Compare this
No, it's not the same thing!
One of the benefits of working with computers,aside from the lack of human contact, is that it makes you very logical. One of the easiest fallacies you can fall into is performing improper comparisons due to aggregations. A fundamental principle of data is that a comparison is valid only between entities of the same type and if it is made in the same units of measure.
If I give you two totally different entities and units, you can see the fallacy at once, as in "Which do you think is bigger, the temperature of the sun or the color of a 1975 Mustang convertible?" But if I hide the differences in the entities by making one an aggregate of the other, it will slip past you. Aggregations are not the same as their individual members.
This fallacy of the levels of aggregation is much more common than you would think. The Loka Institute (www.loka.org) is a group headed by Richard Sclove and devoted to what it calls "community-based research" and "making science and technology responsive to democratically decided social and environmental concerns." It issues an irregular email newsletter, which contained this short piece in the July 1998 edition:
"The Pepsi Challenge: In 1994, Pepsico announced that, following two years of market research conducted among 5,000 people, it would spend a further $50 million to reinvent its Doritos-brand tortilla chip -- intensifying the flavor on the outer surface, rounding the chip's corners, and redesigning the package. Pepsico's principal concern was to ensure that Doritos maintain market dominance in the face of growing competition from the new 'restaurant style' corn chips.
"The expenditure of more than $50 million to ensure that Pepsico's Doritos outsell Pepsico's own competing Tostitos represents approximately five times the total annual U.S. investment in community-based research. A society that can afford $50 million to reinvent the Doritos chip can do better than $10 million for community-based research. That's the new Pepsi Challenge!"
First, assuming that "society" and "Pepsico" are somehow the same sort of thing and that selling snack chips is comparable to funding research are false comparisons. First of all, Pepsico is pretty well defined as an entity; I know its members, the rules for membership, its powers, and the goals of a corporation. But "society" is pretty vague, and I am not sure just who the members are, the rules of membership, or exactly what powers this abstract collective noun has.
Second, while the funds are both measured in dollars, there is a difference between sales and tax revenue. A dollar not spent on Doritos will not be turned into tax revenue and sent to Loka research projects.
If I say the same thing about two individuals and their money, you will see the problem immediately. The comparison is between things of the same type: "Richard Sclove invested $500 of his own money in a savings bank with the expectation of making a profit, but Joe Celko wanted to buy his buddies lottery tickets for $1 each instead! If only our 'society' (mostly Richard) had not been so greedy, 500 people could have had a chance at a fortune. We (Richard, I, and 500 guys at my neighborhood bar who I like) clearly have the economic wherewithal to spend more on community-based lottery ticket sales."
We can make this a democratically decided issue by having me and my 500 buddies vote on it. Of course, taking a vote of any size is not magic that will somehow transform buying lottery tickets into as sound an investment as a savings account. The fallacy here is that Richard and I are not "the same kind of thing" -- that is, we do not have shared funds. If you replace "Richard" with "my wife," they are the same kind of thing -- spouses -- and we have common funds. And there is no way that Jackie would let me buy 500 people lottery tickets from the joint savings account.
Joe Celko is an Atlanta-based independent consultant. He is the author of three
books on SQL -- SQL For Smarties (Morgan-Kaufmann, 1995),
SQL Puzzles and Answers (Morgan-Kaufmann, 1995), and
Instant SQL Programming (Wrox Press, 1997) -- and wrote the SQL for Smarties column for DBMS
magazine. You can contact him via email at www.celko.com or 71062.1056@compuserve.com.
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