Relationship admitting families of candidates

A central theme in social choice is to determine when must there be a relationship among a group's sincere election rankings of several different subsets of candidates. This issue is completely resolved here for positional voting methods. Namely, necessary and sufficient conditions are derived for a family of subsets of candidates to determine when there is a choice of positional voting methods so that there are relationships among the election rankings. The same issue is resolved for a related family of social choice mappings. Then, in part, these necessary and sufficient conditions are used i) to analyze sequential voting procedures, ii) to show how to create new classes of axiomatic representations for social choice mappings that uniquely characterize the Borda Count, and iii) to determine the limits of indeterminacy for positional voting election outcomes.This research was supported in part by NSF grant IRI-8803505 and a Fellowship from the Guggenheim Memorial Foundation.