Asymmetric relations in possible worlds model

I am reading about possible worlds. I understand that if an agent cannot distinguish between two possible worlds, either one of the worlds could be the true world from this perspective.

But what if I have such situation:

I understand that $a$ cannot distinguish between $w_1$ and $w_2$, but what about $b$? My guess is that $b$ cannot distinguish $w_3$ from $w_2$, so if he considers $w_3$ possible, he knows for sure that $w_2$ cannot be the true world (but does this make sense? isn't it the same as just saying that it can never be $w_2$ since if he starts considering $w_2$, he also considers $w_3$, but at the moment he is considering $w_3$, he knows that it cannot be $w_2$.

I am not quite sure what these directions actually mean. I do understand that a person can be indistinguishable between two worlds (I guess it means that from his point of view, there might be 50% of each world to be the true world), but I do not understand what it means when an agent is not able distinguish one world from another, but he is able to do so if it was the other way around?

Does the agent 'walk through' the possible worlds when deciding what world is true?

• one letter s in asymmetric. This is one of the ways of indicating a negative with a prefix, in this case not symmetric – Will Jagy Dec 28 '16 at 20:53
• Thanks :D will remember that! – Jamgreen Dec 28 '16 at 20:54
• There are plenty of words that start out with a double s; there is a saying, probably not ever popular, When you assume, you make an ass out of you and me. Heard it in a movie with Julia Roberts and Tom Hanks. – Will Jagy Dec 28 '16 at 20:57
• Probably much older, but: In the TV Land 2006 documentary The 100 Greatest TV Quotes and Catchphrases, Lowell Ganz credits Belson with including in the script of the season 3 Odd Couple episode "My Strife in Court" (originally aired Friday February 16, 1973) the catch-phrase "Never ASSUME, because when you ASSUME, you make an ASS of U and ME." Ganz noted Belson had heard it used years ago by a teacher in a typewriter repair class. – Will Jagy Dec 28 '16 at 20:59