[FoRK] Crypto protocol for only good news?

[Stephen D. Williams]

The best solution, it seems to me, is to hide whether the "test" (or 
"watched the game" or "consent to tell") was given.  If parents don't 
know that a sex test was done, they can only be surprised positively if 
it is a boy.  If you don't know if your friend has watched the game, 
then it is not telling that he doesn't tell you they won.  At the 
expiration of the suspense period, birth or having seen the game, it is 
fine to share what you knew as the embargo is over.

In cases of mutual  "positive surprise", it might suffice to have both 
parties secretly vote on whether to tell the result of a sub-test.  If 
you don't know whether your mate said "don't tell me the sex" vs. "don't 
tell me the sex unless it is male", then it is not telling when you 
aren't told the sex.

The Heisenberg Positive Certainty Principle, or something.  An unwatched 
test may not exist so a missing answer doesn't tell you anything.

sdw

mattj at newsblip.com wrote:
> Reza had some helpful comments offline which raised the useful idea of 
> adding another actor or step.  Thanks!
>
>> Reza wrote:
>>
>> In other words, what you've outlined is a system that has three 
>> black-boxes:
>> parents, child, and the sonographer... If you introduce a forth, say 
>> a little
>> bird flying around counting quantum spins... and say that:
>>
>> GenderOfBabyToBeToldToTheParents = RealGender [OPERATOR] Randomizer
>>
>> Where Randomizer is the news that the bird tells the sonographer at 
>> the time
>> and under the terms of its own choosing.
>
> So here's my current thinking...
>
> First, to sidestep the geopolitical issues of gender selection, I'll 
> use a new example: you've taped the big game, and you don't want your 
> friend to tell you who won before you've had a chance to watch it... 
> unless your team won, in which case you're glad to hear about it.  I'm 
> going to temporarily call this the Fair-Weather Bit problem, because 
> you only want to hear the bit value in one case; I'm hoping someone 
> can clue me in to any existing terminology.  (The approach below has a 
> Monty Hall Problem flavor, in a sense.)
>
> You cannot have a 100% chance of learning they won without setting up 
> a 100% chance of learning that they lost. So, this becomes a question 
> of how risk averse you are in this situation.  If you mostly want to 
> know about a win, we can structure things to give you a good chance of 
> hearing that news. If you mostly want to avoid hearing about a loss, 
> we can arrange that, too.
>
> But to start, let's just get a basic answer.  Here's my protocol:
>
> 1. Friend watches the game live.
>    If your team wins, he writes "Win" on a piece of paper.
>    If your team loses, he writes "Null" (no answer) on a piece of paper.
>
> 2. Friend seals the paper inside an envelope, and hands it to a 
> trusted third party (say, the bartender at your local pub). Your 
> friend does *not* tell the bartender what the (single bit) message is 
> about, and the bartender does not know about the big game. (I know, 
> "you call that a bartender?", but let's assume it.)
>
> 3. You show up, and per the protocol, trusted bartender flips a coin 
> out of your view.  Then the bartender opens the envelope (also out of 
> view).
>    If it's heads, the bartender reads you the message your friend wrote.
>    If it's tails, the bartender says "Null", pretending he's reading 
> the message.
>
> Assuming your team has a 50-50 chance of winning, we expect to hear 
> "Win" 25% of the time, and "Null" 75% of the time.  But we needn't be 
> too sad if we hear "Null", because 2/3 of the time the "Null" will be 
> a result of the bartender's coin toss.  Hearing "Null" means there's 
> still a 1/3 chance they really won.
>
> We do ask the bartender to be deceptive here (pretending all "Nulls" 
> are equal). However, he can't have a motive to tell you good or bad 
> info, because unlike your friend he has no idea what this particular 
> message means.
>
> Now, if you're not so risk averse, and you want a greater chance of 
> hearing about a win, you replace the coin toss with some random number 
> generator. Have the bartender read you the friend's message 90% of the 
> time, and tell you "Null" for the other 10%.  This way, you have a 45% 
> chance of hearing "Win", and if you hear "Null", there's still an 18% 
> chance that your team won.
>
> Conversely, if you're highly risk averse, you can reverse the 90-10 
> rule, which will give you a 5% chance of learning of a win, and a 45% 
> chance that a "Null" is really a win.  Of course, you can pick any 
> point you prefer on that spectrum.
>
> -Matt Jensen
>  http://mattjensen.com
>  Seattle
>
>> Quoting Matt Jensen <mattj at newsblip.com>:
>>
>>> I'm looking for a technique for revealing info, but only if the info
>>> has one particular value.
>>>
>>> For example: Suppose a couple is pregnant with their second child. The
>>> first kid is a girl, and though the couple will love the second kid
>>> regardless of gender, they'd be extra excited if it turned out to be a
>>> boy.  (Plus, they could start outfitting the nursery.)
>>>
>>> So, we now want to know if there's some procedure whereby they can
>>> have the sonographer tell them if it's a boy, but not tell them
>>> anything if it's a girl.  Obviously, not telling them anything tells
>>> them it's a girl.  Anyway around this?
>>>
>>> Ideally, you'd like a 100% chance of learning that it's a boy.
>>> However, in order trust an answer like "I can't tell you the result
>>> because our protocol forbids it", it seems you have to accept a lower
>>> chance of getting the good news.
>>>
>>> I suppose you could have the sonographer secretly flip a coin, and if
>>> it's heads, she tells the parents the gender.  But if it's a girl you
>>> actually have the sonographer lie to you, and tell you she got tails,
>>> so she can't tell you the gender.  But even that tells you something:
>>> there are two "tails" outcomes for  a girl and only one "tails"
>>> outcome for a boy.
>>>
>>> I feel like there's a better answer to this question, but I'm missing
>>> it.  Ideas?
>>>
>>> -Matt Jensen
>>>   http://mattjensen.com
>>>   Seattle
>>>
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>>
>>
>>
>>
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