Connecting pairwise and positional election outcomes

General conclusions relating pairwise tallies with positional (e.g., plurality, antiplurality (“vote-for-two”)) election outcomes were previously known only for the Borda Count. While it has been known since the eighteenth century that the Borda and Condorcet winners need not agree, it had not been known, for instance, in which settings the Condorcet and plurality winners can disagree, or must agree. Results of this type are developed here for all three-alternative positional rules. These relationships are based on an easily used method that connects pairwise tallies with admissible positional outcomes; e.g., a special case provides the first necessary and sufficient conditions ensuring that the Condorcet winner is the plurality winner; another case identifies when there must be a profile whereby each candidate is the “winner” with some positional rule.

► Conditions ensuring positional (e.g., plurality) and Condorcet winners agree. ► Simple method connects pairwise tallies with all allowed positional rankings. ► Conditions developed that ensure various voting paradoxes must occur. ► Method permits discovering many other voting results.