Posted by: erichosemann | September 27, 2009

Interpersonal Comparisons of Utility

How can we understand the following statement?

“Interpersonal comparisons of utility are not possible.”

Let’s break it down, word by word.

First, the adjective interpersonal, from the Concise Oxford English Dictionary, or COED, for short: “relating to relationships or communication between people.”

And comparison, again from the COED: “an act of comparing,” which is the same as “an act of estimating, measuring or noting the similarity or dissimilarity between.”

And then utility: “the state of being useful, profitable or beneficial.”  In economics, goods provide utility.  Goods can be material, like apples, or immaterial, like friendship.

So, interpersonal comparisons of utility are estimates of the degrees of usefulness or benefit of the same good to different people. And, apparently, they aren’t possible.  But wait.  Here are some interpersonal comparisons of utility:

“I like apples more than you do.”

“You like the Chicago Bears more than I do.”

“Raul hates math more than James likes math, but likes it more than Eric Phillips does.”

How could these statements not be possible?  That seems counterintuitive.  We all make statements like these on a daily basis.  They have, well, utility—they are a type of shorthand that allows us to make decisions and understand relationships.  They work fine at home or around the water cooler, but they break down in economics.

When I bite into an apple and it’s mealy or there’s something funny about its taste, sometimes I will hand it to my wife and ask her to taste it.  “Does this taste funny to you?”  If it’s the last apple, and I really wanted an apple, this little test is important.  If she says “Oh god…that’s gross! I wouldn’t eat that!” I throw the thing away and look for something else.  If she’s on the fence, I’ll probably eat the apple because I don’t want to waste an okay apple.  In other words, the interpersonal comparison of utility we take part in helps us decide what to do with the apple.  She’s saying that, based on her experience, eating a mealy, over-ripe apple will give her less utility, or maybe even negative utility, compared to eating a good, perfectly-ripe apple.

In that last sentence, the “based on her experience” is the part that’s really applicable to economics.  One thing I carried away from the first fifth of Rothbard’s Man, Economy and State was that utility comparisons are ordinal, not cardinal.  If utility were cardinal, it would have a specific number value.  Interpersonal comparisons of utility would be possible in that case, and they would sound something like: “Bob derives about 27 degrees of utility from eating cheese; cheese gives me about 36 degrees of utility.  I like cheese more than Bob by about 9 points.”  Have you ever heard such a statement made?  Unless someone is joking around, probably not.

When things are ordinal it means they are ordered—they have been ranked.  We do things based on their relative utility to each other, not on the basis of their absolute utility, as if we had a list in our minds ranking the utility of each good we consume.  For me and my wife, eating a good apple is ahead of eating a bad apple on our lists of goods.  Nevertheless, eating bad apples is on those lists somewhere, and depending on our circumstances (famine, decimation of the apple crop, a price ceiling on apples, etc.) it might surpass eating good apples—especially if there are no good apples around to eat.

Ordinal utility comparison is derived from scarcity, choice and opportunity cost.  Because goods are scarce—they are outnumbered by wants—we must choose the amounts of each good we consume.  When we choose, we incur opportunity cost, which is the value of the next best alternative to our choice.  That is where the ordinal part comes in.  The opportunity cost of eating that bad apple could be eating a rancid peach, if that’s all that’s in the fridge.  If the peach is really nasty, then the bad is dialed back a bit on the apple—it starts to look more appetizing.  Fortunately, our circumstances allow eating a bad apple to have a higher opportunity cost; that is, if I eat it, I forego the chance to eat an apple that is perfectly ripe and not mealy, or the chance to eat some other snack.

Because personal (not interpersonal, mind you!) utility comparisons are ordinal—an order, or ranking has been assigned to them—they can’t be compared between persons.  We each have our own ranking system, determined by all sorts of cultural, social, physiological and psychological factors.  How would we compare my ranking of rancid apples to yours?  What would be the use of such a comparison?  And why bother, when the actions we take based on our personal rankings of utility pretty much tell everyone where we come out on apples, rancid or otherwise?

We might make interpersonal comparisons of utility every day, but they are more like shorthand statements of relative like or dislike and not outright comparisons of how much utility a good gives us compared to what it gives someone else.  Economics focuses on the relative utilities of goods because economics, in Lionel Robbins’ words, is the study of study of the use of scarce resources which have alternative uses.  In other words, economics studies choices and how they are made.

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