In this paper,algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli le...In this paper,algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients.The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.展开更多
This paper established a general jury theorem on group decision making where the probabilities of the individuals in making correct choice between two alternatives can be different.And we proved that the higher the pr...This paper established a general jury theorem on group decision making where the probabilities of the individuals in making correct choice between two alternatives can be different.And we proved that the higher the probability of any decision maker in the group correctly choosing between two alternatives,the higher the probability of the group correctly choosing the same two alternatives.The general jury theorem also indicates that given two groups of individuals with the same average probability of making the correct choice,the one with a more varied or diverse distribution of probabilities will have a higher probability of making the correct choice.In particular,we proved that as the number of decision makers in the group increases to infinity,this probability tends to the limit 1.The general jury theorem presented in this paper substantially generalizes the well-known Condorcet jury theorem in the group decision making theory,which has not been generalized for 200 years until now.展开更多
基金supported by National Natural Science Foundation of China (Grant No.10891056)
文摘In this paper,algebraic criteria are established to determine whether or not a real coefficient polynomial has one or two pairs of conjugate complex roots whose moduli are equal to 1 and the other roots have moduli less than 1 directly from its coefficients.The form and the function of the criteria are similar to those of the Jury criterion which can be used to determine whether or not all the moduli of the roots of a real coefficient polynomial are less than 1.
文摘This paper established a general jury theorem on group decision making where the probabilities of the individuals in making correct choice between two alternatives can be different.And we proved that the higher the probability of any decision maker in the group correctly choosing between two alternatives,the higher the probability of the group correctly choosing the same two alternatives.The general jury theorem also indicates that given two groups of individuals with the same average probability of making the correct choice,the one with a more varied or diverse distribution of probabilities will have a higher probability of making the correct choice.In particular,we proved that as the number of decision makers in the group increases to infinity,this probability tends to the limit 1.The general jury theorem presented in this paper substantially generalizes the well-known Condorcet jury theorem in the group decision making theory,which has not been generalized for 200 years until now.
