3. Consider the following situation. Alice prefers Carl to David. Barbara prefer

Question

3. Consider the following situation. Alice prefers Carl to David. Barbara prefers David to Carl. Carl prefers Alice to Barbara. David prefers Barbara to Alice. How many different stable marriage solutions are there?

A:0

B: 1

C:2

Multiple Choice point possible (graded) Which of the following situations is unstable? O Joe likes Mary more than his current partner Nancy. Joe's partner Mary is his least favorite woman Joe and Nancy both prefer each other to their current partners. You have used 0 of 1 attempt Multiple Choice 1 point possible (graded) Consider the following situation. Alice and Barbara both prefer Carl to David. Carl and David both prefer Alice to Barbara. A solution to the stable marriage problem is a way to marry the four people into to couples. How many different stable marriage solutions are there? 0 1

Explanation / Answer

1. Which of the following situation in unstable.

       Joe likes mary more than his current partner nancy.

Reason : Third statment clearly states that nancy and joe are partners and they prefer each other.

                Also the situation in statment two says that joe has least priority over Mary

Both the above statement give positive sign to the relation of joe and nancy, hence the affection of joe to mary will be unstable.

Situation 2:

                     1st case : Alice and barbara prefers to carl out of carl and david

                     2nd case: carl and david prefers to Alice out of Alice and Barbara

So Comparing both the cases Alice and Carl has mutual interest over others, so regarding situation 2 there exists only one stable marriage solution exists.

Situation 3:

                   1st case: Alice prefers carl

                   2nd case: Barbara prefers David

                   3rd case : Carl prefers Alice

                   4th case : David prefers Barbara

From all the above cases 1 and 3 are vice versa so carl and Alice score one marriage solution, likewise cases 2 and 4 are vice versa so David and Barbara score one marriage solution.

So finally out of the third situation, there exists two stable marriage solution.

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