一个合理的、充分民主的选举体系应该满足下述公理： 公理1：Decisive(确定性公理)-One and only one winner.(U-公理) 公理2：Pareto principle(帕累托公理或一致性公理)-If all voters rank candidate X above candidate Y,then we oughtn't elect Y.(P) 公理3：Nondictatorship(非独裁公理)-No voter should have the power to always get his way.(D-公理) 公理4：Independence of irrelevant candidates(第三者公理或阿罗公 )-Suppose that,given the voting rule and voters'rankings,candidate X ends up the winner of an election.Now look at another situation that is exactly the same except that some other candidate Y-who didn't win-is no longer on the ballot.Well,candidate Y is,in a sense,"irrelevant;"he didn't win the election in the first place,and so leaving him off the ballot shouldn't make any difference.And so,the independence axiom requires that X should still win in this other situation.(I-) 公理4的含义：合理的选举系统中不应出现搅局者(spoiler)。搅局者的 例子是2000年美国大选中的第三者Ralph.Nader: George W.Bush defeated Al Gore by 537 votes.Nader received 97,421 votes,which led to claims that he was responsible for Gore's defeat.Nader, both in his book Crashing the Party and on his website,states:"In the year 2000,exit polls reported that 25%of my voters would have voted for Bush 38%would have voted for Gore and the rest would not have voted at all." (which would net a 13 12,665 votes,advantage for Gore over Bush.) 6➌❻Ü♥✛✦➾➞➡❒✛➚Þ◆❳❆❚÷✈❡ãú♥➭ ú♥1➭Decisive(✭➼✺ú♥)-One and only one winner. (U-ú♥) ú♥2➭Pareto principle(ø❭÷ú♥➼➌➋✺ú♥)-If all voters rank candidate X above candidate Y, then we oughtn✳t elect Y. (P-ú♥) ú♥3➭Nondictatorship(➎Õàú♥)-No voter should have the power to always get his way. (D-ú♥) ú♥4➭Independence of irrelevant candidates(✶♥öú♥➼❈Ûú ♥)-Suppose that, given the voting rule and voters✳ rankings, candidate X ends up the winner of an election. Now look at another situation that is exactly the same except that some other candidate Y✮who didn✳t win✮is no longer on the ballot. Well, candidate Y is, in a sense, ✴irrelevant;✵ he didn✳t win the election in the first place, and so leaving him off the ballot shouldn✳t make any difference. And so, the independence axiom requires that X should still win in this other situation. (I-ú♥) ú♥4✛➵➶➭Ü♥✛➚Þ❳Ú➙Ø❆Ñ②✟Ûö(spoiler)✧✟Ûö✛ ⑦❢➫2000❝④■➀➚➙✛✶♥öRalph.Nader➭ George W. Bush defeated Al Gore by 537 votes. Nader received 97,421 votes, which led to claims that he was responsible for Gore’s defeat. Nader, both in his book Crashing the Party and on his website, states: ”In the year 2000, exit polls reported that 25% of my voters would have voted for Bush, 38% would have voted for Gore and the rest would not have voted at all.” (which would net a 13 12,665 votes, advantage for Gore over Bush.) 6