Percentages are the Way You Think

Time for another episode in my continuing series People Are Idiots. Previous installments have included how to sell your students wine and how to get rich on the internet.

Car_accident_poland_2008 Today we visit another phenomenon of cognitive misbehavior, what I like to call the Small Percentage Effect.  (It has some other fancy name among behavioral economists. I like mine better.)

Imagine that you have decided to buy the latest, totally cool and sexy, iPod. It retails for $200. You are about to pick it up at a shop near your home when you hear that all the way across town a store is running a one-day special promotion, selling this iPod for only $100. It is a 90 minute round-trip drive, but you gleefully head off to score your bargain iPod.

Unfortunately, after a while you realize that the iPod is not attracting nearly the number of members of the opposite sex that you expected. So you hatch Plan B, an even more totally cool and sexy convertible. The dealership near your house will let you drive it off the lot for $50,000. But then you find out that another dealership, coincidentally next to the place where you got the bargain on the iPod, will sell it to you for only $49,900.

Do you make the same trek across town to save $100 on the car? Most people would not, even though they would to save the same $100 on the iPod. Because people are idiots.

There are two things going on here. One is the natural tendency to think of things like discounts as proportions or percents, rather than as absolute amounts. The discount on the car is a joke, only 1/500 or 0.2% of the total. Most people think of it as being essentially zero. But the discount on the iPod, 50%, is worth getting excited about. Our brains are wired to think in terms of proportions like this. They just are.

(When people predict future downward pressure on mutual fund fees I tell this story about iPods and convertibles. The simple truth is that no matter how many dollars it translates into, hardly anybody will pick a fund because the annual fee is 0.25% lower.)

The other important pseudo-logical failing at work here is that people have trouble believing, or acting as if they believe, that all dollars are worth the same. The $100 saved on the iPod just seems more exciting and useful than the $100 saved on the car. You could use it to buy music to put on the iPod or you could buy a second iPod in another color. The money saved on the car, well, you could use it to start saving for the next car, or apply it to the purchase of some other large-ticket item. Not so exciting.

To a certain extent everybody mentally sorts expenditures like this. The only way to get our heads around the spending of our money on all the things we buy is to separate out the expenditures into buckets, for example housing, clothing, eating out, etc. Every person may have a different set of buckets, but dividing things up and then concentrating our efforts on allocating inside the buckets is the natural and practical approach.

The side-effect is that we have trouble relating savings in one bucket to things we might buy in another. An example from the behavioral economists illustrates this nicely.

Researchers found that people who move from cities with less expensive housing markets to more expensive ones, Toledo to New York perhaps, or vice versa, tend to spend the same on a house that they did in the old city. So a person going from Toledo to New York will squeeze the family into a tiny apartment and the one going the other way will buy a palatial mansion. It seems very likely that the new New Yorkers would be happier if they spent a little more on housing and less on everything else, just as the new Toledoans would be happier spending less on housing and more on the other stuff.

People are idiots.


  • By Adam, July 24, 2009 @ 10:39 am

    Behavioral economics is really interesting. You should write your own book- ‘Predictably idiotic’ does sound so much better than ‘Predictably irrational’…

  • By Kosmo @ The Casual Observer, July 24, 2009 @ 12:17 pm

    Yes, you’re definitely correct. People will spend time clipping coupons to save them 25 cents on a bottle of dish soap, but won’t take them time to spend a few extra minutes negotiating to save a hundred dollars on a car.

  • By Rob Bennett, July 24, 2009 @ 12:48 pm

    The point being made is a great one.

    I don’t at all agree that people are idiots.

    People have lives to live. If we had to do a full and complete and accurate analysis of every spending decision we make, we would not have time to do anything else. So we use shortcuts. The shortcuts generally work. Sometimes they don’t.

    Pointing out the logical flaws in the shortcuts helps people to understand better how they make decisions to spend. But I don’t think it helps to suggest that the shortcuts are a sign of idiocy. The shortcuts are there for a reason. Those who know enough to avoid one sort of shortcut end up adopting another sort, sometimes a worse sort.

    We can never achieve 100 percent rationality. Life itself is not rational. When we achieve 100 percent rationality, we are no longer humans, we are machines.

    I like humans better.


  • By Frank Curmudgeon, July 24, 2009 @ 2:32 pm

    Just to be clear, I am myself a person and I don’t mean to be taken literally when I say that people are idiots. I really mean only that we are not anywhere as rational as we usually assume.

  • By SJ, July 24, 2009 @ 2:34 pm

    I think having separate buckets is okay. But you just need to remember that the buckets all hold water.

    Actually, for the IPOD story it sounds more impressive to other irrationally fools to say you got it half off vs. the car case. Also cars are rarely identical… -)

  • By Jim, July 24, 2009 @ 2:42 pm

    The ipod vs car example is a very good illustration of the idea and it hits home for me. I’d fall victim to that kind of thinking myself. Its natural for me to look at the numbers in terms of % rather than the absolute savings.

