Anonymity, ordinal preference proximity and imposed social choices

The Copeland rule and Condorcet?s principle

“…Therefore, for every R ∈ B, we define the "closeness to Condorcet" ranking 5 C R as follows: 5 At first sight this ranking might seem similar to the Slater [17] ranking. However, the essential difference is that the Slater ranking is of shortest Kemeny distance to the original binary relation whereas the "closeness to Condorcet" ranking ranks the alternatives according to their distances from being Condorcet winners.…”

“…The preservation of proximity, both in an ordinal and in the cardinal framework of distance functions and metrics, is also used as a property for social choice rules (see Baigent [1] and Eckert and Lane [5]). This use is partly justified by the analogy of proximity preservation to the continuity condition used in topological social choice theory (see Baigent [2] and Lauwers [11] for surveys).…”

Abstract Aggregations and Proximity Preservation: An Impossibility Result

“…First, anonymity (which is a stronger condition than nondictatorship) is not used, unlike the results in Chichilnisky (1979Chichilnisky ( , 1982, Baigent (1987), Grafe and Grafe (2001) and Eckert and Lane (2002). 1 In the result below, a new no-veto property is used instead.…”

“…1 In the result below, a new no-veto property is used instead. Infinite populations are allowed following Grafe and Grafe (2001) and Eckert and Lane (2002). Furthermore, in the formulation of proximity preservation, the use of a metric in Baigent (1987) is replaced by the use of distance rankings following Eckert and Lane (2002).…”

Transitive closure, proximity and intransitivities

“…Baigent[1] surveys topological approaches 2. Refer to Baigent[1] for a discussion and survey of the use of the Kemeny metric in the literature 3. However, see Eckert and Lane[3] for a limitation of this characterization.…”