Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A tournament can be vied as a majority preference relation without ties on a set of alternatives. In this way, voting rules based on majority comparisons are equivalent to methods of choosing from a tournament.  consider the size of several of these tournament solutions in tournaments with a large but finite number of alternatives. Our main result is that with probability approaching one, the top cycle set, the uncovered set, and the Banks set are equal to the entire set of alternatives in a randomly chosen large tournament. That is to say, each of these tournament solutions almost never rules out any of the alternatives under consideration.  also discuss some implications and limitations of this result.
['Mark Fey']
I am writing a research paper on a idea Choosing from a large tournament
[{"from": "human", "value": "I am writing a research paper on a idea Choosing from a large tournament"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A tournament can be vied as a majority preference relation without ties on a set of alternatives. In this way, voting rules based on majority comparisons are equivalent to methods of choosing from a tournament.  consider the size of several of these tournament solutions in tournaments with a large but finite number of alternatives. Our main result is that with probability approaching one, the top cycle set, the uncovered set, and the Banks set are equal to the entire set of alternatives in a randomly chosen large tournament. That is to say, each of these tournament solutions almost never rules out any of the alternatives under consideration.  also discuss some implications and limitations of this result."}]