SIGNED ORDERS AND POWER SET EXTENSIONS

The practical necessity of estimating preferences between subsets of an n-item set from preferences between the items themselves has long been recognized. This paper explores a new basis for extension that can be expressed almost as simply as an ordering of items but contains a great deal more information. The new basis, called a self-reflecting signed order, interweaves preferences for the inclusion of items in a subset and preferences for exclusion of items from the subset. Properties of self-reflecting signed orders and defensible conditions for their extension to subset preferences are studied. © 1992.