Observer-relative chances in anthropic reasoning?

John Leslie presents a thought experiment to show that chances are sometime s observer-relative in a paradoxical way. The pivotal assumption in his arg ument - a version of the weak anthropic principle - is the same as the one used to get the disturbing Doomsday argument off the ground. I show that Le slies thought experiment trades on the sense/reference ambiguity and is fal lacious. I then describe a related case where chances are observer-relative in an interesting way. But not in a paradoxical way. The result can be gen eralized: At least for a very wide range of cases, the weak anthropic princ iple does not give rise to paradoxical observer-relative chances. This find ing could be taken to give new indirect support to the doomsday argument.