DeGroot Learning, explained.
DeGroot learning updates each agent’s belief as a weighted average of current beliefs in a specified social network.
Why it happens
Three initial beliefs zero, 0.4 and one update through declared row-stochastic weights. The ordinary network converges to influence-weighted 0.45; fixing the first agent at zero draws the others toward zero.
DeGroot learning updates each agent’s belief as a weighted average of current beliefs in a specified social network.
Read the result
The limiting belief weights initial agents by network influence, not necessarily equal head counts. Stubbornness changes the update rule rather than adding evidence.
A worked example
Compare repeated averaging with a fixed source
Start with beliefs zero, 0.4 and one under the ordinary averaging weights.
Exchange beliefs toward limit 0.45, comparing that with the simple initial arithmetic mean about 0.467.
Reset with agent A stubborn at zero and inspect the others being pulled toward that fixed value.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Three initial beliefs zero, 0.4 and one update through declared row-stochastic weights. The ordinary network converges to influence-weighted 0.45; fixing the first agent at zero draws the others toward zero.
Where this idea is useful
A practical use
Inspect influence weights before interpreting repeated agreement as the average of independent observations.
A common misconception
“Repeated averaging automatically counts each person’s evidence once.”
Network paths repeatedly reuse beliefs and create unequal influence. This deterministic social averaging is not independent-evidence aggregation.
What this explanation leaves out
- Weights and initial beliefs are invented. Repeated averaging adds no new evidence and is not Bayesian inference or a guarantee of truth.
Does convergence prove accuracy?
No. The process supplies no external truth or new evidence, so agreement and correctness remain separate questions.
Which agent’s initial belief receives extra influence from the communication weights?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.