The function only uses the preorders on candidates implied by the utility functions.
I didn’t know what this meant, so I asked someone around me, and now I believe that this means “Your voting function is only allowed to use the information in voters’ ballots, and isn’t allowed to use any information that is in their utility function but that they didn’t write down on their ballot”.
For example if someone is voting strategically, you aren’t allowed to check that by comparing it to their actual preferences; you aren’t allowed to use info that’s only stored in their utility function.
Yeah, that is correct, although note that the ballot could just ask the voters for their utility function. The assumption means the ballot asks for a ranking of candidates, possibly with ties, and no other information.
Yes, although I bet that Condorcet and consistent are still incompatible for deterministic voting systems, even if you allow taking in the entire utility functions
I didn’t know what this meant, so I asked someone around me, and now I believe that this means “Your voting function is only allowed to use the information in voters’ ballots, and isn’t allowed to use any information that is in their utility function but that they didn’t write down on their ballot”.
For example if someone is voting strategically, you aren’t allowed to check that by comparing it to their actual preferences; you aren’t allowed to use info that’s only stored in their utility function.
Yeah, that is correct, although note that the ballot could just ask the voters for their utility function. The assumption means the ballot asks for a ranking of candidates, possibly with ties, and no other information.
Note that this is only true for ranked methods, and not scored methods, like Approval Voting, Star Voting, etc.
Checking my understanding here: is this assumption ruling out quadratic voting, which asks for a weighted-ranking of candidates?
Yes, although I bet that Condorcet and consistent are still incompatible for deterministic voting systems, even if you allow taking in the entire utility functions