Cycles, empty cores, intransitivities, and other complexities affect group decision and voting rules. Approaches that prevent these difficulties include the Nakamura number, Greenberg’s theorem, and single peaked preferences. The results derived here subsume and significantly extend these...

Two theorems are given; the first extends the Sonnenschein-Mantel-Debreu theorem characterizing aggregate demand functions from the set of n (greater than or equal to) 2 commodities to all 2 (superscipt n) minus (n+1) subsets of two or more commodities. The second theorem concerns spatial voting...

Paradoxes from statistics and decision sciences form amusing, yet intriguing mathematical puzzles. On deeper examination, they constitute serious problems that could cause us, unintentionally, to adopt inferior alternatives. It is indicated here how ideas form "dynamical chaos" and orbits of...

It is shown that the source of Sen's and Arrow's impossibility theorems is that Sen's Liberal condition and Arrow's IIA counter the critical assumption that voters have transitive preferences. But if the procedures are not permitted to treat the transitivity of individual preferences as a valued...

Using Brams and Fishburn's report and data, the SC&W election is analyzed with an emphasis on explaining the theoretical reasons for the conflicting outcomes. In the process, some new results are obtained.