If the aggregated preferences are transitive (i.e., ‘not inconsistent’ in your and Manfred’s wording), then this preference relation defines a total order on the objects, and there is a unique object that is preferred to every other object (in aggregate). (Furthermore, this is isomorphic to the set {1,2,3,...,7} under the ≤ relation.)
As I understand things, you have no guarantee of transitivity in the aggregated preferences even if you do have transitivity in the individual preferences.
If the aggregated preferences are transitive (i.e., ‘not inconsistent’ in your and Manfred’s wording), then this preference relation defines a total order on the objects, and there is a unique object that is preferred to every other object (in aggregate). (Furthermore, this is isomorphic to the set {1,2,3,...,7} under the ≤ relation.)
As I understand things, you have no guarantee of transitivity in the aggregated preferences even if you do have transitivity in the individual preferences.
Yes, of course you are correct.
Very helpful—reading about this now. Starting here: http://en.wikipedia.org/wiki/Ranking