Social choice and the continuity axiom

TL;DR: In this paper, the authors studied the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules and showed that the two sets of conditions are nocomparable.

TL;DR: In this paper, the nonexistence of 1 continuous anonymous rule that respects anonymity with two voters and two-dimensional choice spaces is shown to be equivalent to a fixed point problem, and the results can be extended to higher dimensional choice spaces and any finite number of agents.

TL;DR: In this paper, the authors revisited the aggregation theorem of Chichilnisky (1980), replacing, the original smooth topology by the closed convergence topology and responded to several comments (N Baigent (l984, 1985, l987, l989), N Baigent and P Huang (l990), and M LeBreton and J Uriarlc (1990a, b) Theorems l and 2 establish the contractibility of three spaces of preferences: the space of strictly quasiconcave preferences Psco, its subspace of smooth preferences P

TL;DR: In this paper, it was shown that any non-dictatorial voting scheme with at least three possible outcomes is subject to individual manipulation, i.e., an individual can manipulate a voting scheme if, by misrepresenting his preferences, he secures an outcome he prefers to the "honest" outcome.

TL;DR: In this paper, the strategy-proofness condition for voting procedures corresponds to Arrow's rationality, independence of irrelevant alternatives, nonnegative response, and citizens' sovereignty conditions for social welfare functions.

TL;DR: Republication of this book provides social science and mathematics students with a text that is the analogue of mathematical methods textbooks used in the study of the physical sciences and engineering.