# A Prediction Tournament Paradox

## TL;DR

In prediction tournaments, surprisingly, the most accurate forecasters are not necessarily the winners, due to a paradox revealed through simulations, challenging assumptions about forecasting accuracy and tournament outcomes.

## Contribution

This paper identifies and explains a paradox in prediction tournaments where the best forecasters are unlikely to win, highlighting a counterintuitive statistical phenomenon.

## Key findings

- Simulations show winners are often not the most accurate forecasters.
- The paradox persists even outside the most accurate forecaster range.
- Implications for forecasting research and tournament design.

## Abstract

In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate forecasters will likely score better. This is true for one-on-one comparisons between contestants. But consider a realistic-size tournament with many contestants, with a range of accuracies. It may seem self-evident that the winner will likely be one of the most accurate forecasters. But, in the setting where the range extends to very accurate forecasters, simulations show this is mathematically false, within a somewhat plausible model. Even outside that setting the winner is less likely than intuition suggests to be one of the handful of best forecasters. Though implicit in recent technical papers, this paradox has apparently not been explicitly pointed out before, though is easily explained. It perhaps has implications for the ongoing IARPA-sponsored research programs involving forecasting.