The Professor's Trick Question . . . Can You Figure It Out?

[Anthony K. S.]

Several years ago, I had a neighbor who was a Political Science and Philosophy professor at a local university. One day, he told me about a hypothetical scenario he had posed to his students :


A country goes to war. (The country is not necessarily the United States. It could be any country.)

When their military starts running short of troops, the government institutes a draft.

Draft committees are formed in every community to evaluate all male adults for conscription.

A young man named Michael is ordered into military service. He immediately protests, on the following grounds :

The draft committee that evaluated Michael consisted of 12 members, four of whom were female.

Michael stated that it would only be fair to include both men and women on these committees if both men and women were eligible to be drafted.

He argued that since women were exempt from the draft, they should also be excluded from the process of deciding who would be drafted and who wouldn't be.

Michael asked that his draft be declared void, on the grounds that the committee that approved his draft included four individuals who had never faced the possibility of being forced to go to war, and therefore did not have the reference points to understand the situation.


My neighbor, the professor, posed this scenario to six different classes (a total of nearly 200 students) and asked his students to each write a short essay answering this one question :

Is Michael's position correct?

The professor asked his students to consider the question from different angles, such as whether Michael's position had any legal merit, whether it stood up on moral and ethical grounds, and so forth.


He told me that he found it quite interesting to read through the many varied responses he received from his students, making all sorts of arguments both in support of and against Michael's position in this hypothetical scenario.

. . . But out of those nearly 200 students, there were only about 10-15 students who realized that when the professor asked whether Michael was right or not, it was actually a trick question.

(The professor made a point of personally congratulating each of the 10-15 students who wrote down the correct answer to the question.)


Now, the question I would like to pose to all of you . . .

Can you figure out how exactly the professor's hypothetical scenario constituted a trick question, and what the correct answer would have been?


If anybody here thinks they've figured it out, please send me a PM and I'll tell you if you're right. (Please don't post your answers on this thread. I don't want the answer to be given away.)

I will wait 48 hours, and then post the professor's solution here. (It should be around 11 p.m. Eastern Time on Sunday night.)

Good luck!


EDIT :

A friend of mine suggested that at the "halfway mark" (24 hours into the 48-hour period), I should post a couple of hints. Very well, I will, at about 11 p.m. on Saturday night.

[Anthony K. S.]

As promised, here are a couple of hints . . .

I'm presuming the term 'trick' means it's technically unanswerable?

Slytovhand, you’re on the right track here.


Just for a moment, everybody, consider this question :

Should women be allowed on draft committees?

Now, that question can be answered, although the responses you get will vary dramatically from one person to the next. Opinions on political and social issues always have, and always will.

But that wasn’t the question that the professor asked. What he actually asked was :

Is Michael’s position correct?

And, according to the professor, that question cannot be answered with the information we are given.

If you can see the important difference between those two questions, you might be able to figure out why the professor’s question cannot be answered. And if you manage to get that far, you could very well have the whole thing sewn right up.

Here’s a hint :

The fact that there were four women on the draft committee actually IS relevant here . . . But not in the way that people often think.


To take a different tack on it . . .

Ask yourself this question :

If the draft committee that evaluated him had been all-male, would Michael have been any happier in the end?

Now, with that question (and your answer to it) in mind, here’s another hint :

There was at least one key piece of information that the professor deliberately left out of this story.

Without that piece of information, the question that the professor posed was, essentially, unanswerable.

With that information, however, it becomes quite easy to answer.


By the way, I would like to say this :

If I had been one of this professor's students, there is NO WAY that I would have realized it was a trick question. I would definitely have been one of the 90%-95% who failed to figure it out.

In the past few years, I've told this story to many different people, and asked them if they could figure out how the professor's scenario was a trick.

Some people were able to figure it out, but then admitted that it was only because I had told them up front that it was a trick question. They said that had they been in the professor's classes, they would have fallen for it, too.

It’s definitely not an easy one.

[Anthony K. S.]

Okay, here it is . . .

I received a few very interesting responses to this (including e-mails from a few people who aren’t actually members of Customers Suck! but who I know from other websites).

