Self-financed wagering mechanisms for forecasting

Abstract

We examine a class of wagering mechanisms designed to elicit truthful predictions from a group of people without requiring any outside subsidy. We propose a number of desirable properties for wagering mechanisms, identifying one mechanism-weighted-score wagering-that satisfies all of the properties. Moreover, we show that a single-parameter generalization of weighted-score wagering is the only mechanism that satisfies these properties. We explore some variants of the core mechanism based on practical considerations.

Removing arbitrage from wagering mechanisms

“…For example, the average or weighted average of private beliefs can provide a robust prediction, with accuracy improving in the number and diversity of individual beliefs [Jacobs 1995;Surowiecki 2004;Chen et al 2005;Dani et al 2006;Page 2007;Ungar et al 2012]. Researchers have developed one-shot betting mechanisms with various theoretical properties [Kilgour and Gerchak 2004;Johnstone 2007;Lambert et al 2008Lambert et al , 2014. In particular, Lambert et al [2008] proposed a class of weighted score wagering mechanisms (WSWMs), where each participant makes a prediction about an uncertain event and wagers some amount of money.…”

“…Researchers have developed one-shot betting mechanisms with various theoretical properties [Kilgour and Gerchak 2004;Johnstone 2007;Lambert et al 2008Lambert et al , 2014. In particular, Lambert et al [2008] proposed a class of weighted score wagering mechanisms (WSWMs), where each participant makes a prediction about an uncertain event and wagers some amount of money. The total amount wagered is redistributed among the participants after the event outcome is revealed.…”

“…These mechanisms satisfy a set of desirable properties, including (1) budget balance: the sum of participants' payoffs is zero and the center does not need to subsidize the betting; (2) individual rationality: each participant prefers participating to not participating; (3) incentive compatibility: each participant maximizes his expected payoff by predicting his true belief, and (4) sybilproofness: no participant can benefit from splitting his wager and participating under multiple identities. Conversely, Lambert et al [2008] showed that any one-shot wagering mechanism satisfying this set of properties must be a WSWM. Kilgour and Gerchak [2004], Johnstone [2007], and Lambert et al [2008Lambert et al [ , 2014 designed their mechanisms for participants with immutable beliefs.…”

“…Conversely, Lambert et al [2008] showed that any one-shot wagering mechanism satisfying this set of properties must be a WSWM. Kilgour and Gerchak [2004], Johnstone [2007], and Lambert et al [2008Lambert et al [ , 2014 designed their mechanisms for participants with immutable beliefs. While Bayesian agents sharing a common prior can never "agree to disagree", immutable agents persist in their disagreement, never wavering from their prior beliefs even upon observing other players' actions.…”

Computational challenges in e-commerce

“…32 Shared scoring rules can form the basis of self-financing (budget-balanced) wagering mechanisms to obtain multiple individual forecasts. 23 Indeed, the line between scoring rules and markets becomes blurred. For example, the most common automated market maker used for prediction markets can be viewed as a sequential shared scoring rule.…”