One form of the multistage election system is the run-off system, whereby an initial set of candidates is reduced by eliminating from consideration the lowest ranking alternatives at each stage of the process. This paper investigates three run-off systems: the plurality run-off, the Nanson system, and the Coombs system, with respect to five criteria including Partial Non-manipulability, the Uniform Majority Principle, Independence from Individual Orderings, Voter Adaptability, and Inverse Condorcet.
Social choices are often made in stages. In certain instances, the set of available alternatives is not considered all at once, but in segments. In the committee voting system used in the United States Congress, a decision on a multi-alternative issue (i.e., a bill with several proposed amendments) will begin with the consideration of a single pair of alternatives. The winner of a majority vote then faces a third alternative, with the winner of that contest considered agaInst a fourth alternative, and so on until all the alternatives have been considered. The winner of the final contest is the social choice. Another type of multistage voting rule involves introducing the set of available alternatives all at once, and then eliminating the less desirable alternatives from consideration until no more alternatives can be eliminated. The remaining alternatives constitute the social choice set.
The first type of multistage procedure, usually referred to as a sequential elimination procedure, has been discussed by Campbell (1977) and Schwartz (1977). Multistage procedures of the second kind are known as run-off systems. Smith (1973) has obtained some general results concerning such systems, while Fishburn (1977) has investigated some specific aspects of one of those procedures.
This paper involves a comparison of three run-off election systems: the