# Why Being Misinformed Makes You Wrong More Often than Being Uninformed Does

It’s simple math. Here is one type of example.

Suppose that I hold a coin. I’ll flip it, and you call it in the air. We both know that the coin is fair, meaning that it isn’t weighted in a way that will cause it to land one way more often than the other way. You have two choices, heads or tails, and with a fair coin each choice has an equal chance of coming out on top. I flip, you call. What is the chance that you will make the correct call?

This is pretty simple, actually. Most people will know that you will have a 50% chance of being correct. But now, let’s alter the premise a little bit. This time, the process is the same, in that I’ll flip and you call. But this time, I’ll tell you that the coin is weighted, and that it has a 75% chance of coming up one way, and a 25% chance of coming up the other way. However, I won’t tell you which way it is weighted. You know it’s weighted, but you don’t know whether it is weighted in favor of heads, or in favor of tails. Still, I flip and you call. What is the chance that you will make the correct call this time?

This one might make you think a little bit. But it isn’t really that difficult when you think about it. The answer is that you still have a 50% chance of making the correct call. It’s an even guess for you. As far as you know, there is an even chance that it is weighted heads. Or tails. You are uninformed.

But now, we will complicate it more. Suppose I convince you that the coin is weighted so that it has a 75% chance of coming up heads, and a 25% chance of coming up tails. I flip, you call. What is the chance that you will make the correct call in this case?

There are no betting odds to factor into this. You “win” by making the correct call, and you don’t get anything extra because a longshot comes in. Your payoff is the same either way. I flip, you call. What are your chances this time?

You are convinced that the coin favors heads. If I have nothing to gain by telling you something that isn’t true, and you assume that the odds favor heads, then the rational choice for you is to call heads. The odds favor heads, and you don’t get any premium for going against the odds. You pick heads, and you will have a 75% chance of being correct. That is, if you are rational. If you are not rational, then who knows?

But what if, in this last scenario, somebody has paid me to get you to call heads. Suppose I told you that the coin is weighted in favor of heads, and you believed me, but in fact the coin is weighted so that there is a 75% chance that it will come up tails?

Remember, somebody is paying me to get you to say heads. What are your chances of being correct now? If you are rational, you will call heads if you believe my story. What you don’t know is that there is a 75% chance that the coin will come up tails. You are convinced that your chances of being correct are 75%, because of what you have been told. But in reality, there is only a 25% chance that you will be correct. You are misinformed.

Being uninformed, you have a 50% chance of being correct. Being misinformed, your chances of being correct are only 25%.

The difference between you being uninformed and being misinformed is due to the fact that I had an agenda in the case of you being misinformed. I was being paid to get you to say heads. Your odds went down because you made a rational choice based on what you believed, and all I had to do was convince you of something that wasn’t true.

What if you never like to call tails? What if you came into this exercise with your mind made up that you were going to call heads? Would it be easier for me to convince you that the odds favored heads, or that the odds favored tails? If I said that the odds favored tails, would you be more likely to doubt my word? Would you be more likely to make an irrational choice if you had reason to believe that the coin favored tails but you had your heart set on heads?

Think about the answers to those questions, and then ponder why you would choose to accept information only from sources that have an agenda to tell you what you want to believe. If they have an agenda to misinform, they can convince you that you are informed when in fact you are going to be wrong more often than those who are totally uninformed. If you know that these sources are biased, and you choose to believe them because they tell you what you want to hear, then how rational is it for you to think of yourself as being able to make better choices than those you consider to be uninformed?

I used the example of a coin that may or may not be weighted. A similar conclusion can be reached with other types of examples, such as a multiple-choice test in which you have been given information that steers you away from a correct answer and towards an incorrect answer. In that case, your chances of being correct are mathematically less than the chances of somebody who just takes a wild guess. Yet because you are basing your answer on information that you have received, you may be convinced that you are “more informed” than somebody with no information.

You would be wrong.

See on blue-route.org

Author:
Jerry Wyant
Date:
2014-08-07