Nobility and StupidityNobility and StupidityModeling the Evolution of Class EndogamyModeling the Evolution of Class Endogamy

Tim GarnettTim Garnett

3050992030509920

Theodore BeldingTheodore BeldingUni. Of MichiganUni. Of Michigan

May 17,2004May 17,2004

ContentsContents

1.1. What is class endogamyWhat is class endogamy2.2. Anthropological classification of societiesAnthropological classification of societies3.3. Emergence of Endogamy: Verbal Model from Emergence of Endogamy: Verbal Model from

archaeologyarchaeology4.4. Mathematical Model from EconomicsMathematical Model from Economics5.5. The Computer ModelThe Computer Model6.6. Model with Cloned OffspringModel with Cloned Offspring

1.1. Strategy 1: RationalityStrategy 1: Rationality2.2. Strategy 2: LearningStrategy 2: Learning3.3. Strategy 3: Interval Around SelfStrategy 3: Interval Around Self

7.7. Inherited StatusInherited Status8.8. Achieved StatusAchieved Status9.9. Conclusion and Possible ImprovementsConclusion and Possible Improvements

What is Class EndogamyWhat is Class Endogamy

Google defines endogamy asGoogle defines endogamy as A social system in which an individual may A social system in which an individual may

only marry within the same social category or only marry within the same social category or group. group.

Theodore Belding wished to see how such Theodore Belding wished to see how such a system may arise by using agents with a system may arise by using agents with assigned status values and marriage assigned status values and marriage rules.rules.

Anthropological Classification of Anthropological Classification of SocietiesSocieties

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

Hunter Gatherer BandsHunter Gatherer Bands

No one individual allowed to gain No one individual allowed to gain significantly more status or wealth than significantly more status or wealth than any other.any other.

Collective decisions- No one can force a Collective decisions- No one can force a decisiondecision

TribeTribe

Individuals can gain additional wealthIndividuals can gain additional wealth

Status gained (and maintained) by the Status gained (and maintained) by the holding of feasts and/or giving of giftsholding of feasts and/or giving of gifts

Emergence of ‘Big Man’ of tribeEmergence of ‘Big Man’ of tribe

Big Man’s leadership not totalBig Man’s leadership not total

Individuals property often destroyed upon Individuals property often destroyed upon their deaththeir death

Status not InheritedStatus not Inherited

ChiefdomChiefdom

Wealth and rank inherited at birth.Wealth and rank inherited at birth.

Everyone in chiefdom are considered Everyone in chiefdom are considered related to one another.related to one another. Rank Continuous: no clear noble classRank Continuous: no clear noble class

Ruled by Chief: Rules by virtue of officeRuled by Chief: Rules by virtue of office Chief position may be hereditaryChief position may be hereditary

Chief may have lieutenantsChief may have lieutenants General assistants that help chief ruleGeneral assistants that help chief rule

Stratified SocietyStratified Society

Division between chief and commoners.Division between chief and commoners. Chief/King no longer considered related to Chief/King no longer considered related to

commoners.commoners.

Chiefs close relatives constitute the noble Chiefs close relatives constitute the noble class.class.

Lieutenants (often nobles) assigned Lieutenants (often nobles) assigned special roles in government.special roles in government.

StateState

Basically the same as stratified society Basically the same as stratified society except in additionexcept in addition SpecializedSpecialized Bureaucracy developed Bureaucracy developed Supports standing armySupports standing army

Questions in AnthropologyQuestions in Anthropology

Given that the first human societies were Given that the first human societies were hunter-gatherers why did sedentary hunter-gatherers why did sedentary agricultural societies emerge with rank agricultural societies emerge with rank differences?differences?

Hunter-gatherers generally appear to have more Hunter-gatherers generally appear to have more leisure time and less disease.leisure time and less disease.

Goes against human nature to give a portion of Goes against human nature to give a portion of wealth to a chief or king.wealth to a chief or king.

