Papers
Original write-ups developed in this repository. The literature surveys live under bibliography; these are new work.
The Nearest-the-Pin Parimutuel
Peter Cotton · working draft v0.1 · full draft · implementation
A parimutuel pool whose outcomes form a continuum. Each participant submits a predictive density (a cloud of Monte-Carlo samples); when the point $z$ is revealed, the pot is split in proportion to the density each placed at $z$, relative to the crowd — a nearest-the-pin reward. It is the engine behind monteprediction.com.
Three claims, all implemented and unit-tested:
- Self-funding & honest. The split is zero-sum (the operator bears no risk), and for a log-wealth (Kelly) maximiser the unique optimal report is one's true density — the continuous shadow of "bet your beliefs", with growth governed by the logarithmic score against the crowd.
- The projection version. In high dimensions the joint density is hard to estimate, so score the cloud through random one-dimensional projections. By the energy-distance projection identity $$\mathrm{ES}(P,y)=c_d^{-1}\,\mathbb{E}_u\big[\mathrm{CRPS}(P_u,\langle u,y\rangle)\big], \qquad c_d=\tfrac{\Gamma(d/2)}{\sqrt\pi\,\Gamma((d+1)/2)},$$ the average sliced CRPS is the multivariate energy score — a strictly proper score built from cheap 1-D evaluations. This is the projection version used for monteprediction's eleven-dimensional clouds, and it places the mechanism inside the random-projections literature (Johnson–Lindenstrauss, sliced Wasserstein, sliced score matching).
- Two routes to high-dimensional scoring. Turning a joint forecast into a number at $z$ when $d$ is large can go via a structured density (the Schur pseudo-likelihood / Vecchia factorisation, Cotton 2024–25) or via random projection (the sliced energy score). The nearest-the-pin pool runs with either; a conjectured Schur-damped projection score interpolates between them with a single reliability dial $\gamma$.
Read the full working draft for the derivations, the honesty argument, the literature links, and the open questions.
Source material
Survey PDFs that motivate these write-ups:
- Novel Statistical and Market-Inspired Mechanisms for the Elicitation, Aggregation, and Rewarding of Predictive Contributions — the survey organising this repository.
- Perpetual Demand Lending Pools (Chitra, Diamandis, Sheng, Sterle & Yusubov, 2025; arXiv:2502.06028).