Extension of Preferences to an Ordered Set

If a decision maker prefers x to y to z, would he choose orderd set [x, z] or [y, x]? This article studies extension of preferences over individual alternatives to an ordered set which is prevalent in closed ballot elections with proportional representation and other real life problems where the decision maker is to choose from groups with an associated hierarchy inside. I introduce five ordinal decision rules: highest-position, top-q, lexicographic order, max-best, highest-of-best rules and provide axiomatic characterization of them. I also investigate the relationship between ordinal decision rules and the expected utility rule. In particular, whether some ordinal rules induce the same (weak) ranking of ordered sets as the expected utility rule.