Power Laws and Rich-Get-Richer Phenomena (2010) [pdf]

http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch18.pdf

by marojejian • 8 years ago

139 35 8 years ago

cs.cornell.edu

sharemywin• 8 years ago

Here's link to the whole book:

http://www.cs.cornell.edu/home/kleinber/networks-book/

showerst• 8 years ago

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

ForHackernews• 8 years ago

specialist• 8 years ago

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.

mhneu2• 8 years ago

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.)

nateabele• 8 years ago

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

humanrebar• 8 years ago

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.

onion2k• 8 years ago

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.

harry83• 8 years ago

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.

mistermann2• 8 years ago

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?

s-shellfish• 8 years ago

Ignoring reality, or worse rationalizing it, is immoral.

What does it mean to be ignorant of reality?

atmoz• 8 years ago

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

ouid2• 8 years ago

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.

twtw• 8 years ago

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."

ouid2• 8 years ago

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.

Hydraulix989• 8 years ago

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

Nomentatus• 8 years ago

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.

baybal23• 8 years ago

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.)

mjburgess2• 8 years ago

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.

baybal23• 8 years ago

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.

soVeryTired2• 8 years ago

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:

https://arxiv.org/abs/0706.1062

egocodedinsol• 8 years ago

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.

soVeryTired2• 8 years ago

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.

transcranial• 8 years ago

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-...

jk4930• 8 years ago

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

https://spacecraft.ssl.umd.edu/akins_laws.html

arnold8020• 8 years ago

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,

http://www.cs.toronto.edu/~arnold/research/80-20/

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

http://www.cs.toronto.edu/~arnold/research/80-20/

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.

Power Laws and Rich-Get-Richer Phenomena (2010) [pdf]

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