Helping the Poor is Not Always Intuitive

Motivated by my missunderstanding about the Nobel Prize Kahneman’s example, citing Thomas Schelling and why Our Intuition Sucks at Math, I have decided to dig deeply and give a try to the next problem.

This article is inpired by the Chp 34. Thinking, Fast and Slow, and mainly by Thomas Schelling’s book Choice and Consequences (pp. 18-21). Kahneman introduces some variables which may not be well-defined and thus, open to debate. After the hell of reading multiple versions about it trying to understand the point, could be interesting to take a look at the case presented by these two great men.

The essay is summarized here:

In the 1970s, the Nobel Prize-winning economist Thomas Schelling used to put some questions to his students at Harvard when he wanted to show how people’s ethical preferences on public policy can be turned around. Suppose, he said, that you were designing a tax code and wanted to provide a credit —a rebate, in effect— for couples with children. In a progressive tax system such as ours, we try to ease the burden on the less well off, so it might make sense to adjust the child credit accordingly. Would it be fair, do you think, to give poor parents a bigger credit than rich parents? Schelling’s students were inclined to think so. If the credit was going to vary with income, it seemed fair to award struggling families the bigger tax break. It would certainly be unfair, they agreed, for richer families to get a bigger one.

Then Schelling asked his students to think about things in a different way. Instead of giving families with children a credit, you’d impose a surcharge on couples with no children. Now then: Would it be fair to make the childless rich pay a bigger surcharge than the childless poor? Schelling’s students thought so. But—hang on a sec—a bonus for those who have a child amounts to a penalty for those who don’t have one. (Saying that those with children should be taxed less than the childless is another way of saying that the childless should be taxed more than those with children.) So when poor parents receive a smaller credit than rich ones, that is, in effect, the same as the childless poor paying a smaller surcharge than the childless rich. To many, the first deal sounds unfair and the second sounds fair —but they’re the very same tax scheme.

Your intuitive reaction to this question, like that of the students, was probably immediate: “No.” But there’s a problem. Our intuitions say that the rich should not receive a higher credit than the poor, but that they should pay a higher surcharge. But as Schelling pointed out, “surcharge” and “credit” are just two different ways of describing the same thing, a purely verbal distinction created by an arbitrary choice about how many children we assume as the baseline case. So what our intuitions are telling us to do – have the rich pay a higher surcharge but receive a lower credit – is logically impossible.

And Kahneman adds:

The decision of having childs would mean a $20 credit for the poor and $10 for the rich. For the main objective of this policy, it seems to be correct.

(*) Also, in this scenario, if we take into account poor families that decided not to have childs, they would have been 2x worse off ($20), while rich families would have only been 1x ($10). The decision of going childness is a feasible but worse option for poor couples in terms of progressivity. They are not obtaining the same benefit as the rich would. However, we are not assessing that decision in this case because we assume unidirectional axis for children (from 0 to >0) and later, for tax scheme.

Time for the second scheme, which is based on different surcharges:

Tax scheme with surcharge for childless, no tax credit for having childs.

Surcharge – No credit	0 children	>0 children
Poor	$10 surcharge	No tax/credit
Rich	$15 surcharge	No tax/credit

Again, we see that poor families that decide to have kids, they gain (or avoid tax) of $10, while the rich have gained $15. Leading to the opposite conclusion as before; in this specifically tax scheme, poor people are being less favored than rich, which make us to be confused if we are looking for the cited progressivity.

“It delivers an immediate response to any question about rich and poor: when in doubt, favor the poor. The surprising aspect of Schelling’s problem is that this apparently simple moral rule does not work reliably. It generates contradictory answers to the same problem, depending on how that problem is framed.“

As we have demonstrated, intuition may not be the best policy-making. Following Kahneman’s advice “you must want the poor to pay at least the same penalty as the rich for being childless“, we would want the poor to pay the same as rich, forcing the gain (avoid tax) to be the same amount in the second case.

This bias in our intuition systems could be presented as a good point for libertarianism approach, or at least, in a way to be opposed to pushing rich people to pay more taxes. The initial idea of favoring the poor has resulted in the opposite effect; therefore, as it has been demonstrated, poor people should pay at least the same surcharge as rich people.

Once the contradiction has been showed, the article and discussion could have ended here. However, there is a crucial factor in the argument that makes the difference.

On the one hand, Schelling is considering the policy constant (type of tax scheme) and varying wheter or not they have kids; tax system is fixed, number of children not. As the different involved variables have been presented by the author (it is presented as a two-dimensional tax schedule), the result is perfectly matching with the argument. Nonetheless and, since it might not be sufficiently cleared the variables which we are playing with, there is another way of facing the problem.

On the other hand, number of children could have been kept constant, while both policies are being compared. (*) We must record that tax scheme is one-way, same as children before; we are switching “surcharge-no credit” for “no surcharge-only credit”, and not viceversa. Let’s break it down:

0 children default, both tax schemes

0 children	Surcharge – No credit	No surchage – Only credit
Poor	$10 surcharge	$20 credit
Rich	$15 surcharge	$10 credit

Now it seems that poor families are more benefited from this policy compared with rich. The poor only pay $10 surcharge in first tax scheme, where rich pay $15. Varying the tax to “no surchage- only credit”, poor are gaining or avoiding tax of $10 and receiving $20 ($30 in total), whereas rich only sum 15+10($25 in total).

Let’s see what happens with more children:

>0 children default, both tax schemes

>0 children	Surcharge – No credit	No surcharge – Only credit
Poor	No surcharge	$20 credit
Rich	No surcharge	$10 credit

In this second case, poor families are again favored with this policy, specifically, two times more ($20 vs $10). So tax credit (and total benefit) is greater for poor.

If we look at these two tables, we arrive at different conclusions than in the first comparison. Firstly, if the policy is the variable, higher credits for poor people and higher surcharges for rich has, in both cases, more worth for the poorer.

Although, there could be a larger or shorter incentive for richer when having children, since the gain of having kids shifts from $25 to $10, while for poor people drops from $30 to $20. Which gain or loss will be determined by the total surcharge and the amount of tax credit we have previously selected (In this case, it is a higher loss for rich people, but in another example could have been a higher benefit for them).

Even so and, in each case, the overall utility impact of the policy favors the poor person over the rich person, though in the second comparison the rich person gets a higher or lower benefit from one possible choice (having or not kids).

If we reformulate the scenario to please ourselves and find the desire equity seeked for initial intuition, we can solve the problem contradiction, which it is caused by the unique proposition of two alternatives, where the problem lead us to consider the question by the frame.

Therefore, another third option comes up, and it is delightfully possible to avoid contradictions:

Tax scheme with surcharge for childness and tax credit for childs

Surcharge & Credit	0 children	>0 children
Poor	$10 surcharge	$20 credit
Rich	$15 surcharge	$10 credit

Finally, if poor couples, bored of not having childs, decide to conceive another family member, they gain 10+20=$30. On the other side, rich would only gain $25. There is still a $5 higher benefit for the poorer.

Thus, as we have seen, your intuition — and mine — can sucks at math. When helping the poor seems to be the most easy thing to do, it can results in the opposite, favoring the rich and turning into detrimental for the poor.

It generates contradictory answers to the same problem, depending on how that problem is framed . Our preferences are about framed problems, and our moral intuitions are about descriptions, not about substance.

– Daniel Kahneman

The point of this post is not to discuss whether the fairness or ethics of taxes. The point of the post is to show that intuition is not always our best ally. It could be dificult to argue that helping the poor is not intuitive, but it has been also cleared that helping the poor is not always intuitive. Or the point could also be just putting some random polemical title and see what comes next.

References