless they go fully off-grid and self-sufficient, which is perfectly acceptable - but trading outside of the rules of the exchange rate system would have to be as illegal as it currently is to trade counterfeit currency. To take advantage of what society can give that self-sufficiency can't, you have to spend your rating to buy what you want and need - the rating is designed to fluctuate as much as account balances already do. In this way it's not a score to try and keep high at all times, as this penalises you - so it isn't comparable to the dystopian models like the Chinese social credit system.

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### Re: A Pareto Distribution of Wealth

All I know is that modern consumer capitalism can't work and function when you make half the population destitute or poor. That is why I definitely believe in social economic reforms.

I also don't think the current economic systems are able to politically reform themselves because the entire global economy currently is on the verge of collapse. Even if you wanted to reform things you can't, that ship has long since sailed away where it is never coming back again. There is only internal systematic economic destruction dead ahead along with major social and societal disruptions that will be mercilessly brutal. This has all been in the making for the last five decades and there is no stopping it now. Too little, too late. All that is left is violent revolution because all other options were eliminated or taken off the table where the political establishment doesn't even want a public debate on the subject anymore. When all else is extinguished where people have no other available civil recourse violence is all that is left.
"I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! "-$$Zero_Sum Evil Neo-Nazi Extraordinaire. Posts: 2815 Joined: Thu Nov 30, 2017 7:05 pm Location: U.S.S.A- Newly lead Bolshevik Soviet block. Also known as Weimar America. ### Re: A Pareto Distribution of Wealth Zero_Sum wrote:All I know is that modern consumer capitalism can't work and function when you make half the population destitute or poor. That is why I definitely believe in social economic reforms. I also don't think the current economic systems are able to politically reform themselves because the entire global economy currently is on the verge of collapse. Even if you wanted to reform things you can't, that ship has long since sailed away where it is never coming back again. There is only internal systematic economic destruction dead ahead along with major social and societal disruptions that will be mercilessly brutal. This has all been in the making for the last five decades and there is no stopping it now. Too little, too late. All that is left is violent revolution because all other options were eliminated or taken off the table where the political establishment doesn't even want a public debate on the subject anymore. When all else is extinguished where people have no other available civil recourse violence is all that is left. You don't present yourself anywhere close to being someone who is likely to change their mind, regardless of any contrary evidence/reasoning, but in the interest of addressing your opinions: Any internal systematic economic destruction that we may or may not be facing, inevitably or otherwise, the situation we're currently in is in large part due to the inability of our current model to internally keep itself in check. Anything that lacks the internal mechanics to keep it stable will fly apart, break or at least cause avoidable suffering or disharmony. This is why I present a model that corrects the internal mechanics of what we have to not only inherently keep itself in check, but optimally. Perhaps you're right and it's too late, perhaps you're not. Until the fat lady sings, I'm going to fish around for solutions in case the fate of which you're so certain can be avoided. As someone who is not a time traveller, I will consider you no absolute authority on the future beyond the "problem of induction" to which everyone is equally liable. If you'd prefer to do nothing or perhaps even assist in fulfilling your revealed prophecy, just to be more likely to be able to say "I told you so" at the end, I can't stop you. You do you, I'll do me. My next step will probably be to attempt to test this through some kind of programmed simulation. That's a more challenging task, at least to make such a simulation sufficiently true to the real world, but at least the maths is out of the way. Silhouette Philosopher Posts: 4034 Joined: Tue May 20, 2003 1:27 am Location: Existence ### Re: A Pareto Distribution of Wealth Silhouette wrote: Zero_Sum wrote:All I know is that modern consumer capitalism can't work and function when you make half the population destitute or poor. That is why I definitely believe in social economic reforms. I also don't think the current economic systems are able to politically reform themselves because the entire global economy currently is on the verge of collapse. Even if you wanted to reform things you can't, that ship has long since sailed away where it is never coming back again. There is only internal systematic economic destruction dead ahead along with major social and societal disruptions that will be mercilessly brutal. This has all been in the making for the last five decades and there is no stopping it now. Too little, too late. All that is left is violent revolution because all other options were eliminated or taken off the table where the political establishment doesn't even want a public debate on the subject anymore. When all else is extinguished where people have no other available civil recourse violence is all that is left. You don't present yourself anywhere close to being someone who is likely to change their mind, regardless of any contrary evidence/reasoning, but in the interest of addressing your opinions: Any internal systematic economic destruction that we may or may not be facing, inevitably or otherwise, the situation we're currently in is in large part due to the inability of our current model to internally keep itself in check. Anything that lacks the internal mechanics to keep it stable will fly apart, break or at least cause avoidable suffering or disharmony. This is why I present a model that corrects the internal mechanics of what we have to not only inherently keep itself in check, but optimally. Perhaps you're right and it's too late, perhaps you're not. Until the fat lady sings, I'm going to fish around for solutions in case the fate of which you're so certain can be avoided. As someone who is not a time traveller, I will consider you no absolute authority on the future beyond the "problem of induction" to which everyone is equally liable. If you'd prefer to do nothing or perhaps even assist in fulfilling your revealed prophecy, just to be more likely to be able to say "I told you so" at the end, I can't stop you. You do you, I'll do me. My next step will probably be to attempt to test this through some kind of programmed simulation. That's a more challenging task, at least to make such a simulation sufficiently true to the real world, but at least the maths is out of the way. The problem with social economic theoretical philosophers is that very few cross examine their own beliefs with prevailing current data in worldly state of affairs. I try not to make this mistake myself where I very much keep up with global current events. When you take a look at this thread of mine here below, what's the first thing that comes to your mind? Do you still believe things can be salvaged? Factor in your simulations for all of that. viewtopic.php?f=48&t=195312&start=25 "I'm sorry, but the lifestyle you've ordered that you've grown accustomed to is completely out of stock. Have a nice day! "-$$\$

