The Decoy Effect

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“Common sense is the collection of prejudices acquired by age eighteen.” - Albert Einstein

Towards the end of making math more meaningful, I’d like to discuss something in recent news that resonates with that theme.

While listening to NPR, I heard an interesting story about how political candidates affect each other. You can hear a podcast of the same story here. You can also read the Washington Post’s story (which broke first).

The story concerns what is called “The Decoy Effect” or “Asymmetrical Dominance Effect” in psychology.

In simple terms, the Decoy Effect suggests that if you are faced with two popular choices, the outcome of your choice can be subtly affected by the introduction of a third, less popular choice (the decoy). But the outcome may not be affected in the way you might expect. The introduction of the third choice would have you lean towards choosing the popular choice that is most like the decoy.

The above-mentioned article concerns itself with front-running candidates for the 2008 presidential race.

In a (very simplified) example, the Decoy Effect suggests that in the case of Gore vs. Bush in 2004, the introduction of Ralph Nader as a liberal candidate did not (as generally assumed) take votes away from Gore, but actually increased the share of votes that Gore would have gotten had Nader not run.

There are several pitfalls here. You may be tempted to think, “Hmm, so my vote for Nader didn’t help Gore lose the election, after all!” That would not be a conclusion supported by the Decoy Effect. The Decoy Effect postulates that Nader running would not negatively affect Gore. But you voting for him would, of course.

Naturally, the effect doesn’t imply that no one would vote for Nader, just that many more would vote for Gore.

(Caveat – Please don’t flood me with e-mails about your personal politics. I am merely using this to explain a concept).

Here’s a scenario that might help you visualize the effect:

You’re Lou Costello and I’m Bud Abbott (or vice-versa if that’s the way you want to be about it). We’re at a carnival with our beautiful friend, Marjory. We are standing between two rides. One is a Ferris Wheel, and the other is “The PSYCHO-TERROR-CYCLONE from HELL.”

If we choose the Ferris Wheel, we think Marjory might think we are too “chicken” to go on a real scary ride. But we both know that we are probably going to blow lunch on the “P-T-C from H”. We’re going to have to tough it out, though, and hope for the best, because we both want to impress Marjory. So it looks like we may have to opt for the “P-T-C from H.”

Now along comes our friend, Stinky, and he tells that he is going on the bumper-cars.

“Bumper-cars! Are you kidding! That’s for kids! We may not be crazy enough to go on the The Psycho-Terror-Cyclone from Hell, but we’re going on the Ferris Wheel, like sensible, real men!”

Get it?

In some sense, the decoy gives you an “out.” Sort of like when you are offered some expensive product, which you want, but you really can’t afford. You are also offered something that isn’t quite what you want, but you can afford it. You may tend to go for neither.

Then you are offered what is sometimes called a “slum prize.” It’s a piece of junk for free.

The theory is, you’ll say to yourself, “No, that’s junk. I can afford something better,” and you’ll go for the thing you can afford.

(And no, none of the free downloads at Math Mojo are not slum prizes, you cynic, you!)

In some sense, the decoy makes you base your decision on a trait that is less important that what you are really interested in. In the above example, you made your choice based on price, although you are not buying something that you really want.

You might think, “But that doesn’t make sense!”

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Warning: As of here we’ll be talking about insights. If I sound like I’m being a know-it-all, please take it with a grain of salt. This stuff isn’t easy to talk about in public without rubbing some people the wrong way.

Heck, some people get mad if you show them a better way to multiply.

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I can understand your feeling that it doesn’t make sense, it’s the “but” that is the problem. Why would you think that people chose what makes sense? People do not generally process complex information well. We like to oversimplify things. That fits just perfectly with the Decoy Effect.

Understanding that people oversimplify things helps you navigate your world better. Of course, you don’t want to oversimplify things yourself (although we all do it to some extent) you just don’t want to be surprised when other people do.

This tendency to oversimplify things is what we call “intuition.”

• “Of course introducing a similar candidate will hurt the original candidate’s choice.”

• “Well somebody’s got to will the lottery, so why shouldn’t it be me?”

• “If you don’t believe in God, well, then what do you believe in?”

• “If Johnny Jones jumped off the Empire State Building, would you jump off the Empire State building?”

All of those are questions, suggestions or implications that are based on meaningless logical fallacies, but they appear to be sound to people who want simple representations of complex problems.

It is very hard for most of us to look more deeply into things that seem simple on the surface. It is difficult to sort the simple from the complex. So the simplest thing to do is assume that any complex question is simpler than it appears. That keeps us from having to put effort into dealing with it. It keeps us comfortable, up to a point. And it keeps us wrong.

Laziness is no substitute for thought.

There was a time when we may have believed in Santa Claus. When our friend told us there was no Santa Claus, we didn’t believe him, because, “everybody knows, etc.”

Eventually we matured, and understood that much of the stuff we believed when we were children was just convenient nonsense. Then we became adults, and we knew “what the truth is”.

I believe that that moment is the worst moment in most people’s development. It’s the moment when we think we know enough. It’s the moment we have effectively stopped thinking and learning.

If we are very lucky, at some time we are faced with greater truths, which are less apparent than those “truths” we “were told in school,” or “read somewhere,” - insights that not everybody is aware of. Something that most people are too hung-up to even consider. It may even frighten them.

Imagine how some people felt when they saw the Wright brothers’ fly for the first time.

• “Galileo, how dare you believe that the earth revolves around the sun! Everybody knows…”

• “What? Question the President? Of course Saddam has WMDs. Rumsfeld even said he knows were they are. Do you think they would lie?”

• “What do you mean ‘nothing can travel faster than light?’ What if you held a flashlight and walked forward with it? That beam of light would travel faster than if you held the flashlight still! See! I’ve got you there, Professor!”

All of those statements sound (or sounded, at one time) perfectly logical to many adults, in the same way that Santa seems perfectly logical to a child. But at some point everyone should get over them.

Developing counter-intuition is the next step after developing what we generally call “maturity.” Society cannot advance very far until it is expected of everyone. Unfortunately, large portions of society will do anything they can to inhibit your development of counter-intuition. They feel threatened by what they do not understand.

The funny thing is that it’s not that they can’t understand. It’s that they won’t understand. They don’t want to. It’s not as easy as being comfortably dumb.

“What you don’t know can’t hurt you.” Right. That’s like the toddler playing “hide-and-seek” who covers his eyes and says, “You can’t see me!” (Except it’s not pathetic when a child does it.)

Arrested development is the hallmark of humanity, it seems.

Sometimes you can go by your intuition, but unless you have the option of seeing the pitfalls of intuition (which you can only do if you have the benefit of counter-intuition), your intuition is going to be a very poor judge of reality.

Math Mojo is about finding alternative, better ways of understanding simple mathematical principals and arithmetical operations. It is also about critical thinking skills.

There will be more and more articles about how to develop counter-intuitive thoughts as Math Mojo develops.

The conclusion of the Washington Posts’ article is this:
“Don’t let salespeople tell you what issues to care about, and don’t let candidates define one another. More simply, think for yourself and be wary if a difficult choice suddenly feels simple.”

That is also the heart and soul of the message of Math Mojo. It’s also part of its brain.


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