Getting Framed: Part One

Suppose that two chipmunks, Alvin and Theodore, are chasing each other. Neither is catching up on the other, and neither is aware of being chased. Alvin is chasing Theodore gleefully and athletically but not skillfully, just for the joy of chasing. Theodore is chasing Alvin gleelessly and unathletically but skillfully, in order to bring him home. Suppose further that this was the only time that either chipmunk chased the other. An utterance u1 of sentence (1) can be a true report of (some of) what happened, while an utterance u2 of sentence (2) is also true in the same context C.

            (1)  Alvin chased Theodore gleefully and athletically but not skillfully.

            (2)  Theodore chased Alvin gleelessly and unathletically but skillfully.

By itself, that’s not puzzling. Any scenario can be described in many ways. But consider the following hypothesis: u1 is true if and only if the Davidsonian logical form (1a) is true relative to C; and u2 is true if and only if (2a) is true relative to C, with '$' as an existential quantifier.

        (1a) $e[Chased(e, Alvin, Theodore) & Gleeful(e) & Athletic(e) & ~Skillful(e)]

                    (2a) $e[Chased(e, Theodore, Alvin) & Gleeless(e) & Unathletic(e) & Skillful(e)]

Given this hypothesis, it follows that there were two chases, occupying the same region of spacetime: a gleeful, athletic, but not skillful chase of Theodore by Alvin; and a gleeless, unathletic, but skillful chase of Alvin by Theodore. That’s not a logical contradiction. But two chases, with the same participants, in the same place at the same time? Yuck. This suggests that (1a) and (2a) do not correctly specify truth conditions for (1) and (2).

            So much the worse, one might say, for the idea that (1a) and (2a) reflect the logical forms of (1) and (2). Alternatively, one might say that (1a) and (2a) do reflect the logical forms of (1) and (2), and so much the worse for the idea that a Human Language sentence S has the truth condition of an invented sentence that reflects the logical form of S. In thinking about the options here, I’ve found it useful to bear in mind that humans are subject to framing effects of the sort that Kahneman and Tversky made famous. Kahneman’s recent book, Thinking Fast and Slow, is a great overview; and in it, he discusses a beautiful example that Thomas Schelling (University of Maryland Nobel Laureate) used in his classes, presumably without chipmunks in mind.

Schelling asked his students to think about the policy of reducing taxes for those who have (dependent) children. Suppose your income tax depends entirely on your (household) income and how many children you have. For each income i and number c of children, there is a tax t: Tax(i, c) = t. The “child deduction” might be flat, say a thousand dollars per child. That is, each income can be paired with a “base” tax, from which some multiple of 1000 is subtracted: Tax(i, c) = Base(i) – [c • 1000]. Alternatively, one might adopt a system in which the deduction for each child depends on household income: Tax(i, c) = Base(i) – [c • Deduction(i)]. Given these options, there are many policy questions. But consider (3), which seems relatively easy.

(3)  Should the child deduction be larger for the rich than for the poor?

At least for many of us, it seems unfair to adopt the “graduated deduction” policy, and then make the deduction per child larger for those who already have larger incomes. Hold that thought.

By thinking in terms of deductions, we effectively take the “standard household” to be childless. The base tax is what a childless household pays. But we could instead assume two children per household, start with a lower base tax for all incomes, and impose a surcharge on households with fewer than two children (e.g., $1000 for each child less than two): Tax(i, c) = Base*(i) + [(2 – c) • 1000]; where for each income i, Base*(i) = Base(i) – 2000. We could also let the surcharge depend on income: Tax(i, c) = Base*(i) + [(2 – c) • Surcharge(i)]. For simplicity, assume that no household has more than two children. But it doesn’t matter if there is also a tax deduction for each child beyond the second, or if we take the “standard household” to have ten children, reducing the base tax and imposing surcharges accordingly.

Again, this presents various questions. But consider (4), which might also seem easy.

            (4) Should the childless poor pay as large a surcharge as the childless rich?

Given a system that penalizes childlessness, with higher taxes for each income, it seems unfair to make the poor pay as large a penalty as the rich. A childless poor household would sacrifice a greater percentage of income, for being childless, than a childless rich household. One wants to say that any such surcharge should be graduated, with the childless poor paying a smaller surcharge. But if you answered both (3) and (4) negatively, then you endorsed a contradiction.

As Kahneman puts the point, for any given income, the difference between the tax owed by a two-child family and by a childless family can be described as a reduction or as an increase. And if poor households are to receive at least the same benefit as the rich for having children, then poor households must pay at least the same penalty as the rich for being childless. In the abstract, this seems obvious. Still, it can be remarkably hard to shake the sense that both (3) and (4) deserve negative answers. I had to stare, for a long time, at a reductio of (5).

(5)  ~[Deduction(i_high) > Deduction(i_low)] &
                    [Surcharge(i_low) < Surcharge(i_high)]

For each income, high or low, the deduction has to be the same as the surcharge. One family’s deduction is another family’s surcharge. So (6) and (7) are obviously true.

(6)  Deduction(i_high) = Surcharge(i_high)           

(7)  Deduction(i_low) = Surcharge(i_low)

Given (6), the second conjunct of (5) implies (8), which might seem fine by itself. 

(8)  Surcharge(i_low) < Deduction(i_high)                        

But (8) and (7) imply (9), which is incompatible with the first conjunct of (5).                  

(9)  Deduction(i_low) < Deduction(i_high)           

The inferences are uncomplicated: if a < b, and c = b, then a < c; if a < b, and c = a, then c < b. And yet, our—or least my—gut responses to (3) and (4) remain. Quite humbling.

At this point, one might conclude that we must answer (4) affirmatively, like it or not. But it still seems that (10) should be answered negatively.

                        (10) Should there be a flat tax on childlessness?

One might just eliminate the child deduction. But with the current flat deduction, poor households with children get more relief (as a percentage of income) than rich households with children. That raises question (11), which leaves me feeling thoroughly muddled.

(11) Should we eliminate a tax break for poor families with children?

            Kahneman draws a dramatic and disturbing conclusion.

The message about the nature of framing is stark: framing should not be viewed as an intervention that masks or distorts an underlying preference. At least in this instance...there is no underlying preference that is masked or distorted by the frame. Our preferences are about framed problems, and our moral intuitions are about descriptions, not substance.

I take no stand on whether things are this bad with regard to the moral/political. (Though if we get muddled when describing two animals, each targeting the other...) Qua village semanticist, I just think that in thinking about reports concerning “what happened” in a situation, we need to remember that humans are subject to (deep) framing effects. Maybe it isn’t so obvious that a Human Language sentence S has the truth condition of an invented sentence that reflects the logical form of S. Maybe matters are significantly more complicated than the semantics textbooks suggest, given the humble Agent/Patient asymmetry . (Stay tuned for Part Two.)