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### Re: A Pareto Distribution of Wealth

Zero_Sum wrote:The problem with social economic theoretical philosophers is that very few cross examine their own beliefs with prevailing current data in worldly state of affairs. I try not to make this mistake myself where I very much keep up with global current events.

When you take a look at this thread of mine here below, what's the first thing that comes to your mind? Do you still believe things can be salvaged? Factor in your simulations for all of that.

http://ilovephilosophy.com/viewtopic.ph ... 2&start=25

It's a bunch of charts mostly showing some alarming signs of economic downturn, not immediate imminent collapse. You don't think I'm aware of this? I think you're overestimating the amount of collapse required to bring down the entire Western economy in spite of all its infrastructure and the willingness of servile humans to sink to ever lower lows just to keep the illusion of things going in the short to medium term. Historically you need far more of the population to be starving to actually turn to violence, especially in cultures with generations of compliance and complacency like we have in the West.

This is what capitalist advocates thrive on: the ability to dismiss claims that Capitalism is collapsing because things have so much further to go for it to complete its collapse. Don't get me wrong, it's headed in the direction of collapse, I just disagree that any of the data you show necessitates that it's just around the corner, and as long as you're claiming it is just around the corner, the more pro-capitalists can laugh at you in their compliance and complacency.

Instead I'd recommend calling the data as it is - like I am, rather than blowing it out of proportion in an eagerness "to watch the world burn" as you model yourself with this "Joker" persona. You probably won't live to see it, and me neither. It's on an undeniable downturn, but that's it for now - it will continue for as long as people don't look at the root causes like I am, and implement solutions that are workable in the real world and not just the same as we've already been trying and failing for generations now. "Tax this, prohibit that" doesn't work like all the reformists keep suggesting like a broken record, but an internal exchange rate based around the Pareto Principle is a simple solution that nobody's thought of before, that can use the system we already have to solve itself without resorting to government coercion. "Rebel! Violence!" is the same broken record of revolutionaries, in complete underestimation of the strength of the spell that enslaves the vast majority of people to "keep calm and carry on". Revolution and doomsaying has no political power, sorry. Reform is where political power is, and I'm readying my solutions for the point where people finally admit the usual reforms objectively aren't working and things get desperate enough to hint at finally inspiring what you're suggesting, which is a looong way off. But like I said, you have your identity invested in your soothsaying, so there's no way you're going to even consider adjusting your viewpoint.

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