> Gibbard’s theorem assumes that each participant has a set of preferences about the entire outcome of the process. In this case, the outcome of the process is the matching of all candidates to all positions.
Doesn't this mean it's actually not very applicable to voting systems?
Voters generally only care whether their preferred candidate comes first, not about the relative ordering of the other candidates.
I suppose a voter might care how close their preferred candidate came to winning (or their margin of victory), but that's still a slightly weaker requirement than having a total ordering of all candidates relative to each other.
Doesn't this mean it's actually not very applicable to voting systems?
Voters generally only care whether their preferred candidate comes first, not about the relative ordering of the other candidates.
I suppose a voter might care how close their preferred candidate came to winning (or their margin of victory), but that's still a slightly weaker requirement than having a total ordering of all candidates relative to each other.