Suppose someone’s forecasts were systematically underconfident. If we made a binned scatterplot with their predicted probabilities from 50% to 100% on the x-axis and the observed outcome frequencies on the y-axis, then we would expect for most of the dots to lie:

Question

BlackTom AI · Accepted Answer

The question asks about the pattern in a binned scatterplot where x-axis shows predicted probabilities from 50% to 100% and y-axis shows observed outcome frequencies, given that forecasts are systematically underconfident.

Option 1: Above the 45-degree line
- When forecasts are underconfident, the predicted probabilities tend to be pulled toward 50% (0.5), i.e., they are not as extreme as the true underlying risk for many events. In the range from 50% to 100%, this shrinking toward 0.5 means that, for many bins, the actual observed frequencies tend to be higher than the forecasted probabilities relative to the line, causing the points to sit above the 45-degree line. In other words, the empirical frequency exceeds the forecast probability more often than not in these bins, which manifests as an upward deviation from the diagonal.

Option 2: Below the 45-degree line
- If the dots were below the 45-degree line, that would indicate observed frequencies are lower than the forecasted probabilities across those bins. This would correspond to overconfidence in the forecasts (predictions too extreme relative to observed outcomes), not underconfidence. Since the premise specifies systematic underconfidence, this below-line pattern would be inconsistent with that premise.

In summary, underconfidence shifts the calibration so that observed frequencies tend to outpace the predicted probabilities in this x-range, placing most dots above the diagonal. The below-diagonal pattern would instead signal overconfidence and is not aligned with the notion of systematic underconfidence.

Suppose someone’s forecasts were systematically underconfident. If we made a binned scatterplot with their predicted probabilities from 50% to 100% on the x-axis and the observed outcome frequencies on the y-axis, then we would expect for most of the dots to lie: 单项选择题

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