How did stratification into nobles and common How did stratification into nobles and common classes occur?classes occur?

Problem InvestigatedProblem Investigated

Given a chiefdom where individuals both Given a chiefdom where individuals both inherit status and can gain or lose more inherit status and can gain or lose more status during there lifetimes, what status during there lifetimes, what conditions are necessary for a stratified conditions are necessary for a stratified society with class endogamy to occur?society with class endogamy to occur?

How simple (stupid) can the agents be How simple (stupid) can the agents be while ensuring class endogamy occurs.while ensuring class endogamy occurs.

Emergence of Endogamy: Verbal Emergence of Endogamy: Verbal Model From ArchaeologyModel From Archaeology

Marcus and Flannery observed that there was a Marcus and Flannery observed that there was a genealogical gap between the noble and genealogical gap between the noble and common classes.common classes.This was caused by class endogamy.This was caused by class endogamy.Class endogamy occurred through competition Class endogamy occurred through competition for the most advantageous marriages.for the most advantageous marriages. Example: chief ensures his child's succession by Example: chief ensures his child's succession by

marrying the highest ranking female available.marrying the highest ranking female available.

As time passes genealogical gap arises As time passes genealogical gap arises eventually leading to separation into classes.eventually leading to separation into classes.

Model form EconomicsModel form Economics

From Burdett and Coles Marriage and From Burdett and Coles Marriage and Class.Class. Show classes emerge in marriage markets Show classes emerge in marriage markets

given certain conditionsgiven certain conditions In model agents married each other based on In model agents married each other based on

their respective ‘pizazz’ or desirability.their respective ‘pizazz’ or desirability. Agents get bonus based on pizazz of spouse Agents get bonus based on pizazz of spouse

discounted on time waited till marriage.discounted on time waited till marriage. Endogamy still emerges if pizazz can be Endogamy still emerges if pizazz can be

gained during agents lifetime. gained during agents lifetime.

Generalized Model usedGeneralized Model used

Based on economic model Based on economic model Agent with status S will only marry a suitor of statusAgent with status S will only marry a suitor of status

Where Smax is the status of the highest ranking agent Where Smax is the status of the highest ranking agent willing to marry someone of status S and f(H(s))>= 0 willing to marry someone of status S and f(H(s))>= 0 is some function of the distribution of status H(s) is some function of the distribution of status H(s) among those willing to marry an agent of status s.among those willing to marry an agent of status s.

(I.e. f(H(s)) designates what range of status less than (I.e. f(H(s)) designates what range of status less than Smax the agent will still marry (or in other words how Smax the agent will still marry (or in other words how picky an agent about who they marry))picky an agent about who they marry))

Generalized Model usedGeneralized Model used

If we just substitute f(H(s)) for a non negative If we just substitute f(H(s)) for a non negative integer constant integer constant εε we can easily see classes we can easily see classes emergeemerge

NOTE: No discounting occurs in computer NOTE: No discounting occurs in computer model so agents don’t get less selective over model so agents don’t get less selective over time.time.

Demonstration of class Demonstration of class emergenceemergence

The Computer ModelThe Computer Model

Agent StatisticsAgent Statistics Male or FemaleMale or Female Have an integer status valueHave an integer status value Immortal (except for death by marriage!)Immortal (except for death by marriage!)

Process of each iterationProcess of each iteration One randomly selected male and female encounter One randomly selected male and female encounter

each othereach other If they either find the other unacceptable then nothing If they either find the other unacceptable then nothing

happens and agents remain in population.happens and agents remain in population. If both are accepted marriage occursIf both are accepted marriage occurs

The agents immediately have 2 children who are assigned a The agents immediately have 2 children who are assigned a status derived from their parents.status derived from their parents.Parents are removed from population. Parents are removed from population.

