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Question: a decisionmaker is a father who has two sonsthey are...

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A decision-maker is a father who has two sons.They are going to purchase a new house. Suppose there are five possible choices ω1, ω2, ... , ω5. The rankings of houses from the most favorite to the least favorite are as following: • Father: ω2, ω5, ω3, ω4, ω1; • Son 1: ω5, ω4, ω1, ω3, ω2; • Son 2: ω1, ω2, ω3, ω5, ω4. Suppose the decision-maker cares and only cares the feeling of his sons, and thus he comes up the following method to choose the new house: • For houses that are available, he asks both of his sons to rank them according to their preferences and assign a number to them starting from 1. For example, if the available houses are ω1 and ω4 and Son 1 ranks them truthfully, then he will assign number 1 to ω4 and 2 to ω1. After gathering those numbers, the father will then choose the house such that the sum of the numbers are minimum. If there is a tie, then the decision-maker will choose the one that he prefers. Suppose the sons always rank truthfully, will the decision-maker’s choice function satisfy the independence condition? and why?

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