Posted December 17, 2015
This is only correct if you know nothing about any of the pairs. Since you do know your alignment, the chance of hitting scum is 1 in 3 if you are voting for yourself or your partner, or 5 in 9 if you are voting for someone else.
Consider this: There are 3 boxes and one of them has a prize. The chance of picking correctly is 1 in 3. Then, before choosing a box, someone tells you that box 2 is empty. There are still 3 boxes, one of them has the prize, but because you know something, the chance of picking correctly is now 1 in 2, not 1 in 3. Same holds true for the possible combinations here.
Consider this: There are 3 boxes and one of them has a prize. The chance of picking correctly is 1 in 3. Then, before choosing a box, someone tells you that box 2 is empty. There are still 3 boxes, one of them has the prize, but because you know something, the chance of picking correctly is now 1 in 2, not 1 in 3. Same holds true for the possible combinations here.