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Power Laws and Rich-Get-Richer Phenomena (2010) [pdf] (cornell.edu)
139 points by marojejian 9 months ago | hide | past | web | favorite | 39 comments

Preferential attachment, power laws, rich-get-richer, winner-takes-all is just math. Life (fortune, luck) is intrinsically unfair.

Explaining reality is not a moral statement.

Ignoring reality, or worse rationalizing it, is immoral.

Happily, thru the arc of humanity history, numerous societies have chosen to mitigate the unfairness. Some proven strategies are expanding the franchise (enfranchisement), redistributing windfall profits, debt jubilees, jobs programs, social safety nets.

Bloody revolution with the peasant class murdering the elites has been quite a popular way of mitigating the unfairness in the past too. Possibly the most popular in fact.

Most popular? Maybe. Least successful, definitely. It's the nuclear option of "to hell with it all, let's burn down everything we have including the hospitals and schools to get at /them/." You've already got an abject disaster when that really doesn't seem so bad.

But in the past did the elites have a protection force as comprehensive and organized as the one they have now, all funded by the very people it is protecting them from?

Taxes have existed for a very long time.

Indeed they have, but if you reread my comment you may notice that taxes were only one component of the comment.

I'm noticing a distinct increase in ideologically motivated comments and a corresponding decrease in honest discourse. But then, why should HN be immune from it, it is fed by the same institutions as mainstream society.

Yes. The authors basically explain the rich-get-richer macro phenomenon as a consequence of individual interactions.

And it's easy to see this rich-get-richer phenomenon in action. Look at European football (soccer). There, once a team gets wealthy, it can buy the best players and continue to stay on top. That's the winner-take-all phenomenon right there.

Sports in the US have addressed this winner-take-all problem with socialism. Baseball, American football, hockey, and basketball have drafts, where the best new players get distributed to the worst teams. Such non-market, socialistic practices work to the benefit of the league because they put all teams on a more even playing field. (Restrictions on the free agent market, the football scheduling difficulty increase with winning, arbitration, and max contracts are all also forms of socialism that act to restrain the free market for players).

These are not bad examples of how completely free markets lead to unfair winners' advantages, and inequality. They also provide good examples of the kind of market regulations and protections that can level the playing field (no pun intended.)

Sports in the US are exempt from anti-monopoly regulations, so they don't resemble markets in the first place.

Baseball could, theoretically, also be efficient by allowing entrepreneurs to start a new team with new Moneyball-like principles or even deeper pockets. But to buy or start a new team, you need your competition (the other teams) to agree with your plan. That's not an open market even slightly.

The talent pool in professional sports is actually a closed market that runs on the rules of the market operators (i.e. the MLB/NFL league administration). The capitalism/socialism comparisons are easy but wrong.

True natural monopolies are exceedingly rare and usually short-lived — most monopolies created by government[0]. What we observe with startups and venture capital is no exception: the Fed's continuous monetary expansion policy has driven more money into more volatile investments as investors try to achieve 'escape velocity' on their returns, and success has a natural compounding effect.

[0] https://www.youtube.com/watch?v=r6LLQdpY7wU

What he was talking about was the impact of the specific rules that the market operators imposed so I'm a little confused how the market having rules invalidates the comparison.

The team owners of professional sports setting up an employment cartel so that they can systematically pay labour less than its market worth is not socialism or anything like it. These are literally billionaires making the rules in favour of their own bank balance.

disclosure: not a socialist. Don't care for socialism at all. But it's not fair to tar socialism with billionaires feathering their nests driving down the relative return to labour vs capital, imho. It's just regulatory capture by its textbook definition. Total and complete regulatory capture, in fact.

This is about the economic environment composed of teams and games won where the medium of exchange is talent, and how the rules for how access to talent and other restrictions enable a more level playing field that keeps any one team from dominating the talent pool and winning all the games.

It's not about the economic environment of billionaires and how they leverage their cash hordes to underpay their employees. The regulations mentioned would apply no matter how the pay range for talent was scaled relative to the owners.

We can talk about the economics of something without shitting on socialism or shitting on capitalism or having disclaimers about which system the speaker does or doesn't like best.

Thank you. Well-put. Yes, I was referring to the market for talent.

There is an incredible naivete there if you think that the market for talent (ie labour) is being rigged without it being in the owners interests by design, first and foremost. I'm a little flabbergasted that you both don't see it for what it plainly is. Restraint of trade and regulatory capture. (Argue it's good and necessary and patriotic and the owners have done a perfect job that just happens to make them vast amounts of money as an unintended side-effect if you must but it is what it is!)

