Analytical representation of probabilities under the IAC condition

Abstract

This paper extends the work of Gehrlein and Fishburn (1976) and Gehrlein (1982) by providing a general theorem relating to the analytical representation of the probability of an event in a given space of profiles. It applies to any event characterized by a set of linear inequalities regardless of whether the coefficients defining the inequalities are integer or fractional coefficients. An algorithm for the probability calculation is also suggested. This suggested methodology is used to provide a complete characterization of the vulnerability properties of the four scoring rules studied in Lepelley and Mbih (1994) to manipulation by coalitions in a 3-alternative n-agent society. © Springer-Verlag 2000.