By the way, those of you who were exploring the possibilities of Michael having dual citizenship in the two warring countries, that he might be an Israeli citizen who is of Arab descent (or some variation thereof), or that this took place on an alien planet where there could be six different genders . . . I really enjoyed reading your thoughts on this . . . Sadly, though, you might find the actual answer to be a bit of a letdown.

Well, anyway . . .

The vast majority of this professor’s students made one or more of three basic mistakes . . .


Mistake # 1 - Misunderstanding the Question

Is Michael's position correct?

What exactly was Michael’s position?

Most of the students viewed his position as “Women shouldn’t be allowed on draft committees” and answered the question as such. But, in fact, that is, at best, incomplete.

Let me put it to you this way :

If Michael had had a choice between (1) an all-male committee that approved his draft, or (2) a mixed-gender or all-female committee that decided against drafting him . . . Which do you think he would have picked?

Michael isn’t complaining because there were women on his draft committee. He’s complaining because he was drafted! That’s what this is really about.

He may, indeed, have genuinely believed that women shouldn’t be allowed on draft committees. But his position was that his particular draft should be voided.

So when the professor asked his students if Michael’s position was correct, he was actually asking, “Should Michael’s draft be voided on the grounds that he stated?”

Now, you may ask :

“What’s the difference? If we’re going to decide whether or not Michael’s draft should be voided on the grounds that he stated, then we would have to judge the merits of his argument that women shouldn’t be allowed on draft committees. So we would wind up addressing that issue, anyway.”

That’s a good point, except that it leads us directly into . . .


Mistake # 2 - Missing an Important Detail

Only a few of the students realized it, but this professor was actually deliberately playing on the emotions of his students.

The draft is often a sensitive issue, especially among younger college students who have only recently dealt with registering with Selective Service.

Many of these students were in such a rush to address the issue of whether or not male-only draft is discriminatory and, subsequently, whether or not women should be allowed to have a part in deciding who would be drafted, that they failed to notice something important :

The draft committee that evaluated Michael consisted of 12 members, four of whom were female.

I can still vividly remember my neighbor, the professor, explaining it to me (in a rather smug, condescending tone) :

“It’s simple arithmetic, Anthony. If the committee had 12 members and four of them were female, then that means that there were eight men on the committee. Since the men on this committee outnumbered the women 2-to-1, it is far more likely that the decisive votes belonged to the men, not the women.”

Only a relative few of the students picked up on this. The ones who did also soon realized something else :

Nobody ever said that the four female members of the committee had actually supported drafting Michael in the first place.

When the professor was handing back the students’ essays, he revealed that, in fact, the four women on the committee had all opposed drafting Michael. They were simply outvoted by the eight male members of the committee, all of whom voted in favor of approving Michael’s conscription.

And that, in a nutshell, is :

Mistake # 3 - Making a False Assumption

At the heart of it, this was the “trick” to the trick question.

The professor anticipated (correctly) that most of his students would make the exact same mistake that Michael himself had made. They simply assumed, without any evidence to support the belief, that the four women on the committee must have voted in favor of drafting Michael.

Not only that, but the students also assumed (perhaps consciously, perhaps not) that those four women had somehow been instrumental in swaying the committee as a whole to approve Michael’s draft.

The idea that none of that might have been the case simply never occurred to the students, just as it never occurred to Michael himself.


Earlier, I mentioned that the professor viewed his question - Should Michael’s draft be voided on the grounds he stated? - as essentially unanswerable, because there was one key piece of information that he had deliberately left out of this scenario.

Without knowing how the women on the committee had voted, it was impossible to judge whether or not their presence played any part in creating the result that was unfavorable to Michael - his being drafted.

One of the students (who did realize that it was a trick question) noted that we could argue endlessly about whether or not women should be present on draft boards, or even whether or not they should be eligible to be drafted. But, in the end, as far as this case goes, it would be completely moot.

Even if we agreed that women shouldn’t be on draft committees, that would only justify voiding Michael’s draft if the women on his draft committee had actually contributed to making his draft happen. And there was no way of determining that from the information given in the professor’s scenario.


