A good story explains one thing very well. That is its strength and its trap. Once a story fits the facts, we stop looking for other explanations, and the facts it doesn't fit quietly fall out of view.
A model is a story with its assumptions written down. That alone makes it more honest, because you can point at an assumption and ask whether it holds. But a single model has the same blind spot as a single story: it sees the world through one lens. The statistician George Box put it bluntly: "All models are wrong, but some are useful."
Many-model thinking takes that seriously. If every model is wrong in its own way, use several, and let their errors cancel.
The diversity prediction theorem
There is a precise reason this works, and it is one line of algebra. For any set of numeric predictions:
Crowd error = average individual error − diversity of predictions
Here "error" is squared distance from the truth, the crowd's prediction is the average of everyone's predictions, and "diversity" is the average squared distance of each prediction from that crowd average.
Try it with three forecasters predicting next month's sales when the true figure turns out to be 100 units:
| Forecaster | Prediction | Squared error | Squared distance from crowd |
|---|---|---|---|
| A | 80 | 400 | 544.4 |
| B | 110 | 100 | 44.4 |
| C | 120 | 400 | 277.8 |
| Average | 103.3 | 300 | 288.9 |
The crowd's prediction is 103.3, a squared error of 11.1. The identity holds exactly: 300 − 288.9 = 11.1. No forecaster came close to the crowd's accuracy, and the reason is not that they were individually smart. It is that they were wrong in different directions.
The theorem is an identity, not a hopeful empirical claim. It holds for every set of predictions. The practical lesson is that you can make a group more accurate in two ways: make its members more accurate, or make them more different. Different models are a cheap way to buy the second.
Different assumptions, not different parameters
Diversity only counts if the models disagree for real reasons. Ten regressions with slightly different variables are one model wearing ten hats; their errors move together. Real diversity comes from models that make different structural assumptions about how the world works:
- A distribution model asks what shape the outcomes take: bell curve, long tail, or mixture.
- A network model asks who is connected to whom, and how influence travels.
- A game theory model asks what each actor wants and how their incentives interact.
- A dynamics model asks how the system changes over time, and whether it settles.
These families fail in different places, which is exactly what you want. That is why the library is organised by family, and why the apply-three-models skill insists on three models from three different families.
A worked example: customer churn
Say a subscription product is losing customers. Look at it through three lenses:
- Distribution. Plot churn by customer segment. If a handful of cohorts account for most of the losses (a power law), the fix is targeted. If churn is spread evenly, the problem is the product for everyone.
- Peer effects. Do cancellations cluster among customers who know each other, such as teams at the same company? A threshold model says one departure can tip others whose threshold is low, so a small loss can cascade.
- Dynamics. Treat customers as moving between states (active, dormant, cancelled) with a Markov model. The long-run share of active users depends only on the transition rates, so the lever is whichever rate is easiest to change, often the dormant-to-active one.
Each lens suggests a different intervention. Where all three agree, act with confidence. Where they disagree, you have found the cheapest experiment to run next, because the disagreement tells you which assumption you don't yet know is true.
How to practise it
- Name three models before you look at the data. Choosing afterwards invites you to pick the ones that confirm what you already believe.
- Write each model's prediction down. A model that can't be wrong isn't telling you anything.
- Give each model a job. The REDCAPE playbooks list seven: reason, explain, design, communicate, act, predict, explore. A model that is weak at predicting may still be excellent at explaining.
- Keep score. Over time you learn which families work in your domain, and you can weight them accordingly.
When more models don't help
Adding models is not free. If every model shares the same blind spot, say they all assume customers act independently, stacking them adds confidence without adding accuracy. And diversity only lowers the crowd's error for a given average error; a wildly wrong model adds diversity and error in roughly equal measure. The goal is a small set of models that are each reasonable and that disagree for good reasons.
Start with the diversity prediction model, then pick any two others from different families and see where they part ways.