Nobility and Stupidity Modeling the Evolution of Class Endogamy

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Nobility and StupidityModeling the Evolution of
Class Endogamy
Theodore Belding Uni. Of Michigan May 17,2004

• Tim Garnett
• 30509920

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Contents

1. What is class endogamy
2. Anthropological classification of societies
3. Emergence of Endogamy Verbal Model from
   archaeology
4. Mathematical Model from Economics
5. The Computer Model
6. Model with Cloned Offspring
7. Strategy 1 Rationality
8. Strategy 2 Learning
9. Strategy 3 Interval Around Self
10. Inherited Status
11. Achieved Status
12. Conclusion and Possible Improvements

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What is Class Endogamy

• Google defines endogamy as
• A social system in which an individual may only
  marry within the same social category or group.
• Theodore Belding wished to see how such a system
  may arise by using agents with assigned status
  values and marriage rules.

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Anthropological Classification of Societies

• Anthropologists have often broke human societies
  up into 5 categories
• Hunter Gatherer Bands
• Tribes (Autonomous Village Society)
• Chiefdoms (Rank Societies)
• Stratified society (Complex Chiefdoms)
• State

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Hunter Gatherer Bands

• No one individual allowed to gain significantly
  more status or wealth than any other.
• Collective decisions- No one can force a decision

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Tribe

• Individuals can gain additional wealth
• Status gained (and maintained) by the holding of
  feasts and/or giving of gifts
• Emergence of Big Man of tribe
• Big Mans leadership not total
• Individuals property often destroyed upon their
  death
• Status not Inherited

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Chiefdom

• Wealth and rank inherited at birth.
• Everyone in chiefdom are considered related to
  one another.
• Rank Continuous no clear noble class
• Ruled by Chief Rules by virtue of office
• Chief position may be hereditary
• Chief may have lieutenants
• General assistants that help chief rule

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Stratified Society

• Division between chief and commoners.
• Chief/King no longer considered related to
  commoners.
• Chiefs close relatives constitute the noble
  class.
• Lieutenants (often nobles) assigned special roles
  in government.

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State

• Basically the same as stratified society except
  in addition
• Specialized Bureaucracy developed
• Supports standing army

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Questions in Anthropology

• Given that the first human societies were
  hunter-gatherers why did sedentary agricultural
  societies emerge with rank differences?
• Hunter-gatherers generally appear to have more
  leisure time and less disease.
• Goes against human nature to give a portion of
  wealth to a chief or king.
• How did stratification into nobles and common
  classes occur?

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Problem Investigated

• Given a chiefdom where individuals both inherit
  status and can gain or lose more status during
  there lifetimes, what conditions are necessary
  for a stratified society with class endogamy to
  occur?
• How simple (stupid) can the agents be while
  ensuring class endogamy occurs.

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Emergence of Endogamy Verbal Model From
Archaeology

• Marcus and Flannery observed that there was a
  genealogical gap between the noble and common
  classes.
• This was caused by class endogamy.
• Class endogamy occurred through competition for
  the most advantageous marriages.
• Example chief ensures his child's succession by
  marrying the highest ranking female available.
• As time passes genealogical gap arises eventually
  leading to separation into classes.

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Model form Economics

• From Burdett and Coles Marriage and Class.
• Show classes emerge in marriage markets given
  certain conditions
• In model agents married each other based on their
  respective pizazz or desirability.
• Agents get bonus based on pizazz of spouse
  discounted on time waited till marriage.
• Endogamy still emerges if pizazz can be gained
  during agents lifetime.

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Generalized Model used

• Based on economic model
• Agent with status S will only marry a suitor of
  status
• Where Smax is the status of the highest ranking
  agent willing to marry someone of status S and
  f(H(s))gt 0 is some function of the distribution
  of status H(s) among those willing to marry an
  agent of status s.
• (I.e. f(H(s)) designates what range of status
  less than Smax the agent will still marry (or in
  other words how picky an agent about who they
  marry))

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Generalized Model used

• If we just substitute f(H(s)) for a non negative
  integer constant e we can easily see classes
  emerge
• NOTE No discounting occurs in computer model so
  agents dont get less selective over time.