After handing back the essays, none of which had any grades marked on them, the professor explained that this was never intended to be a graded assignment.

Rather, it was an exercise to see how many of the students would really follow the professor’s instructions to look at the scenario from as many different angles as possible . . . Which, as he said, is at the very heart of the analytical thought necessary for students of either Philosophy or Political Science.

Without that piece of information, the question that the professor posed was, essentially, unanswerable.

With that information, it becomes easy to answer.

That last sentence was actually something I added, not the professor’s thoughts.

In my view . . . Once it was revealed that the four women on the committee had all opposed drafting Michael, it becomes easy for me, personally, to answer the professor’s question.

Michael’s entire position was based on the assumption that he would have had a better chance of avoiding being drafted if these four women had not been present on the committee. In reality, without the presence of those women, his draft would have been approved by a wider margin, not a smaller one.

Even if the four women had been replaced by four men who all opposed drafting him, the end result would have been the same.

Michael’s request that his draft be voided should be rejected, because his complaint is completely baseless.


Finally, I would like to congratulate the one person here - Broomjockey - who correctly caught on to the key to the whole thing, which was that we didn’t know how the women on the committee had voted.

I’d also like to thank Slytovhand, MaggieTheCat, and my friends from that other message board (who I won’t name, for privacy reasons), all for taking the time to participate in this. Thank you all very much.

By the way, for everybody who wasn’t able to figure out the answer to this question . . . I’m right there with you. I wasn’t able to figure it out, either.

[DrFaroohk]

I know this has been solved already, but does it ever tell you how the committee works? I might not be a majority vote. Maybe all 12 people have to agree, like its a jury. Or something. Not that it matters.

[Flyndaran]

I'm not sure I agree with that "answer".
He was right in that he didn't want to get drafted so any semi-viable argument against it was right from his view.
It was still true that women shouldn't be involved in drafts when they can't be drafted regardless of how four individuals would have decided.

[lordlundar]

It was still true that women shouldn't be involved in drafts when they can't be drafted regardless of how four individuals would have decided.

Ah, but the question wasn't whether there should be women on draft boards if they are immune to being drafted (personally I agree with you).

The question was "should the decision be voided out because of the women on the draft board?" And the truth is, given the information we were given, you can't really answer properly.

Like the OP said, we don't know:

How the women voted
What are terms for acceptance (majority vote, unanimous vote, veto authority, etc)
The reasons why they voted the way they did
The actual impact of the vote (if all four women voted for him to be ineligible and he was still drafted, it would not have mattered)

The best response anyone could come up with without doing any supposition is "I don't know".

A very interesting riddle Anthony. I like it.

[Pedersen]

The question was "should the decision be voided out because of the women on the draft board?" And the truth is, given the information we were given, you can't really answer properly.

Actually, in this country at least, there exists something close to a legal precedent that could be to used to void out not only Michael's draft, but any draft on which any women were present, regardless of their vote status.

I've heard it referred to as "fruit of the poisoned tree". It's used in criminal cases as a way to prevent cops executing random searches. Basically, if the search was illegal, then any evidence gained from the search is inadmissible in court, resulting in the destruction of the whole case, and the individual on trial walks free.

Using similar logic, it doesn't matter if there is only one person on the panel who would never have been eligible for the draft, or four, 12: If even one person on the draft board could not have ever been drafted, then that poisons the entire process, and the draft board should be disbanded.

Personally, I happen to agree with doing just that. I did have to worry about being drafted if any sort of war did come up. And to have even one person who could not have ever been drafted sitting on the board that decides my future would have pissed me off royally.

Also note: This professor chose words that would incite high emotions, and rekindle a battle of the sexes type debate. I am not using the terms "men" and "women". I am specifically stating that people eligible to be drafted should not have their fate in the face of a draft even partially affected by people who were never (and could never) be eligible for that same draft.

