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Nobility and Stupidity Modeling the Evolution of Class Endogamy. Theodore Belding Uni. Of Michigan May 17,2004. Tim Garnett 30509920. Contents. What is class endogamy Anthropological classification of societies Emergence of Endogamy: Verbal Model from archaeology
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Nobility and StupidityModeling the Evolution of Class Endogamy Theodore Belding Uni. Of Michigan May 17,2004 Tim Garnett 30509920
Contents • What is class endogamy • Anthropological classification of societies • Emergence of Endogamy: Verbal Model from archaeology • Mathematical Model from Economics • The Computer Model • Model with Cloned Offspring • Strategy 1: Rationality • Strategy 2: Learning • Strategy 3: Interval Around Self • Inherited Status • Achieved Status • Conclusion and Possible Improvements
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.
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
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
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 Man’s leadership not total • Individuals property often destroyed upon their death • Status not Inherited
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
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.
State • Basically the same as stratified society except in addition • Specialized Bureaucracy developed • Supports standing army
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?
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.
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.
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.
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))>= 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))
Generalized Model used • If we just substitute f(H(s)) for a non negative integer constant ε we can easily see classes emerge • NOTE: No discounting occurs in computer model so agents don’t get less selective over time.
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.
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
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-ε
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
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
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 s’>= S’max(s) – ε • Agent finds S’max by finding which class its status s belongs too. • ε = 9 for the purpose of the experiment.
Test1: Observations • 10 classes can be seen to develop in the results (around every 10 units of status) with ε = 9 • Can achieve only 2 classes (nobles and commoners) if ε = 49 • Due to cloning status histogram remains unchanged
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
Test 2: Cloning and Learning • Learning • Agents learn the value of S’max(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 S’max is the status of the highest ranking suitor who agreed to marry found in n.
Observations • Although it takes a longer time period classes emerge • Can see noble class emerging at t=10,000 • More classes (3-4) emerge at t=20,000 • 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.
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. • Didn’t test different sizes of n. • If n size increased I would expect classes to emerge quicker.
Test 3: Cloning and Interval around Self • Interval Round Self • An agent will marry anyone of status s’ >= s – ε (ε = 9 in test) • Is basically learning rule without the learning!
Observations • Endogamy doesn’t 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.
Test 4-6 Inheritance • Inheritance • Children of random sex • Each child receives an average of both their parents’ status.
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)
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
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. • Wasn’t observed in paper.
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)