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Demonstration of class emergence
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The Computer Model

• Agent Statistics
• Male or Female
• Have an integer status value
• Immortal (except for death by marriage!)
• Process of each iteration
• One randomly selected male and female encounter
  each other
• If they either find the other unacceptable then
  nothing happens and agents remain in population.
• If both are accepted marriage occurs
• The agents immediately have 2 children who are
  assigned a status derived from their parents.
• Parents are removed from population.

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Computer Model

• Initialisation
• 10,000 agents
• Each agent had 50 chance of being of either sex
  and assigned random status from range (0..99)
• Termination
• Model ran till 100,000 marriages occurred
• Each model run 50 times

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Types of models tested

• Nine models were tested
• Combination of three marriage strategies
• Rationality Agent uses knowledge of what class
  its in to calculate eligibility of suitors.
• Learning Agent learns what is the status of the
  highest ranking agent willing to marry them.
• Interval round self Agents accept marriage of
  agents with status s-e

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Types of models tested

• Also based on how agents get status
• Cloned Offspring Children exact duplicate of
  parents (son gets fathers status and daughter
  gets mothers)
• Inheritance Children get average status of both
  parents
• Achieved Status Child receives or loses a random
  amount of status

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Sample Output
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Hypergamy metric

• s Status of group tested
• t Time interval (In test a of total marriages
  either 10000 , 30000 or 100000)
• M(s,t) of hypergamous (positive) marriages
  occurring during time interval
• M-(s,t) of hypogamous (negative) marriages
• M(s,t) of marriages between members of
  status s

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Test 1 Cloning and Rationality

• Cloning
• Married couple replaced by children who are
  duplicates of parents
• In effect marriage recorded but nothing happens
• Rationality
• Follow rule sgt Smax(s) e
• Agent finds Smax by finding which class its
  status s belongs too.
• e 9 for the purpose of the experiment.

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Result 1 CR (t10,000)
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Test1 Observations

• 10 classes can be seen to develop in the results
  (around every 10 units of status) with e 9
• Can achieve only 2 classes (nobles and commoners)
  if e 49
• Due to cloning status histogram remains unchanged

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Problems with Test 1

• Cloning ensures that model remains static
• As status is unchanging classes status ranges
  would remain constant.
• Rationality method seems redundant
• Would expect class endogamy to occur if agents
  finds out what class they belong to and only
  marry with in that class. So model is a bit
  pointless

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Test 2 Cloning and Learning

• Learning
• Agents learn the value of Smax(s)
• Keeps list of last n encounters for each status
  value
• Records other agents status
• Records result of encounter
• If the n list is not full for a status group then
  agents form group will accept any suitor of rank
  higher than s 9
• If full uses Rational method except Smax is the
  status of the highest ranking suitor who agreed
  to marry found in n.

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Result 2 C L (t10,000)
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Result 2 C L (t20,000)
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Observations

• Although it takes a longer time period classes
  emerge
• Can see noble class emerging at t10,000
• More classes (3-4) emerge at t20,000
• Paper says model then stagnates as no more
  classes clearly emerge (till t 100,000)
• Model could represent archaic societies where
  only the noble and common classes exist.

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Problems

• Paper observed that in real chiefdom the
  initialisation period (when n list not full)
  would never occur.
• I have a hunch that eventually all 10 classes
  will develop because
• The highest rank is defined
• Once rank fully defined is effectively removed
  form model (as no one can access rank)(occurs
  when hypergamy peak approaches -1)
• This should lead to 2nd biggest rank forming and
  isolating itself and so on.
• N list a form of imperfect information.
• Didnt test different sizes of n.
• If n size increased I would expect classes to
  emerge quicker.

