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)