Pareto Distribution & Price's Law Dr. Jordan Peterson

so okay so now there's a number of
things to consider if you're thinking
about performance prediction and one of
them is to what degree do people vary in
terms of their performance capacity and
you might say well there's very little
performance variability or you might say
there's a tremendous amount of
performance variability or you might say
there's an absurd amount of performance
variability and it turns out that the
claim that there's an absurd amount of
performance variability is the proper
claim IQ is normally distributed so is
conscientiousness but productivity is
distributed along the purrito
distribution and I'll show you why and
that follows a law called prices law
from someone named Derek to soul a price
who was studying scientific productivity
in the early 1960s and what he showed
was that a vanishingly small proportion
of the scientists operating in a given
scientific domain produced half the
output and so what you see and this is
what's happening is that to do really
well at a given productive task which
would also include generating money as a
proxy for for creative productivity is
that you have to be a bunch of things
have to go your way simultaneously so
maybe you have to be really really smart
you have to be really really lucky you
have to be really healthy you have to be
really energetic you have to be really
conscientious you have to be in the
right time at the right place and maybe
you also have to have the right social
network right like so it's a lot of
things and each of those are small
probability they're each of those are
small probabilities and then if you
multiply the small probabilities
together you get an extraordinarily tiny
probability and you have to have all
those things functioning before you're
going to end out on the on the extreme
end of the productivity distribution but
if you do end up there then you produce
almost all of everything so it's a tiny
number of people that produce almost all
of everything that's prices law and
technically it is and I mentioned this
to you before it's the square root law
the square root of the number of people
in a productive domain produce half the
output right so if you have ten
employees three of them produce half the
output if you have a hundred ten of them
produce half the output if you have
10,000 a hundred of them produce half
the productive output and so what that
also means is that because there's
massive variability in performance you
don't have to shift your ability to
predict performance very
they're very very much up towards being
better at it to gain substantially on
the positive side because there's so
much difference in productivity and that
actually happens to be also a function
of the complexity of the job if the job
is simple which is means you can this
job has ten rules you know that's a
janitorial job let's say you know you do
you it takes a little while to learn it
but once you've learned that you
basically do the same thing all the time
there's not a lot of performance
variability in those jobs and most of
that would be eaten up by
conscientiousness and also to some
degree by neuroticism because the higher
people who are higher neuroticism would
be more likely to miss work but you're
but but general cognitive ability for
example is not a good predictor at all
it'll predict how fast you learn in the
tasks initially but not how well you
perform the test but if the tasks you're
doing are shifting constantly so your
responsibilities change or you're in a
creative job where you're constantly
solving new problems those are kind of
the same thing then IQ as the complexity
of the job increases the predictive
utility of IQ increases which is only to
say that smarter people can handle
complex situations faster so that
doesn't seem like a particularly radical
claim so prices law dictates that
there's massive individual productivity
differences between people so increasing
your predictive your capacity for
predicting performance even by small
increments has a huge economic
consequence that was established in the
1990s the equations were first developed
in the 1990s and that's part of the
reason that I started working on
performance prediction tests because I
read the economics and I thought oh my
god you can produce a test that costs
$30 x say maybe you have 50 applicants
for the position $1500 to administer and
it'll produce and the increments of
something like thirty percent of salary
permanently for the person that you put
in the position so let's say you hire a
$75,000 employee and it increases their
productivity by 30%
so we'll say roughly $25,000 you get a
$25,000 return on a $1,500 investment
every single year that person occupies
the position on average that's four
years that's $100,000 pay off for your
$1,500 investment I read that I thought
ho-ho that'll be easy
to sell its like wrong wrong even though
the economic payoff was so massive I
told you the other impediments that did
emerge but the arithmetic are the
capacity to produce these calculations
was established in the in the 1990s and
I'll show you the equations in a bit
here ok so we already talked about what
a normal distribution looks like that's
the red line and a normal distribution
emerges as a consequence of chance
processes so we'll take a look at those
here all right so here's a Pareto
distribution this is the distribution
remember I showed you with the creative
achievement questionnaire that almost
everybody stacked up at zero people have
zero creative output the median person
has zero lifetime creative output and
then there's a tiny proportion that are
way the hell out on the you know right
hand end of the distribution right those
are the people have hooves everything is
cycling forward for them and as they get
more well-known of course they get more
opportunities as well so I just I'll
just run this simulation for you ok and
and this shows you why the Pareto
distribution emerges now you have to
watch this quickly because it's a fairly
fast animation so here's what happens
everybody starts out with ten dollars
there's a there's a thousand people
playing the game everybody starts out
with ten dollars we I have a dollar you
have a dollar I flip a coin if I get
heads you give me a dollar if I get
tails I give you daughter we go around
and we trade with everyone okay so the
first thing that happens when people
start to trade is this normal
distribution develops right because some
people lose and some people win it's
just like the golden board that I showed
you okay so you keep playing people
start to stack up a zero watch because
they lose ten times in a row bang
they're done the bottom graph is a graph
of the entropy of the distribution which
increases us the game continues because
at the beginning it's maximally ordered
right everybody has exactly the same
amount now it's being distributed same
equations apply to the distribution of
gas into a vacuum well what happens now
someone you know there are people out
there at the at the 50 dollar range or
at the $60 range at the 70 dollar range
you keep playing it well eventually what
happens if you play it right to its
conclusion is that one person ends up
with all the money
