Choice Group Seminar by Nick Baigent (LSE): ‘An Introduction to Signed Preferences’

Abstract: From a ranking of mutually compatible alternatives, how might a ranking of subsets of alternatives be obtained? This is the extension problem, introduced into choice theory by Kannai & Peleg (1982). Interpretations include ranking committees, including legislatures, obtained from a ranking of possible committee members; and similarly ranking possible work teams, wines for a wine tasting, collections in a gallery/museum and potential clubs to join. But suppose that, while I prefer to chat with a philosopher than an economist, and to an economist than an astrologer, it may also be the case that I would welcome chatting with a philosopher and/or an economist, but prefer not to chat AT ALL with an astrologer. While a preference ranking cannot take such exclusionary preferences into account, a signed preference can. Extensions of signed preferences were first discussed in Fishburn (1992), along with a score based extension. But then the question arises: Which extensions could be obtained by summing Fishburn scores? This paper offers an answer to this question, as well as a wider discussion of extension problems.

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