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Extremizing and aggregating multiple forecasts

SoftCta readers often have several numbers for the same question: two venue prices, a forecasting model, a poll-based estimate and their own range. Combining them can improve accuracy, but it can also double count the same evidence or create false confidence. Research on forecasting tournaments found that simple aggregation helps and that extremizing sometimes helps more. This SoftCta guide explains those tools, when to use them and when to hold back.

Why combine at all

Independent errors tend to cancel when you average, which is the core of wisdom-of-crowds arguments. A blend of a market price, a model and a careful personal estimate is often better calibrated than any single input. The gain depends on how different the sources really are.

Mean, median and log odds

A simple mean of probabilities is easy but pulls toward 50 percent when one source is confident. Averaging in log odds, then converting back, treats a move from 90 to 95 percent as a bigger step than one from 50 to 55, as our log odds guide explains. The median is robust to a single wild input. SoftCta readers pick one method and stick to it in their journal.

What extremizing does

When each forecaster sees only part of the evidence, their average can be too timid. Extremizing pushes the aggregate further from 50 percent. Researchers working on the Good Judgment Project reported benefits from this on geopolitical questions. The adjustment assumes inputs are somewhat independent; if they all read the same headline, extremizing amplifies one source.

Shared information and double counting

Markets often already reflect public models and polls. If you average a market price with a model the market watches, you count the model twice. Two venues quoting the same contract are not independent either. SoftCta readers list each source’s main evidence and drop or downweight duplicates, using model versus market habits.

Weighting by track record

Sources with better calibration on similar questions deserve more weight, but track records need adequate sample sizes. Brier scores on a handful of questions mean little. SoftCta readers record their own forecasts to learn which inputs have helped them.

A worked example

For a policy question, two venues price Yes at an illustrative 30 and 34 cents, a public model says 25 percent, and the reader’s own range is 20–30 percent. The reader notes that both venues likely watch the model, treats the venue prices as one input, and averages in log odds to land near 28 percent. They decide not to extremize because the inputs share evidence, write a 24–32 percent range, and verify live cents. Substantial risk of loss.

Common mistakes

Averaging correlated sources as if independent. Extremizing a blend built on one headline. Weighting by recent wins rather than calibration. Hiding the method so you cannot learn from it. Treating the blended number as certainty; SoftCta pages avoid sure-thing claims and pick-selling.

Primary sources SoftCta readers open

SoftCta readers open the original sources behind each input — venue rules and prices, model methodology pages, and poll releases — and they read published research on forecast aggregation from the Good Judgment Project and related work for context, noting that findings depend on question types and forecaster pools.

Reading the quote step by step

• Read the full title and rules, including the named settlement source and the time zone.
• Convert the Yes and No prices to implied probabilities and note the gap between them.
• Subtract fees and spread to see the effective price you would actually face.
• Write your own probability range and the evidence behind it, then compare.
• Check related and near-duplicate markets on other venues for consistency.

Closing SoftCta checklist

• Re-read the venue definition in your own words before reacting to a price.
• Convert prices with fee and spread awareness; verify live cents on the operator.
• Prefer primary settlement sources over secondary headlines and social summaries.
• Treat ChanceWire hubs, movers, and tools as orientation — not order entry.
• Confirm age, location, and product eligibility; SoftCta pages will not suggest location spoofing.
• If clarity is incomplete, watching is a complete SoftCta outcome — no pick-selling urgency required.

SoftCta habits

• Write your own probability range before checking the crowd price.
• Prefer dated primary sources over social summaries.
• Compare related markets when a single book looks extreme.
• Size curiosity with fees and depth in mind; substantial risk of loss.