Computer ModelComputer Model

InitialisationInitialisation 10,000 agents10,000 agents Each agent had 50% chance of being of Each agent had 50% chance of being of

either sex and assigned random status from either sex and assigned random status from range (0..99)range (0..99)

TerminationTermination Model ran till 100,000 marriages occurredModel ran till 100,000 marriages occurred Each model run 50 timesEach model run 50 times

Types of models testedTypes of models tested

Nine models were testedNine models were tested

Combination of three marriage strategiesCombination of three marriage strategies Rationality: Agent uses knowledge of what Rationality: Agent uses knowledge of what

class its in to calculate eligibility of suitors.class its in to calculate eligibility of suitors. Learning: Agent learns what is the status of Learning: Agent learns what is the status of

the highest ranking agent willing to marry the highest ranking agent willing to marry them.them.

Interval round self: Agents accept marriage of Interval round self: Agents accept marriage of agents with status s-agents with status s-εε

Types of models testedTypes of models tested

Also based on how agents get statusAlso based on how agents get status Cloned Offspring: Children exact duplicate of Cloned Offspring: Children exact duplicate of

parents (son gets fathers status and daughter parents (son gets fathers status and daughter gets mothers)gets mothers)

Inheritance: Children get average status of Inheritance: Children get average status of both parentsboth parents

Achieved Status: Child receives or loses a Achieved Status: Child receives or loses a random amount of statusrandom amount of status

Sample OutputSample Output

Hypergamy metricHypergamy 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

Test 1: Cloning and RationalityTest 1: Cloning and Rationality

CloningCloning Married couple replaced by children who are Married couple replaced by children who are

duplicates of parentsduplicates of parents In effect marriage recorded but nothing happensIn effect marriage recorded but nothing happens

RationalityRationality Follow rule s’>= S’max(s) – Follow rule s’>= S’max(s) – εε Agent finds S’max by finding which class its status s Agent finds S’max by finding which class its status s

belongs too.belongs too. εε = 9 for the purpose of the experiment. = 9 for the purpose of the experiment.

Result 1: C&R (t=10,000)Result 1: C&R (t=10,000)

Test1: ObservationsTest1: Observations

10 classes can be seen to develop in the 10 classes can be seen to develop in the results (around every 10 units of status) results (around every 10 units of status) with with εε = 9 = 9

Can achieve only 2 classes (nobles and Can achieve only 2 classes (nobles and commoners) if commoners) if εε = 49 = 49

Due to cloning status histogram remains Due to cloning status histogram remains unchangedunchanged

Problems with Test 1Problems with Test 1

Cloning ensures that model remains staticCloning ensures that model remains static As status is unchanging classes status ranges As status is unchanging classes status ranges

would remain constant.would remain constant.

Rationality method seems redundant Rationality method seems redundant Would expect class endogamy to occur if Would expect class endogamy to occur if

agents finds out what class they belong to agents finds out what class they belong to and only marry with in that class. So model is and only marry with in that class. So model is a bit pointlessa bit pointless

Test 2: Cloning and LearningTest 2: Cloning and Learning

LearningLearning Agents learn the value of S’max(s)Agents learn the value of S’max(s) Keeps list of last n encounters for each status valueKeeps list of last n encounters for each status value

Records other agents statusRecords other agents status

Records result of encounterRecords result of encounter If the n list is not full for a status group then agents If the n list is not full for a status group then agents

form group will accept any suitor of rank higher than form group will accept any suitor of rank higher than s – 9s – 9

If full uses Rational method except S’max is the status If full uses Rational method except S’max is the status of the highest ranking suitor who agreed to marry of the highest ranking suitor who agreed to marry found in n.found in n.

Result 2: C & L (t=10,000)Result 2: C & L (t=10,000)

Result 2: C & L (t=20,000)Result 2: C & L (t=20,000)

ObservationsObservations

Although it takes a longer time period classes Although it takes a longer time period classes emergeemerge

Can see noble class emerging at t=10,000Can see noble class emerging at t=10,000

More classes (3-4) emerge at t=20,000More classes (3-4) emerge at t=20,000

Paper says model then stagnates as no more Paper says model then stagnates as no more classes clearly emerge (till t= 100,000)classes clearly emerge (till t= 100,000)

Model could represent archaic societies where Model could represent archaic societies where only the noble and common classes exist.only the noble and common classes exist.

