Arrow's impossibility theorem, and the IIA criterion, is about preferences not about uncertain actions. In particular, IIA doesn't mean that you'll vote differently than your preferences in some sort of election, it means that your preferences themselves don't change when you introduce other irrelevant options. In your example, it wouldn't be about how Sidney would vote in an election given the different menu of candidates, it's about who Sidney would prefer win the election.

(with the caveat that it has been a long time since I've thought about these results.)