Descending Solid Coalitions: Difference between revisions

Since DSC satisfies [[Later-no-harm criterion|Later-no-harm]], it's not possible for a voter to get a better result by withholding lower preferences. It is possible, however, for a voter to get a better result for a candidate already ranked by ranking additional candidates below that candidate, or by changing the ranking of candidates ranked below that candidate such that at least one candidate is ranked above another candidate instead of being ranked the same as or below that candidate. The corrolary to this statement is that it is possible for a voter to get a worse result for a candidate by withholding preferences for candidates ranked below that candidate, or by changing the ranking of candidates ranked below that candidate such that at least one candidate is ranked the same as or below another candidate instead of being ranked above that candidate. If the Nashville voters had not listed any preferences after either Nashville or Chattanooga, or had ranked Memphis the same as or above either Knoxville or Chattanooga or both Knoxville and Chattanooga, the winner would have been Memphis, as the number of candidates strictly committed to the set {N,C,K} would have been less than the number of candidates strictly committed to at least the sets {M} and {M,N}, and regardless of the order in which those two sets (along with the set {M,N,C} if Nashville's voters had still all ranked Chattanooga ahead of Knoxville) were considered, Memphis would have been the only candidate remaining after those two or three sets were considered.