Heres a challange that has been wrecking my head for ages.

clearz

A patient p may or may not have a genetic disease x.
p wants to know if the don't have x but also wants to remain blissfully unaware if he does have x.
A doctor d can tell p if he has or has not got the disease x by preforming a test.

Is it possible for p to acquire the information from d only if it is good news without being able to infer the opposite.

For instance if the person tells the doctor to only tell him if it is good news and the doctor comes back and says nothing. Then the
news is inferred as being bad.

The doctor could promise the patient not to tell him either way. Then renege on her promise only if it is good news. The patient has to
be 100% convinced the doctor will not renege before hand otherwise an inferrel can again be made by the doctors silence if it is bad news.

So is it possible?

Valetta

If patient p tells their problem to friend f, then friend f can ask the doctor to do the test and tell patient p that they do not have the disease, regardless of the outcome of the test.

Patient p does not want to know if the test is positive so there is no harm in them thinking it was negative.

If the disease progresses, then they will find out one way or the other.

catallus

clearz wrote: »

A patient p may or may not have a genetic disease x.
p wants to know if the don't have x but also wants to remain blissfully unaware if he does have x.
A doctor d can tell p if he has or has not got the disease x by preforming a test.

Is it possible for p to acquire the information from d only if it is good news without being able to infer the opposite.

For instance if the person tells the doctor to only tell him if it is good news and the doctor comes back and says nothing. Then the
news is inferred as being bad.

The doctor could promise the patient not to tell him either way. Then renege on her promise only if it is good news. The patient has to
be 100% convinced the doctor will not renege before hand otherwise an inferrel can again be made by the doctors silence if it is bad news.

So is it possible?

If the bolded part of your post is the question then yes; the doctor can be instructed to tell the patient that it is good news regardless of the test result.

JoeB-

not quite though.

Then he might be told he has nothing when he does have the problem... he only wanted to be told he had nothing if he actually had nothing.

Solution.

He could tell the doctor to tell him good news, but to tell him the test was inconclusive in two other cases... in cases where the test actually is inconclusive, but also in cases where the test shows bad news.
Then the OP can never be sure if an inconclusive result is due to an inconclusive test, or due to him having a problem.