Three roommates are planning to paint their living room. They have narrowed down the color to Yellow, Green or Red. The roommates' rankings over the colors are as follows: A matrix where Arlo, Bex and Cy rank Yellow, Green and Red either First, Second or Third. The first choices for each are Red for Arlo, Yellow for Bex, and Green for Cy. Second choices are Yellow for Arlo, Green for Bex, and Red for Cy. Third choices are Green for Arlo, Red for Bex, and Yellow for Cy. The roommates have decided to have a two-round vote to determine the color. They randomly select Yellow and Red to go each other in the first round. The winning color is then pitted against Green in the second round. If the roommates all vote truthfully in all rounds, what will be the outcome? Explain your answer. (10 pts.) If the roommates all vote strategically, what will be the outcome? Explain and support your answer. (10 pts.)