Transcript Survival under uncertainty

Dimitri Volchenkov: Probability Models of Survival
/ Communication/ Inequality
Survival Under Uncertainty
An Introduction to Probability
Models of Social Evolution
State secession in 1800-2014
•The mean lifetime
of a state is 122
years;
•Half–life of a state
84.53 years
Survival Under Uncertainty
An Introduction to Probability Models
of Social Evolution
State secession in 1800-2014
• •The mean lifetime
of a state is 122
years;
•Half–life of a state
84.53 years
Structure of uncertainty
Interplay of
many random
factors
May evolve on
the different
time scales
Uncertainty
objective
uncertainty
subjective
uncertainty
A sudden volcanic eruption and an occasional fail to
pass a test manifest the different types of
uncertainty that we may face.
A species subsists as long as the means
available suffice to maintain it
• with probability h , the level of
demand d is chosen from the
probability distribution function F
while the level of supply s keeps the
value it had at time t − 1, or
• with probability 1 − η, the level of
demand d is updated anew from the
probability distribution function F, and
the level of supply s is updated either,
with respect to the probability
distribution function G.
We assume that the species survives as long as d < s, but dies out immediately
after the carrying capacity of the habitat is exceeded, d ≥ s.
Factors of objective and subjective uncertainty may
challenge our survival across different time scales.
s  [0, 1], the available
amount of resources (supply)
s  0,1: Prs  u  Gu 
d  [0, 1], the needs for
subsistence (demand)
d  0,1: Prd  u F u
s revaluated
Prrenewed s  1  h
h  0,1
t  t 1
s unchanged
Prs retained   h
s ≥ d, satisfaction
d >< s
d > s, dissatisfaction
Survival is longer in the case of a stable supply level
(under singular uncertainty) than in the case of the
coherent random updates of supply and demand
(under dual uncertainty).
Probability of subsistence under uncertainty
Transitory subsistence under dual uncertainty


1


Ph 0      dG  y F  y 
0
  
1



1
 dG y 1  F  y .
0
A species has a fairly regular rate of extinction, in
line with the observations of Leigh Van Valen on that
all groups of species go extinct (in million years) at a
rate that is constant for a given group.
Extraordinary longevity under singular
uncertainty
1
Ph 1     dG y F  y  1  F  y 

0
The absence of a characteristic time scale indicates that
virtually all ages may present in a population, including
individuals of extraordinarily long life spans (”centenarians”).
When the factors responsible for the objective and subjective
types of uncertainty evolve on the incomparable time scales,
there are no mass extinction in the population.
Zipf’s longevity in a land of plenty
Probability
What are the best possible chances for subsistence under
uncertainty?
The best possible chances for survival under
uncertainty abide the Zipf law.
On the Optimal Strategy of Subsistence
under Uncertainty
1. Initial destabilization of the
environment at each time
step;
2. Intermediate stabilization
of the environment by
keeping the level of supply
unchanged;
3. A “safe haven in a land of
plenty” is required in order
to enjoy extraordinary
longevity.
Interaction statistics in organizations
The radio-frequency identification sensors reported
on occasions of physical proximity
• H-art
~71 assigned to multiple projects.
employees → functions
• H-farm
~ 75 employees and hosted 9
start-ups
employees → start-ups
• We have analyzed face-to-face interactions in two
organizations over a period of three weeks;
• Data on interactions among ca 140 individuals have been
collected through a wearable sensors study carried on two
start-up organizations in the North-East of Italy.
Interaction Intervals Statistics
minutes
Duration of intervals between
sequent communications (min)
The both distributions are remarkably skewed,
indicating a significant proportion of the abnormally
long periods of activity/ inactivity.
normal distribution
algebraic decay
Zipf’s d. + finite size effects
Duration of intervals between
sequent communications (min)
The both distributions are remarkably skewed,
indicating a significant proportion of the abnormally
long periods of activity/ inactivity.

exp  t 2 22.05
2


exp  t  2  21.78
2 2.05
2
2
2

2 1.78
2
1 t  1t  2   1
t   t 3 , t  1
1
t
1
t2
,   103
decision making model
 t 1 0.09
our individual propensity to be engaged into
an interaction act can be characterized by a
certain threshold;
our potential partner is able to motivate us
at time t to interact with her by providing a
strong enough reason;
If
xt  xc we accept invitation to interact.

exp  t 2 22.05
2


exp  t  2  21.78
2 2.05
2
2
2

2 1.78
2
1 t  1t  2   1
t   t 3 , t  1
1
t
1
t2
,   103
decision making model
 t 1 0.09
the propensity of an individual to keep the
current interaction going can be characterized
by a certain threshold;
If the interacting partner challenges the already
heavy schedule of the individual at time t, the
current interaction stops but keeps going
otherwise.