ProblemsProblems

Paper observed that in real chiefdom the initialisation Paper observed that in real chiefdom the initialisation period (when n list not full) would never occur.period (when n list not full) would never occur.I have a hunch that eventually all 10 classes will develop I have a hunch that eventually all 10 classes will develop becausebecause

The highest rank is definedThe highest rank is defined Once rank fully defined is effectively removed form model (as no Once rank fully defined is effectively removed form model (as no

one can access rank)(occurs when hypergamy peak approaches one can access rank)(occurs when hypergamy peak approaches -1)-1)

This should lead to 2This should lead to 2ndnd biggest rank forming and isolating itself biggest rank forming and isolating itself and so on.and so on.

N list a form of imperfect information.N list a form of imperfect information. Didn’t test different sizes of n.Didn’t test different sizes of n. If n size increased I would expect classes to emerge quicker.If n size increased I would expect classes to emerge quicker.

Test 3: Cloning and Interval around Test 3: Cloning and Interval around SelfSelf

Interval Round SelfInterval Round Self An agent will marry anyone of statusAn agent will marry anyone of status

s’ >= s – s’ >= s – εε ( (εε = 9 in test) = 9 in test) Is basically learning rule without the learning!Is basically learning rule without the learning!

Result 3: C & I (t=100,000)Result 3: C & I (t=100,000)

ObservationsObservations

Endogamy doesn’t occurEndogamy doesn’t occur Classes do not developClasses do not develop Therefore rule insufficient to promote Therefore rule insufficient to promote

endogamyendogamy

It seems agents need to have some It seems agents need to have some knowledge of the world in order for knowledge of the world in order for endogamy to occur.endogamy to occur.

Test 4-6 InheritanceTest 4-6 Inheritance

InheritanceInheritance Children of random sexChildren of random sex Each child receives an average of both their Each child receives an average of both their

parents’ status.parents’ status.

Test 4 Inheritance and Rationality Test 4 Inheritance and Rationality (t=10000)(t=10000)

Test 4 Inheritance and Rationality Test 4 Inheritance and Rationality (t=20000)(t=20000)

Test 4 Inheritance and Rationality Test 4 Inheritance and Rationality (t=100000)(t=100000)

ObservationObservation

Due to averaging status gaps in histograms Due to averaging status gaps in histograms appearappear In each class all agents head towards their mean In each class all agents head towards their mean

value (where hypergamy index = 0)value (where hypergamy index = 0)

Hypergamy no longer becomes a good indicator Hypergamy no longer becomes a good indicator of classes.of classes.Marriage frequency and status histograms Marriage frequency and status histograms indicate if classes forming.indicate if classes forming.All three marriage rules form class endogamy.All three marriage rules form class endogamy.Rank no longer continuousRank no longer continuous Stratified society develops because of rank gaps Stratified society develops because of rank gaps

(even using interval round self rule)(even using interval round self rule)

Test 5 Inheritance and Learning Test 5 Inheritance and Learning (t=10000)(t=10000)

Test 5 Inheritance and Learning Test 5 Inheritance and Learning (t=30000)(t=30000)

Test 5 Inheritance and Learning Test 5 Inheritance and Learning (t=100000)(t=100000)

Additional Learning ProblemAdditional Learning Problem

Population distribution is not Population distribution is not representative of real life. representative of real life. In tests noble class has one of the highest In tests noble class has one of the highest

populations when traditionally the nobility populations when traditionally the nobility occupied a very small section of the occupied a very small section of the populationpopulation

Test 6 Inheritance and Interval Test 6 Inheritance and Interval Round Self (t=10000)Round Self (t=10000)

Test 6 Inheritance and Interval Test 6 Inheritance and Interval Round Self (t=30000)Round Self (t=30000)

Test 6 Inheritance and Interval Test 6 Inheritance and Interval Round Self (t=100000)Round Self (t=100000)

Interval Round Self ObservationInterval Round Self Observation

With inheritance class endogamy occurs.With inheritance class endogamy occurs.

