Mechanism design for the truthful elicitation of costly probabilistic estimates in distributed information systems

Abstract

This paper reports on the design of a novel two-stage mechanism, based on strictly proper scoring rules, that allows a centre to acquire a costly forecast of a future event (such as a meteorological phenomenon or a probabilistic estimate of a specific parameter such as the quality of an expected service), with a specified minimum precision, from one or more agents. In particular, this is the first mechanism that can be applied in a setting where the centre has no knowledge about the actual costs involved in the generation of the agents' estimates and also has no means of evaluating the quality and accuracy of the estimates it receives. En route to this mechanism, we first consider a setting in which any single agent can provide an estimate of the required precision, and the centre can evaluate this estimate by comparing it with the outcome which is observed at a later stage. This mechanism is then extended, so that it can be applied in a setting where the agents' different capabilities are reflected in the maximum precision of the estimates that they can provide, and hence the centre may need to select multiple agents and combine their individual results in order to obtain an estimate of the required precision. For all three mechanisms, we prove their economic properties (i.e. incentive compatibility and individual rationality) and then present specific empirical results. For the single agent mechanism we compare the quadratic, spherical and logarithmic scoring rules with a parametric family of scoring rules. We show that although the logarithmic scoring rule minimises both the mean and variance of the centre's total payments, using this rule means that an agent may face an unbounded penalty if it provides an estimate of extremely poor quality. We show that this is not the case for the parametric family, and thus, we suggest that the parametric scoring rule is the best candidate in our setting. Furthermore, we show that the 'multiple agent' extension describes a family of possible approaches to select agents in the first stage of our mechanism, and we show empirically and prove analytically that there is one approach that dominates all others. Finally, we compare our novel contribution and with the peer prediction mechanism introduced by Miller et al. (2007) [29] and show that the centre's total expected payment is the same in both mechanisms (and is equal to total expected payment in the case that the estimates can be compared to the actual outcome), while the variance in these payments is significantly reduced within our mechanism.

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ORCID for Enrico H. Gerding: orcid.org/0000-0001-7200-552X

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