herder model calculator

What the Herder Model Measures

The herder model is about social learning: people observe what earlier people did, then combine that public information with their own private signal. Over time, a group can drift into a herd (or information cascade), where individuals mostly copy prior behavior instead of relying on personal evidence.

This calculator gives a practical estimate of that process. It converts prior beliefs, signal quality, and observed choices into a posterior probability and a suggested next action.

Inputs Explained

1) Prior probability of Option A

This is your starting belief before observing the crowd. A value of 50% means no initial preference. Higher values mean you already think A is more likely.

2) Private signal accuracy

Think of this as how reliable each person’s private information is. If accuracy is 60%, each decision contains weak but useful information. If it is 80%, each choice is much more informative.

3) Previous counts for A and B

These represent the public decision history. A large imbalance (for example, A far greater than B) often creates strong pressure to follow the majority.

4) Your private signal

This is the direction of your own personal evidence right now. The calculator combines it with the public history to estimate your rational next move.

Model Formula (Simple Bayesian Version)

We use log-odds updating:

Public log-odds = ln(P(A)/(1−P(A))) + (A−B) × ln(q/(1−q))

where q is signal accuracy, and A−B is the net crowd difference. Then your private signal adds one more step:

Final log-odds = Public log-odds ± ln(q/(1−q))

“+” is used if your private signal favors A, and “−” if it favors B.

How to Interpret Results

• Public posterior tells you what the crowd history implies before your own signal is included.
• Posterior with your signal is your updated belief after adding private information.
• Suggested action is whichever option has posterior probability above 50%.
• Cascade warning appears when one side leads by at least two decisions, a common threshold used in introductory cascade examples.

Example

Suppose prior = 50%, signal accuracy = 60%, and the observed choices are A=4 and B=1. Public evidence is now strongly in favor of A. Even if your private signal says B, the model may still recommend A, which is exactly what herding looks like.

Limits and Practical Notes

• This is a stylized model, not a full behavioral simulation.
• It assumes each observed decision reflects a private signal with similar reliability.
• Real groups may have correlated information, reputational pressure, or strategic behavior.
• Use this as a decision aid and intuition builder, not a guaranteed predictor.