Interestingly interval round self seems to Interestingly interval round self seems to generate the most realistic population generate the most realistic population distributiondistribution The population of each class shrinks as status The population of each class shrinks as status

increases.increases. Wasn’t observed in paper.Wasn’t observed in paper.

Test 7-9 Achieved StatusTest 7-9 Achieved Status

Achieved StatusAchieved Status Inheritance rule usedInheritance rule used In addition each child was given additional In addition each child was given additional

status Sa where Sa was drawn form a status Sa where Sa was drawn form a distribution of mean = 0 and standard distribution of mean = 0 and standard deviation of 2. deviation of 2.

(Sa ranged from -2 to 2 with values around 0 (Sa ranged from -2 to 2 with values around 0 being most common) being most common)

Test 7: Achieved & RationalityTest 7: Achieved & Rationality(t = 100,000)(t = 100,000)

Test 7: Achieved & LearningTest 7: Achieved & Learning(t = 100,000)(t = 100,000)

Test 7: Achieved & Interval Round Test 7: Achieved & Interval Round Self (t = 100,000)Self (t = 100,000)

ObservationsObservations

Achieved status helps counteract the Achieved status helps counteract the effects of inheritanceeffects of inheritance Slows the development of status gaps.Slows the development of status gaps. If deviation of Sa increased then gap reducing If deviation of Sa increased then gap reducing

effect increased.effect increased.

Once again the interval round self is Once again the interval round self is interestinginteresting Seems to still develop a small noble and Seems to still develop a small noble and

peasant class with a large middle class.peasant class with a large middle class.

ConclusionConclusion

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

That agents can learn the status of their That agents can learn the status of their highest ranking suitor.highest ranking suitor.

Inheritance develops status gapsInheritance develops status gaps

ConclusionConclusion

Paper observed that a possible reason Paper observed that a possible reason that class stratification didn’t occur that class stratification didn’t occur immediately in chiefdoms in real lifeimmediately in chiefdoms in real life Small size ensures agents less selectiveSmall size ensures agents less selective Non stratified chiefdom may be more stableNon stratified chiefdom may be more stable

Future WorkFuture Work

Addition ofAddition of Noise to decision makingNoise to decision making Death and reproduction ratesDeath and reproduction rates Discounting metric from economic modelDiscounting metric from economic model Additional factors to status (i.e. education)Additional factors to status (i.e. education)

See why chiefs had higher status than rest See why chiefs had higher status than rest of tribe (how chiefdoms arose)of tribe (how chiefdoms arose)See how genetic stains develop in classesSee how genetic stains develop in classes Inbreeding produces certain traits in classInbreeding produces certain traits in class

My Idea for ImplementationMy Idea for Implementation

Incorporate this work into SugarscapeIncorporate this work into Sugarscape Instead of random status achievement have achievement Instead of random status achievement have achievement

based on wealth (sugar) gatheredbased on wealth (sugar) gatheredShow how upper class owns most of the wealthShow how upper class owns most of the wealth

Add desirability rangeAdd desirability rangeThe higher status an agent has the greater the range that suitors can The higher status an agent has the greater the range that suitors can be drawn frombe drawn from

Realistic (In Medieval times nobles from separate countries marry, Realistic (In Medieval times nobles from separate countries marry, commoners generally don’t)commoners generally don’t)

Add locality considerationsAdd locality considerations May cause noble and common classes to separate quicker.May cause noble and common classes to separate quicker.

Experiment to see how we can get correct population Experiment to see how we can get correct population distribution (many in poor class, few in rich)distribution (many in poor class, few in rich)

Try using achieved status with cloning and see if Try using achieved status with cloning and see if classes develop.classes develop.

The End!The End!