that's to those who have everything more
will be given from those who have
nothing everything will be taken that's
the law of economic productivity
it's called Matthew is the Matthew
principle and it's actually an economic
principle that was derived from a saying
in the New Testament I'll tell you some
more about this on Tuesday because I
didn't get through all of it I want to I
want to finish up the performance
prediction lecture and show you a couple
of things I didn't get to show you the
last time that we talked and then I want
to do the closing lecture since we're
done today so we'll start with the
performance prediction and so I've been
thinking more about this Pareto
distribution issue because it's it's a
really big deal and and I it's it's
difficult it's still difficult for me to
understand see I didn't really learn
about this till about ten years ago
which is quite a shock to me because
it's such a fundamental phenomena that
it seems to me that it would have been
addressed in my training somewhere along
the way and so and so I'm still thinking
it through what it means exactly now
here's here's an interesting thing you
know that IQ is normally distributed and
it's a good predictor of long-term
performance and conscientiousness is
normally distributed and it's a good
predictor of long-term performance and
so and openness is also normally
distributed and it's a good predictor of
creative behavior but creative output is
not normally distributed it is
distributed in this weird Pareto
distribution that that's indexed here
and I showed you that with the creative
achievement questionnaire most
specifically because that provides a
really concrete example of it so it
looks like the capacity to think
creatively might be normally distributed
that would be openness say and
intelligence but the consequence of that
turns into this strange Pareto
distribution and the Pareto distribution
with regards to creative achievement was
best the the catastrophe of it in some
sense is best indexed by the fact that
if I remember correctly 70% of people
who complete the creative achievement
questionnaire which indexes lifetime
creativity score zero so and zero is a
strange number you know zero isn't like
other numbers and that part of the
reason for that is that it's difficult
to do anything with nothing
so you know if you if you buy a stock
and them and the price syncs to you like
- Sansa Stark you're still alive but if
the price sinks to zero you're done
right that's it the game's over and
that's the thing about zero when you're
hit zero or maybe when you're at zero
the game is over and so there's these
weird barriers to moving forward in life
and you see this there's a poverty trap
that's sort of like this - like if
you're if you're so broke that you can't
keep up with paying your bills it's
really really difficult to get out of
that because you can't get a bank
account for example and you can't pay
your rent I said and that there's
there's there's economies of scale that
you can't take advantage of because you
don't have any money at all and so you
can't get going in the game and then so
there's the problem of starting out with
zero which is a big problem and very
difficult to get out of and then there's
the problem of falling to zero if you
are in the game because when you fall to
zero that it's very difficult to get
going again and so now I want to show
you something about how how trading
games work so I think we stopped we
closed with this last time but so this
is a this is a graph that shows you how
a Monopoly game starts roughly speaking
but you could say this is how you would
set up the world if you wanted perfect
equity if you wanted everybody to have
the same outcome everybody would have
the same amount of money in this case
it's ten dollars and so it's it's it's
dollars along the along the bottom axis
and it's number of players along the
left hand a axis and you can think about
this as a Monopoly game everybody starts
since the same amount of money and then
you start trading randomly and you know
if if you have $10 and you're trading $1
each trade if you have enough people
some unlucky person is going to end up
with zero dollars after ten trades and
if they end up with $1 after nine trades
they still have a chance of recovery
it's a low chance but it's not zero but
once they hit zero they're out of the
game and so what happens is if you run
this simulation you have people flip a
coin to determine how they're going to
trade then this is what happens so the
first thing that happens is you generate
a normal distribution because some
people win and some people lose and most
people sort of half win and half lose
but some lose continually and some win
continually and so it turns into a
normal distribution that's
but then when the game continues to play
then what happens is that people start
to stack up on 0 end of things and a
tiny proportion at the upper end and if
you play the game right to cessation
which is what you do if you play
Monopoly for example somebody ends up
with all the money and the funny thing
about playing Monopoly as you know if
you've played Monopoly multiple times is
that the probability that you'll win
continually across games is pretty low
you know there's a lot of randomness and
monopoly and if you play with the same 5
people 10 games the probability is
pretty good you're not going to win more
than two games so so there's chance
elements that come into play that
determine the outcome and and so anyways
I was thinking about this more a little
bit more last night and somebody asked
me I was talking about it with somebody
and he asked me if the Pareto
distribution was a necessary consequence
of the fact that production is number
one measured and number two social and
that's that I thought that was a really
interesting question it's like do you
get a preeto distribution every time
creative output ends up being measured
in some way and even if you can
conceptualize it so because it might be
the the idea might be that anything that
you can assign monetary value to is
first of all is something you can
measure because assigning monetary value
to something is in fact measuring it
right you're measuring it with money and
then as soon as you assign a monetary
value to it you can you can trade it you
can trade it and it also takes on some
aspects of a zero-sum game and most of
the things that we talked about with
regards to the production of period of
distributions were measured entities and
were were were trading games as well so
even because I mentioned to you for
example that number of of basketball
hoops successfully managed by NBA
players is freed or distributed but
that's also those are measurable with
money because of course you get paid to
do it and it's an it is a social game
and so maybe it is inevitable
consequence of trading in a social game
that you produce pre Doyle comes and
then I was trying to figure out why and
I've always had the suspicion that what
happens to people is that as they move
toward zero
the feedback loops get set up so they're
more likely to hit zero and as they move
away from zero positive feedback loops
get set up so that they're increasingly
more likely to move away from zero