
Power Laws and Rich-Get-Richer Phenomena (2010) [pdf] - marojejian
http://www.cs.cornell.edu/home/kleinber/networks-book/networks-book-ch18.pdf
======
specialist
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.

~~~
mhneu
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
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](https://www.youtube.com/watch?v=r6LLQdpY7wU)

~~~
tdb7893
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.

~~~
harry8
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.

~~~
thwarted
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.

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

~~~
harry8
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?

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soVeryTired
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](https://arxiv.org/abs/0706.1062)

~~~
egocodedinsol
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.

~~~
soVeryTired
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.

------
sharemywin
Here's link to the whole book:

[http://www.cs.cornell.edu/home/kleinber/networks-
book/](http://www.cs.cornell.edu/home/kleinber/networks-book/)

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

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baybal2
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.)

~~~
mjburgess
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.

~~~
baybal2
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.

~~~
mjburgess
> 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.

~~~
baybal2
Are you a professional economist?

------
ouid
>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
> 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."

~~~
ouid
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_.

------
Nomentatus
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.

------
ForHackernews
Related [https://ofdollarsanddata.com/why-winners-keep-
winning-4e7f22...](https://ofdollarsanddata.com/why-winners-keep-
winning-4e7f221f5b84)

------
atmoz
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](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](http://networksciencebook.com/images/ch-05/figure-5-4.jpg)

------
arnold8020
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/](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/](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/](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.

