Thursday, January 18, 2007

Why similarity is way beyond the similar, II: the poverty line

What defines a poor person? Is a poor person someone below the poverty line, someone whose income is less than a precise number? If you think so, as the US government does, you're putting in the same category homeless people from New Orleans and some Chicago Economics grad student who might work as a TA and still get a shiny golden Rolex from proud wealthy daddy for Christmas. Oh, and perhaps you're throwing out those above the poverty line, but whose expenses dwarf their capabilities, such as garbage collectors of expensive New York City.

We must say Bravo, unfogged! Bravo!

Many English words (well, words in any natural language), particularly the kinds of words that are important in political arguments, have imprecise referents that shift with context. "Poor" and "poverty" refer generally to a state in which one's lack of economic resources is a problem; whether that specifically means Pat Moynihan's 'underclass', or a grad student living on ramen noodles, or even a house-poor family who overspent on a McMansion and are now, despite a decent income, fearing foreclosure. In some contexts, poverty refers to grinding hardship; in others, it can describe a state that doesn't involve a great deal of hardship at all. But these are all correct usages of the word 'poor '-- while it's not of infinite extension, it doesn't have a sharp edge. Given any situation, you can argue about whether 'poverty' is a valid description of it, but there are always going to be borderline cases where there isn't a solid yes or no answer.

In order to facilitate public policy analysis, on the other hand, the US Government has created a defined term -- 'the poverty line' -- which does have a sharp edge. If your income is three times the cost of an economy food budget in 1963 (adjusted for inflation) or below, you're below the poverty line; if not, you aren't. The poverty line is a precise measure, and it's necessary for some purposes, but that doesn't make it more accurate than the vague natural-language word 'poverty'. A grad student from a wealthy family with a lot of possessions and family assistance who's earning a below poverty level stipend for a year isn't poor, despite being under the poverty line; a family living in an area with high housing costs and making an income slightly over the poverty line is poor, despite not meeting the definition of the defined term. That's not a reason not to use the defined term, but it's important to remember that the defined term is a tool, rather than a reality; a public policy intended to address 'poverty' and directing its aid toward the temporarily low-income grad student (no implication that there aren't genuinely needy grad-students intended, of course) in preference to the genuinely needy family would be misdirected, even though the first is below the poverty line and the second isn't. For accuracy's sake, it's important to focus on the vague natural language word, which refers to some state of hardship due to lack of economic resources, and remember that the defined term is simply a tool for analysis.

Similarly, in natural language 'the economy' describes the whole system of exchanges of goods and services that go on in our society -- it's incredibly complex, and certainly can't be reduced to one or two statistics. We're interested in the economy because it has all sorts of measurable characteristics that affect the welfare of people in our society. There's a defined term, 'Gross Domestic Product', whose size and growth are equated with the size and growth of the economy. This is precise, and it's not wrong if the reason you're discussing the economy is something that's going to be strongly affected by GDP, but its precision can make it terribly misleading when you're talking about the economy in terms of the economic welfare of individuals. If you find yourself thinking "Well, the economy is strong; even though wages are flat and income volatility is high, it's surprising that people aren't reacting positively to the economic good times" it's because your equation of 'the economy' with something that can be precisely defined, GDP, has left you with an inaccurate picture of what economic good times mean. The vague word is less likely to lead you astray than the defined term.

A lot of people have a tendency to privilege defined terms over naturally used words; if there's a tightly defined sense a word can be used in, they want to call usages that don't fit the tight definition as wrong, or improper. The problem is that you can't shake all of the connotations and baggage away from the natural word; when you say that 'poverty' means only 'the state of having an income below the federal poverty line', you implicitly state that someone who isn't poor by that definition isn't suffering from economic hardship -- while you can explicitly disavow the implication, it's still hard not to be affected by it. Better, and more accurate, to use words naturally, and save defined terms for the contexts where their precision is necessary.

[note: Free Exchange also has a say on the subject].

A small addendum: Regarding the cases where there is no sharp edge between "similar" categories, or English words for that matter, we should perhaps substitute "many English words", for "all English words". Afterwards, why not go to "all human concepts"? Perhaps all human concepts are fluid and change according to context. The connotation explosion will allow us to see someone above the poverty line as a very needy, poor person. It will also allow us to see that many people below that line are not to be considered in any sense needy. Even precisely defined concepts which make the glory of economists; even mathematically defined terms, such as number, or a square, will dance the context dance.

A number is a number is a number, right? A square is a square is a square, right? Though these are precisely defined categories, our cognition tricks us for responding 'yes', while we should perhaps take another look.

In number theory a number is a number. But it also can be a well-formed formula, or not. And those that actually are well-formed formulas can also refer, or talk about, in a Gödelianesque way, the entire nature of mathematics. Numbers have more than a single connotation; and the chosen connotation will change according to the context it is considered.

The Russian Scientist Michail Bongard brought forth a great challenge to computer scientists. Find out what is the difference between six visual figures on the left side, and six visual figures on the right side. Here are some Bongard problems. You can solve them in a minute or two.

The answers are in the first comment. Now, look at problem 91, and ask yourself: have I been consistent?

The answer is that you have not been consistent. A square is a square is a square? For that to happen, you would have to classify "three squares on the left side", versus "one square on the right side". Or perhaps you might want to think in terms of line segments: "twelve on the left", versus "four on the right". Those views lead to no correct answer.

If you solved it, you have been inconsistent; categorizing the "same" thing differently according to context.

Not to worry; wasn't, after all, Ralph Waldo Emerson, who said that "consistency is the hobgoblin of small minds"?

We have been pointing this out for a while now:
Linhares, A, (2000). A glimpse at the metaphysics of Bongard Problems. Artificial Inteligence 121, 251-270. Available HERE.


Alexandre Linhares said...

Problem 85: three versus five
Problem 87: four versus five
Problem 6: triangles versus quadrilaterals
Problem 91: three versus four