A better way of levelling the playing field would be league appropriation of all revenue above $x on a sliding scale for redistribution to poorer teams, yet have the players able to play where they want with no restraint on the market for their salaries.

What you'd get there is owners making dramatically less profit and players making vastly higher salaries. So why not that model? It's un-american! There are other models you can use if you want equality between teams. If you think it has anything to do with factors other than the owners want the money in their pocket and have the power to get it where the players presently don't I can't really help you resolve that. I do note that it is difficult to think of things in a fresh way when you've grown up with them constantly being in the background with an oft-repeated justification. Hard for all of us. I didn't grow up with american accented sports so I guess that's easier for me?

The owners would all scream, shriek and wale if anything like the restraints on the players was placed on literally any of their business interests. Imagine if for the good of all of america's industry the market for senior executives was subject to the same restraint of trade to level the playing field between mining, steel, tech, banking, retail, building materials, etc etc. So that all of America's industry can be strong and compete. No exec getting paid a million a year could complain, surely. Sportsmen can't because they're rich, right?

> Ignoring reality, or worse rationalizing it, is immoral.

What does it mean to be ignorant of reality?


True, though that brings up other ethical dilemmas.

For instance?

The guillotine? The ethical question is whether it is right kill someone. Most folks find that troubling in standard circumstances.

I disagree; I think that most people would consider whether or not the guillotine is being used in service of justice, against cruelty to the powerless by the powerful.

For what it's worth, showing a straight line on a log-log plot isn't really enough to demonstrate existence of a power law.

Most papers that test for the existence of power laws don't test goodness-of-fit for other distribtions. The lognormal distribution is often just as good a fit to the data. This paper covers a lot of the frequent problems in academic literature that tries to fit power laws:


Yes! And that paper is a fantastic example of making clear criticisms with actionable fixes and the code to perform the comparisons properly.

Preferential attachment is such a beautiful theory because it gives power law distributions of node degree. But real world networks seem to have systematic deviations from power law so often one wonders why more work wasn’t done to find schemes that generate, e.g. lognormal distributions.

It’s possible that preferential attachment isn’t even a good theory for the underlying principle, it’s just that the underlying principle gives fat tails in degree distribution and power laws give okay fat tails.

Sometimes, though, one doesn’t care if it’s a power law per se or just that it has fat tails. In that case why use a power law and not just a better fitting lognormal (or say kernel density estimation)? But power law seems sexy because of its importance in physics (eg scale free, renormalization stuff), so people ran with that when network literature blew up in the mid 2000s.

The cynic in me says the econ literature cares much more about elegant theory than how the data fits the theory, so they just go with a low-power test that makes their pet theory credible.

Here's a recent follow-up paper [1] testing exactly that on many diverse datasets, positing that scale-free (power-law distributed) networks are actually not that common in the real world. Quanta has a nice article about it [2].

[1] https://arxiv.org/abs/1801.03400

[2] https://www.quantamagazine.org/scant-evidence-of-power-laws-...

"6. (Mar's Law) Everything is linear if plotted log-log with a fat magic marker."


This is one of my favorite textbooks. Super readable, and great intros to the links between graph theory and economics.

This is not a case of this being some kind math or graph theory phenomenon. In the Western world, it is to very big extend thanks to the rich being given a privileged status by the monetary policy.

In all Western countries - the state is the ultimate creditor. The bigger you are, the closer you are in line to the money water tap, the easier it is to get loan financing for your businesses or (more often this days) LBO play. It is few rich people in the West who "made" their own money through business revenue.

Second to that is the existence of stock market, where the people closer to the financial water tap, park all money they got from it.

As for why it happens in poorest counties, it easier to understand there. In much of them the top 10 "businessmen" will be former officials (if not acting one.)

The whole point of this is that explanation isn't true. Productivity is not a conspiracy theory. 80% of the output is done by 20% of the people.

At some time t=0 advantages are randomly distributed. At t=1, those who happened to have them capitalized on them to increase their productivity (20%). At t=2, 20% of those increase. At t=3, 20% of those increased.

This happens without any corruption, "teats", "governments", and equally resentful conspiracies.

No, the banal statistical explanations are not applicable here. If one does not see this point, they are very detached from reality.

>The whole point of this is that explanation isn't true. Productivity is not a conspiracy theory. 80% of the output is done by 20% of the people.

