> If one of the other participants change the ratio of two slices to 0.5/1.5 This is not what happens. From the point of view of the first cutter, he got a pie

> If one of the other participants change the ratio of two slices to 0.5/1.5 This is not what happens. From the point of view of the first cutter, he got a piece he values at 1 and the others got pieces he values at 1-x and 1. Then they make the repartition of the remaining x. The person who got previously the piece that the first cutter valued at 1-x chooses first, but can’t get more than 1 (as valued by the first cutter) in total. And the first cutter chooses before the other person who got a piece he values at 1, so he cannot end worse off.