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<EM> Schwartz Sequential Dropping: <BALLOT> Rank-balloting definitions: To rank a candidate means to assign to that candidate a postive integer that will be referred to as a rank number. To rank X over Y means to assign to X a rank number that is lower than the rank number that one assigns to Y, or else to assign a rank number to X, but not to Y. Balloting: The ballot shall provide a way for voters to rank any or all of the candidates listed on the ballot--as many or as few candidates as they wish to rank. </BALLOT> <VOTING> A voter may assign the same rank number to more than one candidate if s/he wants to--as many as s/he wishes to. A ballot is spoiled and not counted if it assigns more than one rank number to any one candidate. </VOTING> <IRRV> Definitions involving pairwise defeats: "Ballots", as used here, means "valid ballots". X beats Y if the number of ballots ranking X over Y is greater than the number of ballots ranking Y over X. A defeat is an instance of one candidate beating another. If X beats Y, then the strength of that defeat is defined as the number of ballots ranking X over Y. Among any particular set of defeats, the weakest defeat is the one that has the lowest strength. <VICTORY_SET> Definition of the Schwartz set: 1. An unbeaten set is a set of candidates none of whom are beaten by anyone outside that set. 2. An innermost unbeaten set is an unbeaten set that doesn't contain a smaller unbeaten set. 3. The Schwartz set is the set of candidates who are in innermost unbeaten sets. Note: In public elections, where pairwise ties are vanishingly rare, there will only be one innermost unbeaten set. </VICTORY_SET> <WINNER> Count: If, by the rules of this count, there are more than one winner, then one winner shall be chosen from among them by whatever tiebreaking statute is already in effect at the time of this statute's enactment. If there are one or more candidates who are not beaten then they win and the count ends. If there are no candidates who are not beaten, then the winner shall be determined by repeatedly carrying out, in their labeled numerical order, the defeat-dropping instructions that follow this paragraph, until there are one or more candidates who are not beaten. They win and the count ends. <DEFEAT_DROPPING> <DEFEAT_STRENGTH> [define "weakest defeat"] </DEFEAT_STRENGTH> 1. Determine, by the above-stated definition of the Schwartz set, disregarding any defeats that have been dropped, which candidates are in the Schwartz set. 2. Drop the weakest defeat among those candidates who are in the Schwartz set. If, instead of one weakest defeat among them, there are two or more equally weakest defeats among them, then drop all of those equally weakest defeats among them. </DEFEAT_DROPPING> </WINNER> </IRRV> </EM>