Joshua Della Vedova

Probability Weighting Index (PWI)

Trade-count-weighted non-bot Prelec alpha. Alpha = 1 is rational pricing; below 1 is the classical inverse-S weighting.

As of 2026-04-20, the PWI stands at 0.722, with a 52-week rolling z-score of -0.56. 13-week moving average: 0.705. 52-week moving average: 0.795. Based on 17,588 non-bot trades this week.

Weekly history

Light line: weekly alpha. Bold line: 13-week moving average. An alpha of 1.0 would mean the market prices binary outcomes rationally.

Components (weighted averages across non-bot wallets)

ComponentLatest valueWhat it captures
Trade-weighted mean calibration error0.0448Absolute gap between trade price and realized frequency
Trade-weighted longshot fraction0.5040Share of trades at prices below 10%

52-week rolling statistics

StatisticValue
Mean0.795
SD0.130
Min0.534
Max1.034
Observations52

Methodology

Each week, a one-parameter Prelec weighting function w(p) = exp(-(-log p)^alpha) is fit by weighted nonlinear least squares separately to each wallet class (active retail, sophisticated, casual, one-shot, bot). The PWI is the trade-count-weighted mean of the alphas across all non-bot wallet classes that week. Bots are excluded (trades_per_day > 50 OR n_trades > 1000) so the index reflects human probability weighting rather than algorithmic liquidity provision.

Interpretation: an alpha of 1.0 corresponds to rational pricing with no probability distortion. An alpha below 1 is the classical inverse-S weighting (small probabilities over-weighted, mid probabilities under-weighted) documented in Tversky and Kahneman (1992). An alpha above 1 implies the rarer opposite pattern. The 52-week rolling z-score requires at least 13 non-null observations and is blank before that.

Data

pwi_history.csv (160 weeks, from 2023-02-27) · pwi_latest.json · pwi_timeseries.json

Cite

@misc{dellavedova2026pwi, title = {Probability Weighting Index}, author = {Della Vedova, Joshua}, year = {2026}, version = {0.1.0}, publisher = {University of San Diego}, url = {https://jdellavedova.com/pwi}, note = {Part of the Della Vedova Prediction Market Indices (DV-PMI)} }