Misleading the witness

These sorts of brain-teasers are of limited help in developing your critical thinking skills for dealing with real world problems. Here the problem is presented to you and you just have to figure out what went wrong with a train of thought. In the real world, the BIG problem is noticing that there is a difficulty in the first place.

From advertising via a friend: Apparently a specific technique used in advertising a product with a known weakness is to promote it as a strength. Eg when first feedback from consumers shows that the taste of a particular toothpaste is disliked, the response may be to put a prominent "Great New Taste!!!" label on the pack.

While I'd seen the missing dollar problem before, I think I have a new appreciation for it now. I seem to recall puzzle books presenting this problem, but even when they present the solution, they present it in terms of "here's where the missing dollar is". But as you, Wikipedia, and Paulos point out, the whole problem is that the dollar is only "missing" relative to an invalid comparison.

So, to solve the problem by finding a missing dollar is to fail to learn from it.

This riddle made me remember reading about how beginning magicians are very nervous in their first public performances, since some of their tricks involve misdirecting the audience by openly lying... they learn to be more comfortable once they find out how easily the audience will pretty much accept whatever false statements they make.

It makes me wonder how dangerous magicians can become in their regular lives.

One technique is to look carefully for fallacies and/or gaps in the reasoning by summarizing the key theses of the argument and then considering what assumptions (and definitions) have to be made for the theses to be accepted and what has to be true for each to follow deductively from what has already been given. A book on "critical thinking" (e.g., this one) will have lots of exercises to develop this kind of skill. They typically have lots of examples drawn from politics just because political discussion is so frequently chock full of fallacies and bad arguments.

When you're trying to be critical of your own arguments and to identify cognitive biases at work, there are many simple and practical techniques mentioned in The Psychology of Judgment and Decision Making. To give just one example, poor calibration can be improved and overconfidence can be attenuated by considering the reasons why what you believe isn't so might actually be so. The mere act of trying to find reasons for the hypotheses you don't believe will make you less overconfident in the hypothesis you do believe. In general, iterating through the biases discussed in that book (and many others), and considering how each bias might apply in the particular circumstance, is a widely applicable and very useful technique.

I don't know, I felt the correct sign the first time I read it. I also didn't get confused by the cognitive reflection test (in the sense that there is no confusion, the correct way of seeing the problem is all there is). It's really hard to imagine how a person with math training can miss that.

But from what I heard, a sizable portion of math students still manage to get confused by these. Tracing the analogy to cognitive biases, there may be a qualitative difference between a person who just knows about it "in theory" and even done a lot of reading on the topic ("typical" math student), and a person who thought about the techniques at every opportunity for a number of years.

I remembered shortly after writing this that there was an example of outright lying in an attempt to get one to conform to a certain pattern of thought in Initiation Ceremony (hooray fictional evidence).

I had heard it before a while back but I decided to think through it myself and see what was going on. The first thought that occurred to me was that the bellhop's two dollars should be subtracted, just as each of the 1 dollar bills given back to the guests was (to get 27 from 30). Then, I imagined that the guests had not paid with $10 dollars bills, but in 30 ones. The hotel has 30, then each of the three guests is given 1and the bellhop takes two. Here is where the money is:

• Guest 1: 1
• Guest 2: 1
• Guest 3: 1
• Bellhop: 2
• Hotel: 25
• Total: 30

It is basically following all the individual dollars to see where they are and make sure none are missing. Alternately, you can imagine that the price really was 27 in the beginning, they all paid 9, and then the bellhop just stole 2 on the assumption that the owner wouldn't notice.

A while back on here somebody mentioned that they were at a College, and then later on somebody else mentioned MIT, so I drew the conclusion that they were at MIT. This is a power which must be used wisely...

Can anyone think of good ways to notice when outright deception is being used? How could a rationalist practice her skills at a magic show?

Most "rationalists" are quite smart people, so tricks that are designed by a trickster to fool the masses rarely work on us. For example, I doubt that many on this site would invest heavily in a pyramid scheme or get fooled by a used car salesman. This is because these tricks are targeted at the average idiot.

However, I have recently noticed that there is, for each of us, a stalker who stalks us and at each and every turn attempts to deceive us, and is just as smart as we are. That stalker/trickster is your own cognitive biases, and by far and away inflicts the greatest material losses on you. This is certainly true in my case.

I cannot even remember the last time I was fooled by someone else, but now that I am working on reducing my losses due to self deception, I realize that basically every day I engage in successful self-deception: I get into some emotional state, myopic, irrational algorithms take over, and I make up little excuses to myself for why they reached the right conclusion.

The real enemy is already inside your head.

Can anyone think of good ways to notice when outright deception is being used?

I suspect one of the best ways may be to try to re-create their reasoning from the beginning, so you engage the logical inference part of your brain in trying to (re)reason, rather than the 'listening to and believing' part, as we now know that we first believe, and have to consciously reject, new ideas, rather than the other way around.

Where money is concerned, I suppose you could check whether income matches expenditures.

other examples of flagrant misdirection

I can think of many examples of cases where candidates evade the most basic of economics, but as Politics is the Mind-Killer, I think it's probably best not to bring them up.

Ask people to write/draw the problem and I bet you get far better responses.

Restating the problem in simpler terms, without narrative, would help with this example.