Papers
Original write-ups developed in this repository. The literature surveys live under bibliography; these are new work.
Scoring Point-Cloud Distributional Submissions
Nearest-the-pin parimutuels, the KDE seam, and mollified scoring
A parimutuel over a continuum splits the pot in proportion to the density each participant placed at the realised outcome: the nearest-the-pin reward behind monteprediction.com. When the submission is a cloud of samples smoothed into a KDE, scoring at the raw outcome pays the deconvolution of the belief; jittering the pin with the same kernel restores strict propriety, and repeating the repaired score across smoothing scales splits the edge into Fisher-divergence payments.
Peter Cotton · Microprediction · July 2026 · full draft · pdf · interactive demo · implementation · prior-art audit
An Algebra of Prediction-Rewarding Mechanisms
Scoring rules, market makers, and pools as composable transducers
An expository account of how the forecast-elicitation mechanisms connect. A proper scoring rule is a convex potential; its Fenchel conjugate is a cost-function market maker and a level-set dual is a constant-function market maker; the linear and logarithmic opinion pools are the two Kullback-Leibler barycenters; and merging market makers is infimal convolution, so liquidity adds. A common transducer signature lets the mechanisms chain, and records where propriety survives a transformation of message or outcome. The mathematics is classical; the note gathers it in one convention. Companion papers carry the new results: point-cloud elicitation, and the parimutuel account of a conformal predictor's information gap.
Peter Cotton · working draft v0.4 · full draft · pdf
Multi-Stage Solicitation of Probability Distributions
Experiments, theory and perspective on conformal prediction
The microprediction platform ran several chained-elicitation games at once: a pool on a live number, a stream predicting that pool's own calibration, dependence streams that priced copulas through a space-filling curve, and a stacked lottery of calibration maps. This note describes those experiments and then asks, of each, whether it was a valid game: whether truthful reporting was really the best move. A chain is proper where an exogenous outcome anchors every stage, and a downstream contribution can then be scored in its own market or, for the log score equivalently, folded up to the top level. The base pool scored smoothed samples at the raw outcome and would have been improper, but an accidental jitter for discrete outcomes stood in for the fix the theory prescribes; the copula streams settled through a curve whose nearness is not the joint's. A chain is as valid as its weakest anchor and its settlement transform.
Peter Cotton · working draft v0.3 · full draft · pdf
Likelihood versus CRPS: A New Perspective
Composition, chained elicitation, and the score under which density refinements add up
The choice between the logarithmic score and CRPS is usually argued on locality, propriety, robustness, and interpretability. This note adds a fifth consideration the debate rarely weighs. When the elicited object is a reusable density and forecasts are chained, each stage refining the residual of the last, only the log score's per-stage increment is itself the proper score of what that stage added, the prequential and logarithmic-market-scoring structure. The mathematics is classical; the contribution is to make composability the organizing axis of the choice and to tie it to chained elicitation. A worked example shows the two scores preferring measurably different Gaussians on heavy-tailed data, and conformal prediction appears as the limiting case: a method that need not produce a density, scored on the one metric that does not notice.
Peter Cotton · working draft v0.1 · full draft · pdf