Introduction
The efficiency of within-group coordination
depends on communication ability, the costs associated with the network, and
the presence of leaders or elites.
A hierarchical network structure can have an
effect on the efficiency of collective action.
There may exist a “wisdom of the crowd” effect in
the absence of any leader. However, group-level coordination can also benefit
group members even when there is variation in some relevant trait.
Merit: defined as ability of knowledge that
allows one individual to influence the decisions of others.
There have been two families of models on the
origins of social inequality:
(1) winner-loser:
assumes that a set of individuals form a group for the sake of some
group-derived benefits, and takes the existence of the group as a given. Social
hierarchies emerge endogenously even if agents have no initial differences.
These are models of accumulation, and the resulting social status hierarchy is
independent of communal action.
(2) division-of-labor:
imply a more complex payoff function. The group is formed to actively do
something together: communal action with distinct and distinguishable parts.
A weakness of both these approaches is they
typically (NOTE: the authors claim “invariably”) assume that the population’s
social network is panmictic (well-mixed). In reality, social structure matters
(for things like positive assortment, dispersal, etc.). Some empirical evidence
from animal behavior suggests that a restriction on the number of social
partners can lead to highly structured social groups.
The use a behavioral
synchrony approach to mode restricted social networks.
Model 1
Assume a set of n agents who care connected in a random network, so that each agent
has k links. The network is not fully
connected. Each agent has a directional vector between 0 and 360 degrees,
initially chosen randomly from a uniform distribution.
The agents face a behavioral synchrony problem
(such as a coordinated social action) that yields some resource payoff, which
is shared by the group. To solve this problem, the agents go through a
synchronization process.
A synchronization
run is a set of T dyadic
exchanges, each of which takes place between 2 agents if there is a network
edge between them. During an exchange, they exchange information. Information
received is associated with a weight, which agents use to determine the extent
of social influence. One node, TI, is
randomly selected at the beginning of a run to be the holder of “true
information,” and does not change her information variable during the
synchronization process.
During information exchange, each node’s
information closes the distance between them via a weight x, such that if x = 1,
they go to the midpoint of their information variables.
For this study, n and k are fixed, and
the focus is on the process whereby agents choose the weights they associate
with others.
Memory and weights. Agents remember all
interactions from all runs, and use this to calculate weights. An individual’s
weight for a given agent is approximately that which minimizes the distance
from the true information. “In other words, to calculate the weight agent i associates with agent j, she first chooses the part of her
memory that contains the records of her information exchanges with agent j and then chooses the weight
coefficient that minimizes the least squares of the distance of the weighted
average of the 2 information values from the true information.” Initial weights
are all set to 1.
Simulation
results
A particular pattern emerges: the weight agent i associates with the agent j is dependent on their network
distances from the recipient of the true information, TI.
In other words, status (weight) is determined by
the network distance to the true information.
Model 2:
Stratification
In this second model, we relax the assumption that
only one agent can receive the true information, and thus allow for variation
in merit. Thus, agents can rank each other in terms of merit.
Each agent now has an index number representing the probability that the node is the
recipient of true information. The parameter \sigma denotes the steepness of merit inequality.
As the personal network size is fixed, the
emergence of ranking in terms of preference is akin to befriending, and can
lead to a restructuring of the network. Because network size is limited and
everyone prefers high-merit nodes, positive assortment for quality emerges.
NOTE: This is a lot like a mate choice/mutual
search model (e.g., Kalick & Hamilton 1986) in which individuals all prefer
high quality partners. You end up with assortment for quality. The argument
here is that it works for information.
When an information exchange occurs, all agents
observe the information of the two agents.
Once the weights are estimated by the agents after
a round of information exchange, they rank their partners as well as all other
agents. If there is an unlinked partner that is better than the agent’s worst
link, she can express a desired to form a new link. If the desire is mutual,
they both drop their worst links and form one with each other.
This is repeated until there is no unconnected
agent pair left that would prefer to be connected to each other.
There is also a process through which the same
connectivity k is maintained for all
agents.
Results: Positive assortment for quality.
Assortment for “cliques of elites.”
As the merit inequality (\sigma) increases, the weight differences increase and so does the
pressure toward social stratification. We eventually get “elite delineation,” in which there is a discontinuity in the
relationship between index and the average index of one’s partners.
Efficiency
and inequality.
Are social stratification and elite delineation
adaptive?
Test this with three types of networks:
1. A mesh
network: a random n-node
uniformly k-degree network.
2. A stratified
network: the average index numbers of an agent’s partners are assortative
with respect to index numbers, but without elite delineation.
3. An elite
network: a stratified network, with the agents with the highest index
numbers delineated from the other agents in a distinct module.
Two outcome variables:
Payoff for
the group as a whole: define a measure of synchronization efficiency, h, the average distance of the agents’
individual information values from the true information at the end of the
synchronization run.
Inequality
of payoff among members of a group: Define an inequality measure, q, defined as the average distance from
the group average, h.
Results:
Allowing the nodes to optimize the weights they
assign to their partners increases the group’s synchronization efficiency and
decreases inequality in all cases.
Variation of merit does not necessarily affect
synchronization efficiency, but always increases inequality.
Stratification decreases efficiency and increases
inequality.
Elite clique formation leads to a large loss of
efficiency and equality, even if weights are adjusted. This effect is much
larger than that arising from stratification.
These results suggest that we can separate social
inequality into 3 markedly different types.
1. Status
inequality, which emerges when there is variation in merit and inevitably
increases the group’s efficiency.
2. Social
stratification, which requires status inequality but introduces an
information bottleneck that leads to loss of efficiency and increased payoff
inequality.
3. Elite
formation, which requires stratification and results in a collapse in
efficiency and is associated with extreme payoff inequality.
Thus, the 3 different kinds of inequality,
although closely linked, have opposite effects on societal efficiency and
inequality.
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