The Difference Between Relative and Absolute Difference

By Graham Peterson

20091118-no-pumpkin-pieAsk just about any economist if she believes economic growth trumps the concerns people have about relative inequality, and she will say yes.  Why is that?  Well, no matter how big the difference between your slice and my slice of the pie is, if the pie is growing — both of our slices are getting bigger.  So pull up to a low-cal sliver of GDP!

Now that doesn’t stop economists from studying relative inequality (no, they don’t just legitimate neoluburil hegermany).  And so too for other social sciences, paying attention to the difference between absolute outcomes within-group (slice expansion) shouldn’t stop us from paying attention to the difference between relative outcomes between-group (slice envy — try some slice Viagra?).

Take an example.  The Huffington Post has reliably delivered another sex survey, and found that Australian men lie in bed more than Australian women.  It’s a cute finding.  We’ll leverage this cuteness to reason over the differences between relative and absolute social outcomes — without the distracting ethical baggage — because these outcomes get a lot more important when we approach matters like relative racial outcomes.

So check this out: 25.4% of Australian men admit to fibbing the “I love you” during sex versus 6.1% of women.  Eek.  Men lie when they say a sweaty “I love you” MORE THAN FOUR TIMES as often as women (the relative difference).  But don’t forget to evaluate the absolute occurrence of the behavior, which is quite low: 74.6% of men, and 94% of women, are being honest in bed.  That’s the great majority.  This is a check one should always perform as they evaluate their ethical and political feelings about a social fact.  More importantly, it’s a crucial check for evaluating the social scientific significance of studying X.

If relative differences between groups are large, but the absolute occurrence of that outcome is small — there are just bigger fish to fry.  Lots of relative-variation studiers, like sociologists say, report on how “blacks end up in Y at two times the rate of whites.”  Sure, if 2% of blacks end up in Y, against 1% of whites, that’s certainly true.  But that still means we’re picking fights and investing resources into the study of something that 98.5% of the entire population don’t struggle with.

Every relative difference between groups is not born equal.  So no, the mere existence of one or another troubling social phenomenon does not deserve equal attention.  That is, unless, you would jump onto a subway track to save both a mouse or your son.  Think about it: “Today NBC 5 reports that a clerk was shot to death on the 1400 block of Milwaukee Ave. [and billions of people all over the world had a mostly peaceful day with one another].”  Successful social coordination, progress, and the often times strikingly low incidence of malevolence and misery, deserve our attention.

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12 thoughts on “The Difference Between Relative and Absolute Difference”

  1. Agreed that we need to spend more time thinking about levels, esp when considering how to allocate scarce time and resources. Still, something that 25% of men are doing seems like a sufficiently large number.

    I.e., The converse is also true: small inequalities that impact tons of people demand attention.

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  2. Honestly I think this argument if pursued sufficiently would really boil down to a philosophical one on the ethics of inequality, because at bottom what I’m calling into question is whether we should focus on the various inequalities between people or not. They are usually, by definition, “small.” That is, the extreme of an inequality between two people would be 100% difference. Anything less than that, and you get to start making my “is the glass half empty or the glass half full” argument: “two two folks are 20% different in their outcomes and that’s bad.” “But don’t you see! That means they’re 80% the same!” So yeah, it really comes down to a much more profound argument over whether and when relative differences between people and their social outcomes are necessary or desirable. And I’m not sure I can really defend my “optimism in the face of inequality” point totally consistently yet.

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  3. Sure, but the one does not preclude the other. cf. Tyler Cowen’s recent book. And both can be completely important. It may be more useful to emphasize one over the other at particular moments for pragmatic reasons.

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  4. Also, there are many — many! — areas where the price signal either does not exist, is murky, or is restricted/regulated for political reasons. Saying “I love you” in bed may be one such area. Other may be access to the mechanisms of politics, or winning/losing a genetic or demographic lottery, etc. These are inequalities and they are not easily resolvable by price mechanisms for a variety of reasons.

    Honestly, it’s like you think there’s no such thing as power. If there is power, then there is inequality by definition.

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  5. On the first point: saying something that happens 20% of the time doesn’t happen 80% of the time does not indicate whether the fact that something happens 20% of the time is significant. Not am I sure that it is merely philosophical. Philosophically, I would say that something that happens 20% of the time can be *quite* significant, particularly if the 20% is highly clustered amongst particular groups. This is true whether we care about absolute or relative differences. Scientifically, I would say that something that happens 20% of the time is a substantive importance for social scientists.

