Heaps of Trouble

The United States national debt recently reached roughly 34 trillion dollars in debt with CEOs of large financial institutions like JP Morgan, Jamie Dimon, warning that the United States is on the quick road to a fiscal cliff. This has been brewing for decades with politicians of both major political parties in the United States spending more money than is collected in tax revenue. This wasn’t always so: for much of the history of the United States, national debt was manageable or non-existent. The likely explanation for the explosion of the national debt: widespread political support for expensive social programs among voters, and the lack of support for higher taxes or major reductions in spending. 

Situations like this arise because of what economists call collective active problems: problems that require action of many to solve, but where each individual has an incentive to prioritize their own interests over helping solve the problem. The incentives for the individual voter do not align with fiscal discipline: it costs the individual little to vote for expensive social programs, even though in aggregate such votes favor policies that are expensive and unsustainable. Cutting spending on current programs would be politically unpopular, and would likely terminate the career of any politician who supported budget cuts. The logic of collective action problems is only part of the explanation though. There is another aspect to the explanation that has been largely overlooked: the national debt in the United States has the logic of a sorites paradox — the word ‘sorties’ comes from the Ancient Greek word for ‘heap.’

To appreciate why paradox partly explains our rapidly increasing national debt, we must first understand the nature of sorites paradoxes. And like with most philosophical ideas, it sounds trickier than it is — the paradox is straightforward. Begin with a simple heap of sand. Taking one grain of sand won’t destroy a heap. And that’s true of each and every individual grain of sand. However, even taking just one grain won’t destroy the heap, taking one over and over again will eventually destroy the heap — eventually there won’t be any sand left to form a heap. There is no obvious line or threshold that can be drawn where, if one more grain of sand is taken from the heap, it will cease to be a heap. We can formulate this paradox as follows:

A pile of one trillion grains of sand is a heap. A single grain of sand isn’t a heap. Taking one single grain of sand won’t create/destroy a heap.

This is the nature of a paradox: a set of statements that individually look as though they must be true, but when taken together cannot be. If we took a single grain of sand from a heap over and over, we wouldn’t destroy the heap. We can reverse it too: adding one grain of sand doesn’t make a heap. So, then you would never arrive at a heap, even if you added a grain of sand over and over again. And obviously that cannot be correct.

How does this relate to the national debt? Good question. Consider that if we keep borrowing more money than we take in, to fund social programs, the military, and whatnot, the situation will become financially untenable. In one possible scenario, interest payments on the national debt will engulf the Federal budget, hurting poor people who rely on social programs that must be scaled back or abolished to cover interest payments. The claim isn’t that we know the exact point when something like will happen — perhaps it won’t happen at all — but if we continue to haphazardly spend more than the tax revenue we take in, and we fail to address this issue in the future, this situation could be our financial future.

However, adding a single dollar of deficit spending to the national debt likely won’t produce financially calamitous results. What’s one more dollar after all? And there are many advantages to the level of spending that we’re engaged in. Who doesn’t have a favorite social program they want to keep? We would, if we could, prefer to keep funding our social programs a bit longer. We want both to keep our favorite Federal programs, but we don’t want interest payments on the debt to devour the budget. The national debt sorites paradox can be stated as:

Spending a single borrowed dollar on social programs won’t devour the budget. Eventually, if we continue to spend more than we tax, interest payments on the Federal debt will devour the federal budget. American citizens and voters want to continue spending on their favorite social programs as long as possible.

How does this work? For each borrowed dollar we spend, one could argue that spending one more borrowed dollar is insufficient, by itself, to swamp the Federal budget in interest payments. And so forth and so on. One could keep running this reasoning until some unknown line or threshold is breached, and interest payments do devour the Federal budget, forcing us to make politically difficult fiscal cuts to social and other programs. The issue here is the lack of limiting principle. Consider a smoking analogy. The philosopher, Chrisoula Andreou, explains:

Consider a smoker who wants to avoid poor health, enjoys smoking, and believes that if she never kicks the habit, she will end up in poor health. She might correctly believe that if she is going to quit, she is better off quitting after the next cigarette rather than right away. For she will greatly enjoy having another cigarette and having another cigarette cannot take her from a state of decent health to a state of poor health. Yet if she keeps smoking cigarette after cigarette, she will, let us suppose, end up in poor health.

Perhaps a more relatable example: eating one piece of cheesecake by itself won’t make someone fat. And eating another piece of cheesecake will not make one fat either. And so forth and so on. The same logic applies to spending borrowed money on social programs: one more borrowed dollar on social programs by itself won’t make the difference between devouring the debt with interest payments, until it eventually does.

The logic of sorites looks fatalistic. How can we solve the paradox? Here an economist has what looks like a simple solution to the sorites logic: one should continue spending until the marginal cost of spending that dollar exceeds the marginal benefit. There are a couple of problems with this otherwise sensible solution. First, it is somewhat unclear who enjoys the benefits, and who bears the costs, except that it looks like older Americans enjoy many of the benefits — based on the structure of the budget — while the costs fall on younger taxpayers. Second, and more importantly, the process of nailing down who benefits and who is harmed by continued deficit spending is difficult, even if we know the broad strokes. 

Often questions of this sort are hard to get right, and easy to get wrong, when trying to give too specific of an answer. That’s why the best approach to address the sorites logic of the national debt is to embrace the arbitrary. The reason sorites logic is so difficult to diffuse is that there is no obvious line or threshold to be established somewhere between the incremental steps that begin with a budget surplus and end with a budget consumed by interest payments. Since it is so difficult to find a principled line to draw, where one more dollar would in fact be the ruin of the budget, it is better to coalesce around an arbitrarily chosen line or threshold and announce — like Jean-Luc Piccard in First Contact in his frustration with the ever-advancing Borg — ‘the line must be drawn here! This far, no further!’ If the choices are between arbitrary lines, on the one hand, and financial and political ruin on the other, then we must embrace the arbitrarily line — or the sorites logic of the Federal debt will, eventually, choose it for us.