| Summary: | Proper scoring
rules are scoring methods that incentivize honest reporting of subjective
probabilities, where an agent strictly maximizes his expected score by
reporting his true belief. The implicit assumption behind proper scoring rules
is that agents are risk neutral. Such an assumption is often unrealistic when
agents are human beings. Modern theories of choice under uncertainty based on
rank-dependent utilities assert that human beings weight nonlinear utilities
using decision weights, which are differences between weighting functions
applied to cumulative probabilities. In this paper, we investigate the
reporting behavior of an agent with a rank-dependent utility when he is
rewarded using a proper scoring rule tailored to his utility function. We show
that such an agent misreports his true belief by reporting a vector of decision
weights. my findings thus highlight the risk of utilizing proper scoring rules
without prior knowledge about all the components that drive an agent's attitude
towards uncertainty. On the positive side, we discuss how tailored proper
scoring rules can effectively elicit weighting functions. Moreover, we show how
to obtain an agent's true belief from his misreported belief once the weighting
functions are known.
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