    Put another way: what scientific approach is compatible with a view that the only things *not* worth studying is variation? None. Study of variation is what scientific models demand. So while I fully agree that it is worthwhile to reiterate the good outcomes that occur to the majority — often the vast majority — that does not preclude study of, or reporting of, less-good (or outright bad) things that happen to smaller groups.

    There’s also the question of magnitudes: someone being shot is more of a “bad” thing than my having sushi for lunch is a “good” thing. This is why it’s not okay for me to rob you and redistribute your wealth to 100 other people. (If you bring up “consent” here to contradict me, then realize that you are also contradicting the conclusion of your post.)

    On the second point: power absolutely exists outside of instances of outright violent coercion. Coercion is one manifestation of power (there are others, such as possessing outside options). The *threat* of coercion, if it is effective in deterring behaviors that otherwise would have occurred, is another. Even in a strictly Pareto-optimal world, where along the Pareto frontier you are matters quite a lot for distribution, i.e. outcomes that occur in the material (i.e. non-philosophical) world. Those are determined by the underlying distribution of bargaining power.

    For philosophical reasons you, like many other libertarians, may not particularly care. But you cannot simply say it’s not “a thing” and then walk away. It is a thing. It can even be described in terms of the price mechanism. Buyers prefer low prices and sellers prefer high prices. Whichever of them has power — typically in the form of outside options, which can be operationalized as competition — is able to shift the distribution of a Pareto-improving exchange closer to their ideal point. See? It’s a thing.

    All of which to say that you can only refuse to take power seriously if you also deny that scarcity is a meaningful condition. Obviously scarcity is a meaningful condition. Therefore, distribution of resources is a worth being concerned about — as a social phenomena in need of explanation by social scientists and, possibly, as citizens — and that is determined largely by the distribution of power.

    If we consider power to be a systemic rather than merely relational “thing” this becomes even more clear.

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  6. I mean, if you equate the demand elasticity of a good to power, then I can’t disagree. Demand elasticity is a thing. I don’t think redefining it as power is helpful. I read a “resource dependency model,” pace Wallerstein, paper in my organizations course which essentially walked through the basic point of demand elasticity going down in the number of available substitutes for an input, and I didn’t think it was particularly illuminating.

    You make an interesting point about there being an inherent bias in scientific methods to look for variation. I’ll have to think on that more.

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  7. Looking for variation is not a bias per se. It’s just what the traditional scientific method requires.

    I strongly suggest you broaden your definition of power. If you do not then quite a large number of social and economic phenomenon will remain far outside your reach. For example: if demand-elasticity-as-power is not helpful, then why did OPEC bother cartelizing? And why did the US government (and many major corporations) work to try to break the cartel up? This was one of the biggest cleavages in the world political economy in the 1970s, and you seem to suggest that it just wasn’t “a thing”. Why does the IMF attach conditionalities to its loans? Who determines what these conditionalities are? Why do publics subject to them protest them? I could go on forever.

    You don’t have to go all the way to Wallerstein for this. All of public choice econ is concerned with these questions. As are folks like Hirschmann and Schelling. Adam Smith was *very* concerned about monopolies, for precisely demand elasticity reasons. Is Adam Smith not helpful?

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  8. (I should probably add that I’m not necessarily impartial in this discussion. A lot of my research tries to use network models/metrics to highlight who possesses power in markets and institutions. But… I don’t think I’m wrong.)

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  9. The last time I made a loan to a friend, I didn’t do so without talking to him about how he’d gotten into his financial squeeze in the first place. And it’s not clear that OPEC has a significant impact on global oil prices given their combined global market share and constant cheating of production quotas among themselves. Even a pure monopolist faces a downward sloping demand curve.

    I don’t disagree that people agglomerate into clusters on networks, and that such behavior gives to long run path dependencies. Such trends do not negate Hirschmann’s point about exit, voice, and loyalty. The existence of hierarchies does not imply the existence of power which ever-increases, and that’s the problem with calling inelastically demanded goods, organizational hierarchies, and financial networks “power” — it reinforces the 18th and 19th century sky-is-falling political intuitions about the incessant increase of power in the world.

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  10. I was referring to OPEC in the 1970s, when they very definitely had the power to move prices, as evidenced by the fact that they did just that. The fact that they no longer have the same extent of power just means that they are less powerful and someone else is more powerful. In particular, the states that responded to OPEC’s 1970s-level of power by boosting their own capacity so as to improve their bargaining leverage (i.e. power).

    Hirschmann’s point about exit, voice, and loyalty is about ways of exercising power that are different from starting a revolution.

    I’m not sure what you mean by the 18th and 19th century stuff. I’m talking about contemporary dynamics and using contemporary examples. I would probably agree that power is more diffuse than it used to be, but that doesn’t mean it’s gone entirely.

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