To begin with, what mainstream economists count for productivity is, excuse me, purest BS. Making money out of thin air does not count for producing anything, by the very definition.

You deny a simple fact that the richer the person is, the easier it is for him to secure a loan on a more favorable terms than a poorer person. This also works without any "conspiracies," this is purely a feature of the economic system where somebody can print and loan away money.

This works to the extend that a person with person with good connections with bankers in 1st tier banks can secure a deeply subprime loan in many Western countries.

> You deny a simple fact that the richer the person is, the easier it is for him to secure a loan on a more favorable terms than a poorer person.

No, that's exactly how it should be. Productivity increases reputation, which is rewarded by people betting on your future productivity.

Banks lend according to expected returns, of course they lend to those who can return. There is no other stable system of lending: it is always a bet on expected future productivity. Anything other than this would be self-destruction.

> Making money out of thin air does not count for producing anything, by the very definition.

The value of money is how productive an economy is. You can create money out of thin air (ALL MONEY IS), but you cannot create value-producing economic transactions out of thin air.

> this is purely a feature of the economic system where somebody can print and loan away money.

No that's tabloid economics used to justify prior resentment. Human history, and any system of production, follows power-law distributions. It hasnt anything at all to do with quantitative easing or finalization: these just, at worse, dilute the value of a currency.

Are you a professional economist?

>the question of how popularity is distributed over the set of Web pages ... A natural guess is the normal, or Gaussian, distribution — the so-called “bell curve”

If this is your guess, then you have absolutely no idea what you are doing.

> absolutely no idea what you are doing.

Isn't that sort of the idea of a textbook? The authors emphasize how poor of a model the normal distribution is in that case less than a full page after introducing it as a "simple hypothesis."

It's not a simple hypothesis, and it's extremely lazy pedagogy. It's not a reasonable guess if you can't establish any reasoning that would lead you to it, and even if you could, in a textbook, I expect your guesses to be more than reasonable, I expect them to be actually reasoned.

The author Jon Kleinberg literally invented the HITS algorithm -- the precursor to Google PageRank.

The collapsing black hole, as I called it many years ago. Eventually there's not enough power outside the inner circle to reverse the concentration of wealth and power: at least, that was Marx's analysis, particularly of the cycles of warlordism (of a few centuries) in Chinese history, if I remember rightly. Enough time and the aristocracy becomes incompetent and dissolves into revolution and the cycle starts again.

I just happened to deliver an assignment today about The Barabási-Albert Model. We use this book in class (you can read it online): http://networksciencebook.com

I had to plot the degree distribution against a power law. Looked something like this (taken from chapter 5): http://networksciencebook.com/images/ch-05/figure-5-4.jpg

Below is a repost, but fits very appropriately here, the results are very similar! The pdf pre-dates my small work on this, but you may find the simulation interesting,


Basically you need two things:

1) Some slight advantage

2) The network effect, that is, for example, the probability of competing depends on the current winnings.

(compare with the linked pdf, pg: 548 'Why do we call this a “rich-get-richer” rule? Because the probability that page L experiences an increase in popularity is directly proportional to L’s current popularity.')

If you have these two things, you get 80-20 like distributions, you get the explanation for why winners keep winning. If you are interested, you can find my simulation and analysis at


Kind of shocking how well this works. The intuition is, why has Coke won, well they had some initial advantage, and so they won a bit. Now that they have won a bit, they can finance themselves into more competition. For example, they can place themselves into more stores, into more restaurants etc. Now they get a chance to compete more. When I run with rules:

r1) Actors have normally distributed abilities,

r2) Actors are chosen randomly based on current winnings, the more you have won, the more you compete,

r3) Winner of competition wins one point from the loser,

You get interesting results, for example, in the two columns below, the left is Household income in 1970 broken into quintiles. The right column is simulation results.

    4.1%                         6.7%

   10.8%                        11.5%

   17.4%                        16.0%

   24.5%                        23.3%

   43.3%                        45.6%
Interesting how well the top 3 or 4 quintiles match between the simulation and the real world data.

More such comparisons can be found at http://www.cs.toronto.edu/~arnold/research/80-20/

If you run the simulation with different rules, the real world quintiles do not match the simulation quintiles nearly as well. You can tweak the simulation to see this as well.

The simulation can be tweaked to handle cases such as inheritance, so an actor with different ability inherits the wealth of a past actor. When I run this simulation, around 80-90% of top 20% actors lose all wealth in 3 generations.

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