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\section{Discussion}
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\label{sec:discussion}
Our investigation of strictly proper IP scoring rules reveals that, unlike in the classical precise setting, forecasting under imprecision demands careful attention to the decision-making aspect within forecast elicitation. In traditional frameworks with strictly proper scoring rules, forecasters are simply expected utility maximizers, making the reporting decision straightforward. However, when forecasts are imprecise—represented as sets or intervals—forecasters cannot internally aggregate their epistemic uncertainty. Instead, they require an external aggregation rule to reconcile their credal set-induced preferences into a single forecast. 

This need for external decision guidance naturally connects to social choice theory. In our framework, the DM provides a collective aggregation rule that guides forecasters in resolving their uncertainty. This approach not only preserves incentive compatibility in the imprecise setting but also highlights the importance of designing scoring rules that balance accuracy and robustness. By explicitly integrating a social choice–inspired aggregation function into the elicitation process, our work offers new perspectives on collective decision-making, where imprecise forecasts can be viewed as forecasts of the ``collective.'' This highlights promising directions for future research on imprecise scoring rules. 

% Our investigation into the truthful elicitation of imprecise forecasts reveals that, unlike the classical setting of precise probability reporting, forecasting under imprecision requires critical attention to the decision‐making aspect of forecasting. In traditional frameworks based on strictly proper scoring rules, forecasters are assumed to be expected utility maximizers, so the decision about which probability to report is straightforward. However, when forecasts are imprecise—expressed as sets or intervals—forecasters cannot internally aggregate their own epistemic uncertainty. Instead, they require guidance in the form of an external aggregation function that serves to reconcile the preferences induced by distributions in the credal set into a single, actionable forecast.

% This need for external decision guidance naturally invites a connection to social choice theory. In our framework, the decision-maker’s role is to provide a collective aggregation rule that informs the forecaster how to combine the extremes of their uncertainty. Such an approach not only preserves incentive compatibility in the imprecise setting but also underscores the value of designing loss functions that reflect both accuracy and robustness. By explicitly incorporating a social choice–like aggregation function into the elicitation process, our work opens new avenues for collective decision–making where imprecise forecasts can be interpreted as forecasts of the ``collective''.