Multiattribute signed orders

A self-reflecting signed order is a preference relation that compares relative likes and dislikes for items in a set X by jointly ordering X and a disjoint copy of X. If you would like Jones but not Smith appointed to a committee, and also think it more important to exclude Smith than include Jones, your self-reflecting signed order records this information. We review basic representational theory for signed orders, then examine them when X is multiattributed. Axioms for additive measurement of multiattribute self-reflecting signed orders are specified for several X-structures.