exp  t 2 22.05
2


exp  t  2  21.78
2 2.05
2
2
2

2 1.78
2
t   t 3 , t  1
1 t  1t  2   1
1
t
1
t2
,   103
 t 1 0.09
1. Casual interaction: Short time intervals largely remain unmanaged and
unregulated, occasional interactions/breaks in communication are tolerated;
2. Spontaneous interaction: Time intervals of intermediate durations are
thoroughly managed by individuals demonstrating the high propensity to keep
the current interaction going while filtering out the potentially unimportant
forthcoming communications;
3. Institutional interaction: where the Zipf's Law manifests itself, the top-down,
almost mandatory interaction occurs.
Ordering of demographic pyramids
World Fertility Data United
Nations Population Division
(UNPD) information.
An entropic force acting in a system is a phenomenological force
resulting from the entire system's statistical tendency to increase its
entropy.
Ordering of demographic pyramids
Maximum entropy (MaxEnt)  Maximum age diversity 
the demographic shift to older ages in the population
Planning under uncertainty:
Divide and conquer strategy
Even though an immediate shortterm decision is deemed imperfect
later, it has the benefit of reducing
uncertainty in the near future.
How many “cuts”/intermediary decisions do we
need to perform in average?
Survival under uncertainty
Combinatorics
Mortality
• the r-selection strategy of reproducing
as quickly as possible, to
• the K-selection strategy of doing time
T in just a few generations, to the
marginal child-free strategy of
promoting personal longevity till time T
while neglecting reproduction.
are the sequent times of reproduction.
The Stirling partition number
(Stirling’s number of the second kind)
When all partitions are equiprobable under
uncertainty, configurations with mT present
overwhelmingly.
The most likely strategy under uncertainty for a long enough
period of time T ≫ 1 would consist of approximately T/ log T
short-term segments
The most likely survival strategy and
environmental stability
Empirical facts:
• Individuals from desperation
ecologies tend to reproduce
earlier and faster, clearly
emphasizing offspring quantity
over quality.
• Girls whose fathers are absent
from home exhibit earlier age of
menarche, first sex, and first
child, as father absence might
signal high male mortality rates
and unstable pair bonds;
• Individuals from desperation
ecologies become more risk
taking and present-oriented.
The most likely survival strategy and
environmental stability
The degree of environmental stability
η(m) - the rate of behavioral strategy
attuned to cues of home ecology.
η(m) → 0: m → T
η(m) → 1: m → 1
• reproduction at each step/ as quick as
possible  ecologies of the desperate end
exert physical strain on the individual and are
characterized by the high degree of random
fluctuation in environmental events;
• slower” behavioral strategies ->
hopeful ecologies;
The most likely survival strategy and
environmental stability
The degree of environmental stability
η(m) - the rate of behavioral strategy
attuned to cues of home ecology.
T
1
1
mmax T  
 hmax T   1 
 1
log T T T 
T 1 log T
The progressive
decay of reproduction
rate with time.
For T < Tc, the survival process can be viewed as
adaptation to the relatively stable conditions of
their habitat;
For T > Tc the survival success is threatened by an
evolutionary trap, since the species (presumably
well adapted) produces not enough offspring.
When adaptations become liabilities
If the rate of environmental changes is higher than the rate of
adaptation to the variable environment, the adaptations once
enhanced fitness of the species become rather its liabilities,
so that the species is fall into the evolutionary trap.
When adaptations become liabilities
If the rate of environmental changes is higher than the rate of
adaptation to the variable environment, the adaptations once
enhanced fitness of the species become rather its liabilities,
so that the species is fall into the evolutionary trap.
Survival by endurance running
• Harsh and perfectly stable ecologies alike equally
threaten the survival success.
• The optimal survival strategy in any foreseeable time
consists of a regular change of scenery by innovation and
migration to other environments.
Survival by endurance
running
The evolution of certain human characteristics can be viewed
as an evidence for selection for endurance running. Human
endurance running capabilities exceed those of mammals
adapted for running, including dogs and equids.
Income inequality rising from risk taking
under uncertainty
Utility refers to the perceived value of a good
(or wealth), and the utility describes the
attitudes towards risky projects of a ”rational
trader”, who would attach greater weight to
losses than he would do to gains of equal
magnitude -- The risk aversion implies that the
utility functions of interest are concave.
u  log w
Income inequality rising from risk taking
under uncertainty
Utility refers to the perceived value of a good
(or wealth), and the utility describes the
attitudes towards risky projects of a ”rational
trader”, who would attach greater weight to
losses than he would do to gains of equal
magnitude -- The risk aversion implies that the
utility functions of interest are concave.
u  log w
Inequality rising from risk taking under
uncertainty
