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The Dot Town Suicides appears to be incorrect as stated. Suppose there are 100 residents and 2 blue dots. The stranger tells everyone "there are not 98 blue do

The Dot Town Suicides appears to be incorrect as stated. Suppose there are 100 residents and 2 blue dots. The stranger tells everyone "there are not 98 blue dots" This meets the condition of the question's "non-trivial" but the residents can relax: nobody has learned anything new. The proposed induction is broken, in my opinion.

Hoagy 8y ago
I thought this initially as well: if there are many of each colour, and the only information is that there is at least one blue dot, how could this be new information to trigger the suicides? But this isn't correct. Let's say n = 6, a-c are blue, d-f are red, and the information is that there is at least one blue dot. a knows there are at least two, but thinks b may believe there is only one blue dot. Moreover, a believes b may believe that c may believe that there are no blue dots. So if a was red, the information would mean that b would commit suicide if c did not initially commit suicide, but since neither has happened, a must have a blue dot and therefore must commit suicide. A convoluted process to be sure but does it make sense how the information transmits by ruling out hypotheticals?
22c 8y ago
The question is stated correctly, I believe the mix up is in the part about triviality. > “Non-trivial” means here that there is some number of blue dots for which the statement would not have been true. I think this is supposed to say "Trivial means..." If there were 98 blue dots, your statement would not have been true, so it was trivial information. Essentially, if the people of dot town can figure it out themselves, then you've given them a trivial piece of information. They know there aren't 98 blue dots, because they can already see that for themselves.
chronolitus 8y ago
Unless "There are not 98 blue dots" also means "There are not 2 red dots"? Then the process starts and months later all red dots leave. This requires that everyone know only blue or red eyes are allowed.

Hoagy 8y ago

I thought this initially as well: if there are many of each colour, and the only information is that there is at least one blue dot, how could this be new information to trigger the suicides? But this isn't correct. Let's say n = 6, a-c are blue, d-f are red, and the information is that there is at least one blue dot. a knows there are at least two, but thinks b may believe there is only one blue dot. Moreover, a believes b may believe that c may believe that there are no blue dots. So if a was red, the information would mean that b would commit suicide if c did not initially commit suicide, but since neither has happened, a must have a blue dot and therefore must commit suicide. A convoluted process to be sure but does it make sense how the information transmits by ruling out hypotheticals?

22c 8y ago

The question is stated correctly, I believe the mix up is in the part about triviality. > “Non-trivial” means here that there is some number of blue dots for which the statement would not have been true. I think this is supposed to say "Trivial means..." If there were 98 blue dots, your statement would not have been true, so it was trivial information. Essentially, if the people of dot town can figure it out themselves, then you've given them a trivial piece of information. They know there aren't 98 blue dots, because they can already see that for themselves.

chronolitus 8y ago

Unless "There are not 98 blue dots" also means "There are not 2 red dots"? Then the process starts and months later all red dots leave. This requires that everyone know only blue or red eyes are allowed.