Analysis on the Comparison Methods of Two Sorted Lists in Total-Order Set

The comparison methods for two sorted lists on total-order set have been discussed. Several cases are put forward to and the maximum value, the minimum value and the calculation formula for expected value of comparison times between two sorted lists are given and its correctness is proved. The relations between the comparison times and the size of the problem have been discovered by the experiment results and some advices are proposed for the design of lottery and some other activities of this type. The method has been applied in computer simulation for one kind of sports lottery and the consistency is shown by the experiment results between the values of computer simulation and the values of theory method.