Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a new algorithm for the Unighted Coalitional Manipulation problem under the Maximin voting rule.  prove that the algorithm gives an approximation ratio of 1 2/3 to the corresponding optimization problem. This is an improvement over the previously known algorithm that gave a 2-approximation.  also prove that its approximation ratio is no better than 1 1/2, i.e., there are instances on which a 1 1/2-approximation is the best the algorithm can achieve. Finally,  prove that no algorithm can approximate the problem better than to the factor of 1 1/2, unless p = NP.
['Michael Zuckerman', 'O. Lev', 'Jeffrey S. Rosenschein']
I am writing a research paper on a idea An algorithm for the coalitional manipulation problem under Maximin
[{"from": "human", "value": "I am writing a research paper on a idea An algorithm for the coalitional manipulation problem under Maximin"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce a new algorithm for the Unighted Coalitional Manipulation problem under the Maximin voting rule.  prove that the algorithm gives an approximation ratio of 1 2/3 to the corresponding optimization problem. This is an improvement over the previously known algorithm that gave a 2-approximation.  also prove that its approximation ratio is no better than 1 1/2, i.e., there are instances on which a 1 1/2-approximation is the best the algorithm can achieve. Finally,  prove that no algorithm can approximate the problem better than to the factor of 1 1/2, unless p = NP."}]