And in the original scenario, we don't know what those four women were like. They could have been absolute angels, making a clear and logical case for why Michael should not be sent, who then got overrulled by the rest. They could have been absolute harpies who were screaming about the inequities of everything, thereby driving the remaining men to vote against them just to piss them off. Their mere presence might have very well affected the vote in a way that we cannot know. So, yes, their presence is relevant, and their actual number is not.

Using the logic above, I'd advocate for tossing out all drafts which were made when non-eligible persons participated in the draft board, not just Michael's. In case anybody needs me to say it, this also means that, yes, Michael's draft should be voided out.

[Slytovhand]

Actually, the question was: Is Michael's claim correct - that his draft should be revoked, because of the women on the panel (who were not subject to being drafted, themselves).

The answer is quite simply - no.

There was a process put in place.. Michael just happens not to like it, cos he got the raw end of the stick. Now, if he wanted to argue that all drafts would be invalidated, then that's a different kettle of fish... one which he'd have a greater chance of getting listened to.

Let's consider another side to this 'draft' thing... who else was on this draft committee?? What if it consisted of 4 women, and 6 men over the age of say, 45 (cos that seems to be above the usual cut-off), who would also be ineligble to be drafted... does the same argument apply? The answer should be 'yes', but bet your boots no-one's going to argue that way too much...

In most societies, a rule for an individual usually only has merit if it can apply to the rest of those affected. (ie, my extenuating circumstances must also apply to anyone else's extenuating circumstances... even if they're aliens )

[PepperElf]

i came in late to the story but i was also thinking this...

were the people on the draft committee civilians or military

because you can't claim that a woman might be placing him in a situation where she would have no chance of being there herself... if she's already in the military

[DesignFox]

That was my original thought, Pepperelf!

[BroomJockey]

because you can't claim that a woman might be placing him in a situation where she would have no chance of being there herself... if she's already in the military

Due to the fact that the draft was only for adult males, I would submit the place is not so enlightened as to allow females in the military. Also, if the place has run short of soldiers, and there are multiple draft boards scattered across the country, I highly doubt that they can afford the hundreds of soldiers it would take to staff the boards fully. The main person might be military, but that would likely be it. Thus, even if women WERE allowed in the military, the ones in this question are unlikely to be those women anyway.

[Slytovhand]

But they might have the other sexes out doing their bit, and have only gotten around to conscripting males. So, it sounds like the drones are dying off, the Queen's are now resorting to full males...

Oh, sorry, not the alien races.. that's right!

[anriana]

Due to the fact that the draft was only for adult males, I would submit the place is not so enlightened as to allow females in the military. Also, if the place has run short of soldiers, and there are multiple draft boards scattered across the country, I highly doubt that they can afford the hundreds of soldiers it would take to staff the boards fully. The main person might be military, but that would likely be it. Thus, even if women WERE allowed in the military, the ones in this question are unlikely to be those women anyway.

?

America allows women in the military but doesn't draf them.

[PepperElf]

Due to the fact that the draft was only for adult males, I would submit the place is not so enlightened as to allow females in the military. Also, if the place has run short of soldiers, and there are multiple draft boards scattered across the country, I highly doubt that they can afford the hundreds of soldiers it would take to staff the boards fully. The main person might be military, but that would likely be it. Thus, even if women WERE allowed in the military, the ones in this question are unlikely to be those women anyway.

hmm. i figured it was the US and in the future... if a draft was re-started.

though, there are some countries that draft women too

http://en.wikipedia.org/wiki/Conscription

but in my opinion... the potential recruit was just grasping at anything he could to get out of serving. if all the reviewers were male (instead of 8 of 12) then he'd just harp about something else, like their race or age

[BroomJockey]

America allows women in the military but doesn't draf them.

hmm. i figured it was the US and in the future... if a draft was re-started.

It's like the first line of the question.

A country goes to war. (The country is not necessarily the United States. It could be any country.)

Thus, your assumption of "the US" is incorrect. Either way, my points of "short of troops" and "only drafting men" stand. If they're short of troops, there is no way they can spare enough soldiers to run every draft board, so any woman on the board is more than likely not in the army, nor are they are risk of being drafted.