  Wagering mechanisms are one-shot betting mechanisms that elicit agents'
predictions of an event. For deterministic wagering mechanisms, an existing
impossibility result has shown incompatibility of some desirable theoretical
properties. In particular, Pareto optimality (no profitable side bet before
allocation) can not be achieved together with weak incentive compatibility,
weak budget balance and individual rationality. In this paper, we expand the
design space of wagering mechanisms to allow randomization and ask whether
there are randomized wagering mechanisms that can achieve all previously
considered desirable properties, including Pareto optimality. We answer this
question positively with two classes of randomized wagering mechanisms: i) one
simple randomized lottery-type implementation of existing deterministic
wagering mechanisms, and ii) another family of simple and randomized wagering
mechanisms which we call surrogate wagering mechanisms, which are robust to
noisy ground truth. This family of mechanisms builds on the idea of learning
with noisy labels (Natarajan et al. 2013) as well as a recent extension of this
idea to the information elicitation without verification setting (Liu and Chen
2018). We show that a broad family of randomized wagering mechanisms satisfy
all desirable theoretical properties.
