Naive Learning with Uninformed Agents
Arun G. Chandrasekhar
- American Economic Review (Forthcoming)
The DeGroot model has emerged as a credible alternative to the
standard Bayesian model for studying learning on networks, offering
a natural way to model naive learning in a complex setting.
One unattractive aspect of this model is the assumption that the
process starts with every node in the network having a signal. We
study a natural extension of the DeGroot model that can deal with
sparse initial signals. We show that an agent’s social influence in
this generalized DeGroot model is essentially proportional to the
degree-weighted share of uninformed nodes who will hear about an
event for the first time via this agent. This characterization result
then allows us to relate network geometry to information aggregation.
We show information aggregation preserves “wisdom” in
the sense that initial signals are weighed approximately equally in
a model of network formation that captures the sparsity, clustering,
and small-worlds properties of real-world networks. We also
identify an example of a network structure where essentially only
the signal of a single agent is aggregated, which helps us pinpoint
a condition on the network structure necessary for almost full aggregation.
Simulating the modeled learning process on a set of real
world networks, we find that there is on average 22.4% information
loss in these networks. We also explore how correlation in the
location of seeds can exacerbate aggregation failure. Simulations
with real world network data show that with clustered seeding, information
loss climbs to 34.4%.
Forthcoming Article Downloads