The Disgruntled Alien Visitor

[eligitine]

Mankind has had its first encounter with an Alien species. As mankind's ambassador, you have been beamed aboard the ship, into a blank room, facing one of the alien species. You have been tasked to find out the alien's agendas.

From prior contacts, you have come to know that the aliens completely understand all of our language, but only respond with a grunt, a snort, or a screech. [edit] The best minds on the planet have figured out that one means yes, one means no, and one means maybe. [/edit] These aliens are not the patient type however, and after n questions, it will beam you back down to earth. You have whatever you have in your pockets right now and your words to communicate.

For this exercise, take n as 5, 10, and 20. Is it possible to find out the alien's intentions for each?

[Yakk]

Spoiler:

no

[eligitine]

I apologize, I forgot a part, when I pulled out the paper I originally sketched this out on, The visitor could only answer yes no and maybe.

[ahammel]

Spoiler:

I'm going to assume the aliens are honest and will not give a 'maybe' answer when a 'yes' or 'no' answer exists and they know it. Otherwise I'm quite sure it's impossible. It is pretty easy to decode the alien language in two questions:

1. (Trivially true question)?
2. (Trivially false question)?

The sound they made in response to 1. means 'yes', and the sound they made in response to 2. means 'no'. The third one means 'maybe'. That leaves you n >= 3 questions to discover their intentions. "What are their intentions?" is kind of a vague question, so you'd have to make reasonable guesses and prioritize. I'd go:

3. Will your plans significantly decrease the average well-being of the current autonomous inhabitants of Earth? (Rules out extermination, war, etc.)
4. Do you plan to remove any of the autonomous inhabitants of Earth without their consent? (Rules out mass abductions)
5. Do you plan to significantly influence or replace the current governing bodies of the Earth? (Rules out conquest)

If 'no' to all of those, I'd report that ambassadorship or scientific research are most likely. Seeking asylum is another possibility, I suppose.

Time permitting:
6. How the hell did you build a spaceship with only a three-word language.

[lorb]

Spoiler:

[...]
That leaves you n >= 3 questions to discover their intentions. "What are their intentions?" is kind of a vague question, so you'd have to make reasonable guesses and prioritize. I'd go:

3. Will your plans significantly decrease the average well-being of the current autonomous inhabitants of Earth? (Rules out extermination, war, etc.)
4. Do you plan to remove any of the autonomous inhabitants of Earth without their consent? (Rules out mass abductions)
5. Do you plan to significantly influence or replace the current governing bodies of the Earth? (Rules out conquest)

With 3 questions we should be able to ask about 8? possible plans (I only figured out how to get a useful information about 6)

3. Are your intentions one of: A, B, C, D?

if Yes:
4a. Are your intentions one of: A, B
if No:
4b. Are your intentions one of: E, F?

if Yes to 4a:
5. Are your intentions A?
if Yes: A is the answer, if No: B is the answer
if No to 4a:
5. Are your intentions C?

[Gwydion]

Spoiler:

[...]
That leaves you n >= 3 questions to discover their intentions. "What are their intentions?" is kind of a vague question, so you'd have to make reasonable guesses and prioritize. I'd go:

3. Will your plans significantly decrease the average well-being of the current autonomous inhabitants of Earth? (Rules out extermination, war, etc.)
4. Do you plan to remove any of the autonomous inhabitants of Earth without their consent? (Rules out mass abductions)
5. Do you plan to significantly influence or replace the current governing bodies of the Earth? (Rules out conquest)

With 3 questions we should be able to ask about 8? possible plans (I only figured out how to get a useful information about 6)

3. Are your intentions one of: A, B, C, D?

if Yes:
4a. Are your intentions one of: A, B
if No:
4b. Are your intentions one of: E, F?

if Yes to 4a:
5. Are your intentions A?
if Yes: A is the answer, if No: B is the answer
if No to 4a:
5. Are your intentions C?

Spoiler:

if Yes to 4b:
5: Are your intentions E?
if Yes: E is the answer, if No: F is the answer
if No to 4b:
5: Are your intentions G?

Fixed - there are "8" possibilities, the eighth being "none of A-G".

[HonoreDB]

Spoiler:

You can get more mileage out of your questions by making "Maybe" a possible response. So once you've identified "Yes" and "No", and you have a partition of possible planspace into equiprobability chunks {A,B,C}, you can ask "Is it true that either your plan is in A, or both this coin will come up heads the next time I flip it and your plan is in C?" Then "Yes" means the plan is in A, "No" means it's in B, and "Maybe" means it's in C. If you've come prepared, with a coin and an exhaustive numbered list of M possible alien plans, you can narrow it down to M/(3^(N-2)) possible alien plans.

[Pelli]

We could be more efficient if we could figure out how to

Spoiler:

find out answers to our questions without knowing which of the three responses are which. Then we don't need to waste two questions at the beginning.

E.g. if the possible responses are da/ja meaning yes/no then asking "Is it true that (da mean yes) xor (X is true)?" returns "ja" if X is true and "da" if X is false.

It ought to be possible to make a question about a statement X such that grunt means X is true, snort means X is false, and screech means X is maybe true.

[mfb]

We could be more efficient

... but I am sure that this would be bad for future communication. However, if you manage to combine this idea with HonoreDB's approach, you can show that you get best possible information out of n questions.

By the way, how do we know that the alien will respond honest (and know everything about their plans)?
Who would answer "yes" to "Will your plans significantly decrease the average well-being of the current autonomous inhabitants of Earth?" - and let the human report this answer to others afterwards?

[mward]

Having worked out the meaning of the three responses, a question along the lines of "Is your agenda something too weird for our human brains to comprehend?" might save a lot of fruitless questions, if the answer is "Yes".