Multi-outcome and Multidimensional Market Scoring Rules

TL;DR

This paper investigates the limitations of existing market scoring rules in multi-outcome and multidimensional prediction markets with budget-constrained agents, proposing a modified rule that ensures market prices move towards traders' true beliefs.

Contribution

It introduces a modified market scoring rule that guarantees price movement towards agents' beliefs in budget-limited settings, overcoming limitations of previous rules.

Findings

Modified rule ensures market moves towards true beliefs with budget constraints

Original rules do not always move prices towards beliefs under reasonable conditions

The new mechanism retains strategic properties of traditional scoring rules

Abstract

Hanson's market scoring rules allow us to design a prediction market that still gives useful information even if we have an illiquid market with a limited number of budget-constrained agents. Each agent can "move" the current price of a market towards their prediction. While this movement still occurs in multi-outcome or multidimensional markets we show that no market-scoring rule, under reasonable conditions, always moves the price directly towards beliefs of the agents. We present a modified version of a market scoring rule for budget-limited traders, and show that it does have the property that, from any starting position, optimal trade by a budget-limited trader will result in the market being moved towards the trader's true belief. This mechanism also retains several attractive strategic properties of the market scoring rule.