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Test 3 Cloning and Interval around Self

• Interval Round Self
• An agent will marry anyone of status
• s gt s e (e 9 in test)
• Is basically learning rule without the learning!

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Result 3 C I (t100,000)
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Observations

• Endogamy doesnt occur
• Classes do not develop
• Therefore rule insufficient to promote endogamy
• It seems agents need to have some knowledge of
  the world in order for endogamy to occur.

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Test 4-6 Inheritance

• Inheritance
• Children of random sex
• Each child receives an average of both their
  parents status.

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Test 4 Inheritance and Rationality (t10000)
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Test 4 Inheritance and Rationality (t20000)
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Test 4 Inheritance and Rationality (t100000)
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Observation

• Due to averaging status gaps in histograms appear
• In each class all agents head towards their mean
  value (where hypergamy index 0)
• Hypergamy no longer becomes a good indicator of
  classes.
• Marriage frequency and status histograms indicate
  if classes forming.
• All three marriage rules form class endogamy.
• Rank no longer continuous
• Stratified society develops because of rank gaps
  (even using interval round self rule)

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Test 5 Inheritance and Learning (t10000)
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Test 5 Inheritance and Learning (t30000)
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Test 5 Inheritance and Learning (t100000)
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Additional Learning Problem

• Population distribution is not representative of
  real life.
• In tests noble class has one of the highest
  populations when traditionally the nobility
  occupied a very small section of the population

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Test 6 Inheritance and Interval Round Self
(t10000)
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Test 6 Inheritance and Interval Round Self
(t30000)
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Test 6 Inheritance and Interval Round Self
(t100000)
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Interval Round Self Observation

• With inheritance class endogamy occurs.
• Interestingly interval round self seems to
  generate the most realistic population
  distribution
• The population of each class shrinks as status
  increases.
• Wasnt observed in paper.

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Test 7-9 Achieved Status

• Achieved Status
• Inheritance rule used
• In addition each child was given additional
  status Sa where Sa was drawn form a distribution
  of mean 0 and standard deviation of 2.
• (Sa ranged from -2 to 2 with values around 0
  being most common)

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Test 7 Achieved Rationality(t 100,000)
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Test 7 Achieved Learning(t 100,000)
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Test 7 Achieved Interval Round Self (t
100,000)
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Observations

• Achieved status helps counteract the effects of
  inheritance
• Slows the development of status gaps.
• If deviation of Sa increased then gap reducing
  effect increased.
• Once again the interval round self is interesting
• Seems to still develop a small noble and peasant
  class with a large middle class.

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Conclusion

• It has been shown that class endogamy occurs if
  agents are only willing to marry suitors with
  status no less than some fixed value below the
  status of their highest ranking suitor.
• That agents can learn the status of their highest
  ranking suitor.
• Inheritance develops status gaps

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Conclusion

• Paper observed that a possible reason that class
  stratification didnt occur immediately in
  chiefdoms in real life
• Small size ensures agents less selective
• Non stratified chiefdom may be more stable

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Future Work

• Addition of
• Noise to decision making
• Death and reproduction rates
• Discounting metric from economic model
• Additional factors to status (i.e. education)
• See why chiefs had higher status than rest of
  tribe (how chiefdoms arose)
• See how genetic stains develop in classes
• Inbreeding produces certain traits in class

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My Idea for Implementation

• Incorporate this work into Sugarscape
• Instead of random status achievement have
  achievement based on wealth (sugar) gathered
• Show how upper class owns most of the wealth
• Add desirability range
• The higher status an agent has the greater the
  range that suitors can be drawn from
• Realistic (In Medieval times nobles from separate
  countries marry, commoners generally dont)
• Add locality considerations
• May cause noble and common classes to separate
  quicker.
• Experiment to see how we can get correct
  population distribution (many in poor class, few
  in rich)
• Try using achieved status with cloning and see if
  classes develop.

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The End!