Mechanism design and social choice critically rely on having access to preferences over outcomes from a set of participants, implicitly assuming these preferences are known and correct. However, using the example of voting, it is well-understood that voters often submit preferences that are dissonant with their policy positions [20, 29]. We propose a stylized model of representing informational externalities causing some of this dissonance, in which voters update and move their “true” (but unacted upon) preferences based on a piece of global, external information. We propose a modified voting rule that recovers true preferences while querying only ordinal, rather than cardinal preferences. This enables us to learn enough about the strength of preferences to understand changes to votes, without fully learning cardinal preferences. With this modified voting rule, we are then able to understand the robustness of a large class of voting rules to these informational externalities, bounding the probability of voting outcomes changing because of informational externalities.