Bayesian Persuasion, explained.
Bayesian persuasion studies how a sender’s commitment to an information structure changes a receiver’s posterior beliefs and actions.
Why it happens
The project’s good-state prior is 0.3. Every good state gets a positive signal; a chosen fraction of bad states also do. A receiver invests at posterior at least 0.5, including ties; the boundary fraction 3/7 produces investment probability 0.6.
Bayesian persuasion studies how a sender’s commitment to an information structure changes a receiver’s posterior beliefs and actions.
Read the result
The positive message’s posterior falls as more bad states enter it. A more frequent message can become unpersuasive once it crosses the receiver’s decision threshold.
A worked example
Pool states up to a credible boundary
Start with every good state labelled positive and forty percent of bad states labelled positive.
Set the exact bad-state boundary three-sevenths to obtain posterior one-half and total investment probability 0.6.
Increase pooling beyond that boundary and inspect the receiver’s refusal under the declared threshold and tie rule.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The project’s good-state prior is 0.3. Every good state gets a positive signal; a chosen fraction of bad states also do. A receiver invests at posterior at least 0.5, including ties; the boundary fraction 3/7 produces investment probability 0.6.
Where this idea is useful
A practical use
Inspect a signal’s selection policy before treating its content as an unfiltered observation.
A common misconception
“Adding more positive messages always increases persuasion.”
A receiver who knows the selection policy updates on how the message was produced. Excess pooling can destroy the message’s decision relevance.
What this explanation leaves out
- Binary states, fixed payoffs, credible commitment and a declared tie rule are essential. This is an information-design teaching model, not advice to mislead real people.
Why does the exact boundary use investment at equality?
The model explicitly resolves posterior one-half in favour of investment. A different tie rule changes the boundary outcome.
Which commitment and selection policy makes the message credible to its receiver?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.