  • By Dave C., July 24, 2009 @ 3:20 pm

    I can relate to this – recently I considered setting up multiple accounts (buckets) in my ING Direct profile to help manage savings for different things (buckets): emergency fund, car payments, fun money, etc.

    While doing that would help me to control my behavior (preventing the use of emergency funds for vacation) it is irrational because of the resulting loss in compounded interest by having small balances (instead of one large account).

    In the end, I just need to exercise greater discipline and control, instead of reducing my financial gains for the benefit of a mental crutch.

  • By My Journey, July 24, 2009 @ 3:29 pm


    Regardless of whether you have $100 in one account or 4 buckets of $25 your interest will be the same (go do the excercise on Excel).

    Notwithstanding, I have done this and it hurts when you point it out!

  • By Rob Bennett, July 24, 2009 @ 3:29 pm

    I really mean only that we are not anywhere as rational as we usually assume.


    And this is the biggest story in personal finance today. I believe that it is impossible for most of us even to let in to our consciousness how big it is.

    I read a great story about this told by one of the leading behaviorists. There were a bunch of guys on a mountain and they were lost and running out of food. One of them found a map in a pocket and they became excited that now they knew how to get back to civilization. They got back and told the story. Someone asked to see the map. He looked at it and said: “I’m glad you fellows made it, but this map is not a map of that mountain range.”

    The map provided no actual help. But they were scared and needed something to give them hope. In that sense it helped.

    That’s where we are in personal finance today, in my assessment. We have no idea what we are doing. Our knowledge is primitive. But we know this stuff is important and we cannot stand the thought of not knowing as much as we don’t know. We grab hold of any theory that sounds half plausible and act as if it reveals every possible truth because it scares us to death to admit that we don’t yet possess a good map.


  • By RT, July 24, 2009 @ 3:48 pm

    Hey Frank,
    Gary Belsky and Thomas Gilovich make this exact same point in Why Smart People Make Big Money Mistakes And How To Correct Them: Lessons From The New Science Of Behavioral Economics. I know, long enough title? Anyway, it’s been a while since I read it, but I’m pretty sure they’re the first ones who pointed out to me that people divide their purchasing habits into buckets. And those buckets somehow don’t overlap in our heads, so $100 worth of iPod is somehow not equal to $100 worth of convertible car. Behavioral economics is fascinating.


  • By Dave C., July 24, 2009 @ 6:20 pm

    MyJourney – yeah you are totally right, I just sat down and did the math and see that my original assumption was completely wrong.

    Heheh, I guess I should have done that in the first place, eh? I just assumed my erroneous idea of how it worked was the way it was, maybe from somebody else who told me before.

    It just goes to show, its better to do the math and find out for sure, than to just operate on conjecture! Thanks MyJourney

  • By ryan, July 24, 2009 @ 8:12 pm

    It’s funny, I was thinking about just this sort of thing today, before reading this.

    I was wondering how we might behave differently if we paid for everything we every buy with $20 bills–iPods, convertibles, the mortgage, etc. I was writing out the mortgage check, and for some reason, thought “how many $20 bills is this?” I was actually surprised by the answer. Try it now, for your big bills.

    I think it would help to eliminate some of this idiocy from which we all suffer.

  • By Holly, July 24, 2009 @ 9:25 pm

    Ryan, you’re right…I hired a helper for $400. When I took the 20 dollar bills from the ATM, I thought, “WHOA! That’s a LOT of money.” He was just caulking around windows and doors…I think I was duped :^P

  • By Frank Curmudgeon, July 25, 2009 @ 11:26 am

    Back when I had a job in a world where a guy could get a $1M bonus and be bitterly resentful and angry that it wasn’t the $1.2M he thought he deserved, I often thought that the bonuses should be paid in cash, counted out on your desk by the CEO.

  • By Dasha, July 26, 2009 @ 9:18 pm

    I was just thinking the other day that I always thought that $4 for a jar of dried cranberries is outrageous and force myself to ration them while I spend $4 on a frappuccino about once a week during the summer without thinking about it. I’m an idiot too :)

    PS- I’ll take the $1M, k, thx.

  • By Patrick, July 29, 2009 @ 10:15 am

    Actually it’s not that illogical. You make a lot more $200 purchases in your life than $50,000 purchases. If I save myself $100 on each $50k purchase in my life, I’ll probably save myself a grand total of maybe $300. If I save myself $100 on all the $200 purchases, I could retire early.

    So, looking at an individual transaction, preferring $100 off an iPod over $100 off a convertible is silly. Looking it as a lifelong attitude toward money management, it makes perfect sense.

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  • By Paul Williams, May 31, 2012 @ 8:14 am

    Heh, count me as one person who would pick a fund because the expense ratio is 0.25% lower. But I guess that’s because I think of what that 0.25% could amount to when compounded over 30+ years. :)

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