Axiomatic Consensus Theory in Group Choice and Biomathematics
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Author(s): W. H. Day and F. R. McMorris
Publisher: SIAM
ISBN: 0898715512
Format: softback
155pp
Price: $54.00
Review Date: 16 January 2004
Review: This book focuses on bioconsensus, a field where consensus methods, which were originally developed for use in social choice theory, are adapted for use in areas such as systematic biology and evolutionary or molecular biology. It describes formal models of consensus rules and introduces axiomatic paradigms with which to investigate them. It goes on to use the paradigms to investigate Arrow’s impossibility theorem for weak orders and applies Arrow’s paradigms to obtain possibility results. The impost of Arrow’s impossibility theorem for weak orders is that dictatorships, which are undesirable, are a consequence of desirable properties. Formalisms of Arrow’s paradigms that reveal general conditions under which the paradigms can be applied are given. Finally, the consensus concept is extended to problems where consensus objects may include subsets or supersets of the alternatives that are associated with the individual objects; such problems may arise in systematic biology and may benefit from axiomatic investigations of possibilities and impossibilities.