# Design and Analysis of a Synthetic Prediction Market using Dynamic Convex Sets

arXiv: https://arxiv.org/abs/2101.01787 · HTML: https://mlsanity.com/paper/2101.01787/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 61 references that are in the map.
- First posted on arXiv 5 Jan 2021.

## Builds on (most cited first, 3 of 3)

- [Multi-period Trading Prediction Markets with Connections to Machine Learning](https://mlsanity.com/paper/1403.0648/) (2014)
- [Augur: a decentralized oracle and prediction market platform](https://mlsanity.com/paper/1501.01042/) (2015)
- [Decentralized Prediction Market without Arbiters](https://mlsanity.com/paper/1701.08421/) (2017)

## Built on by (most cited first, 3 of 3)

- [A Synthetic Prediction Market for Estimating Confidence in Published Work](https://mlsanity.com/paper/2201.06924/) (2021)
- [A prototype hybrid prediction market for estimating replicability of published work](https://mlsanity.com/paper/2303.00866/) (2023)
- [Human-AI Collaboration for Estimating Scientific Replicability](https://mlsanity.com/paper/2605.27394/) (2026)

## Abstract (arXiv)

We present a synthetic prediction market whose agent purchase logic is defined using a sigmoid transformation of a convex semi-algebraic set defined in feature space. Asset prices are determined by a logarithmic scoring market rule. Time varying asset prices affect the structure of the semi-algebraic sets leading to time-varying agent purchase rules. We show that under certain assumptions on the underlying geometry, the resulting synthetic prediction market can be used to arbitrarily closely approximate a binary function defined on a set of input data. We also provide sufficient conditions for market convergence and show that under certain instances markets can exhibit limit cycles in asset spot price. We provide an evolutionary algorithm for training agent parameters to allow a market to model the distribution of a given data set and illustrate the market approximation using two open source data sets. Results are compared to standard machine learning methods.