We are interested in the probability distribution of wealth over the
population pw with maximum entropy under the condition of maximum
risk avoidance.
The Pareto
distribution of
wealth!
Wealth inequality can be viewed as a direct statistical
consequence of making decisions under uncertainty
Cross-database analysis suggests the worldwide
growth-inequality relation (U-curve)
The American economist S. Kuznets
had suggested that as an economy
develops, market forces first increase
and then decrease economic
inequality.
As a country develops, more capital is
accumulated by the owners of industry,
introducing inequality. However, more
developed countries move then back to
lower levels of inequality through
various redistribution mechanisms,
such as social welfare programs.
We have used all existent data series (1870 - 2014) in the World Top
Incomes Database -- F. Alvaredo, T. Atkinson, T. Piketty and E. Saez
– Paris School of Economics.
The GDP historical database of the Maddison Project on the Gross
domestic product (GDP) per capita (per person) as the main source
of data on economic development and evolving living standards.
the mean GDP
level of the World
(US$14,402 for
2013)
Inequality is closely correlated with low
growth, yet with high growth either.
the mean GDP
level of the World
(US$14,402 for
2013)
As the economic growth is a
global worldwide
phenomenon, rising
inequality accompanying
that is a global worldwide
phenomenon either,
occurring once the national
economy is out of step with
the World average.
Inequality is closely correlated with low
growth, yet with high growth either.
A stagnant planned/command
economy aiming at the
complete elimination of risks
(by rationing food, for example)
engenders scarcity of virtually
everything in the society.
Industrial economy /
Planning is possible
Scarcity fuels ultimate
inequality, as just a few
redistributing people get the
unfettered access to the scarce
resources while the shares of
others dwindle continuously.
Inequality is closely correlated with low
growth, yet with high growth either.
As economy had developed,
inequality were mostly down
due to the generosity of
wealth redistribution.
Industrial economy /
Planning is possible
The economic and social
policy regimes, providing
important social protection for
millions of industrial workers
in developed countries, had
proven to be adequate for a
globally dominant industrial
economy.
Inequality is closely correlated with low
growth, yet with high growth either.
The ever rising need to
propel growth through
risky entrepreneurship
and innovation has bent
incentives toward the
short-term maximization
of share prices rather
than planning for longterm growth.
Industrial economy /
Planning is possible
Inequality is closely correlated with low
growth, yet with high growth either.
The sharp picks of inequality level visible synchronously for
many countries at once do announce the periods of global
conflicts and uncertainty of international relations a good
deal in advance.
Rational country leaders are likely to gamble on a risky
diversionary war aiming to divert attention of the public away
from domestic issues, increasing that available time the
government has to address the internal troubles.
Rampant inequality may transform uncertainty of national
economic development into uncertainty of international
relations.
• Ancient states had almost no economic growth & internal
politics: the rate of variations of subjective uncertainty was
low, incomparable with the rate of variations of objective
factors;
• Modern sates exist under dual uncertainty, being subjected
to the law of Van Valen.
Certainty
(the ensemble of
microstates is kept fixed):
• Principle of least action
Nature always finds the
most efficient course from
one point to another.
Uncertainty
(the ensemble of microstates
may be broader than initial):
• Principle of maximum
entropy (over the maximal
possible ensemble of
states)
A shattered vase is more likely
than intact one, as smithereens
allow for more disordered
”microscopic” states than a
single state of intact vase.
Certainty
(the ensemble of
microstates is kept fixed):
• Principle of least action
Uncertainty
(the ensemble of microstates
is broader):
• Principle of maximum entropy
(over the maximal possible
ensemble of states)
A crowd is also more likely to occur under uncertainty than a well coordinated team
of individuals, as once individual identity disappears crowd members are unable to
resist any passing idea or emotion.
Certainty
(the ensemble of
microstates is kept fixed):
• Principle of least action
Uncertainty
(the ensemble of microstates
is broader):
•
Principle of maximum entropy
(over the maximal possible
ensemble of states)
While the survival of the fittest rewards the talented under certainty,
the community members experiencing uncertainty may cut
”tall poppies” down, as their talents and achievements distinguish
them from their peers.
Evolution has not stopped yet!
Now we are selected by our own
choice: to be or not to be, to go or not
go, to do or not to do.
In the face of upcoming uncertainty,
we are as much responsible for
everything that happens to us in this
life as we were once upon a time in
savannah, at the early dawn of our
history. We had managed to survive at
the time, as being the most enduring in
race among all other living species.
So … let’s keep jogging!