Question 12
Below are the observed proposals from the traditional male propose-and-reject algorithm. After the algorithm terminates, only B is married to the man she likes the most. Also, it is known that A has the same preferences as B and every man likes C better than A. Reconstruct the complete preference lists of men and women in the given information.
| Round | Women | Men | Round | Women | Men |
|---|---|---|---|---|---|
| 1 | A | - | 5 | A | - |
| B | 1,2 | B | 4 | ||
| C | 3 | C | 2 | ||
| D | 4 | D | 1,3 | ||
| 2 | A | - | 6 | A | - |
| B | 1 | B | 3,4 | ||
| C | 2,3 | C | 2 | ||
| D | 4 | D | 1 | ||
| 3 | A | - | 7 | A | - |
| B | 1 | B | 3 | ||
| C | 2 | C | 2,4 | ||
| D | 3,4 | D | 1 | ||
| 4 | A | - | 8 | A | 2 |
| B | 1,4 | B | 3 | ||
| C | 2 | C | 4 | ||
| D | 3 | D | 1 |
Based on the above data, answer the given subquestions.
What is the preference ordering of woman D?