Nature may not abhor a vacuum, but game theory definitely abhors logical inconsistency. If you allow the possibility that what an individual
WHAT IS THE OTHER GUY’S LOGIC
(NOT HIS LANGUAGE)?
On account of the above, it may have become readily apparent to you that game theory alerts us to be careful in how we express and understand our interests and those of others. It’s easy to make logical mistakes, and they can be hard to spot, which can often disguise or obscure the meaning of the thinking and actions of individuals. That is why game theorists use mathematics to work out what people are likely to do.
Ordinary everyday language can be awfully vague and ambiguous. A friend of mine is a linguist. One of his favorite sentences goes like this: “I saw the man with a telescope.” Now that is one vague sentence. Did I look through a telescope and spot a man, or did I look over at a man who was carrying a telescope, or does the sentence mean something entirely different? You can see why linguists like this sentence. It gives them an interesting problem to work out. I don’t like sentences like that. I like sentences written with mathematics (and so do many linguists). They don’t produce poetic beauty or double entendres, which makes them boring, but it also gives them a great virtue. In English, saying things are equal often means “more or less;” in math, “equal” means just that, equal, not almost equal or usually equal, but plain simple equal.
We humans have devised all sorts of clever ways to cover up sloppy or slippery arguments. As I am fond of telling my students, my suspicions are aroused by sentences beginning with clauses like “It stands to reason that” or “It is a fact that. …” Usually, what follows the statement “It stands to reason that” does not. The clause is being asked to substitute for the hard work of showing that a conclusion follows logically from the assumptions. Likewise, “It is a fact that” generally precedes an expression of opinion rather than a fact. Watch out for these. This sort of rhetoric can easily take a person down a wrong line of thinking by accepting as true something that might be true and then again might not be.
Consider, for example, what policies you think our national leaders should follow to protect and enhance our national interest. When we think carefully about how to further the national interest, it becomes evident that sometimes things that seem obviously true are not, and that a little logic can go a long way to clarify our understanding.
It is commonplace to think that foreign policy should advance the national interest. This idea is so widespread that we accept it as an obvious truth, but is it? We hardly ever pause to ask how we know what is in the national interest. Most of the time, we seem to mean that policies benefiting the great majority of people are policies in the national interest. Secure borders to prevent foreign invasions or illegal immigration are thought to be in the national interest. Economic policies that make citizens more prosperous are thought to be in the national interest. Yet we also know that money spent on defending our national security is money that is not spent on building the economy. There is a trade-off between the two. What, then, is the right balance between national security and economic security that ensures the national interest?
Imagine that American citizens are divided into three equally sized groups. One group wants to spend more on national defense and to adopt more free-trade programs. Call these people Republicans. Another wants to cut defense spending and shift trade policy away from the status quo in order to better protect American industry against foreign competition. Call them Democrats. A third wants to spend more on national defense and also to greatly increase tariffs to keep our markets from being flooded with cheap foreign-made goods. Call this faction blue-collar independents. With all of these voters in mind, what defense and trade policy can rightfully call itself “the national interest”? The answer, as seen in figure 2.1 (on the next page), is that
Figure 2.1 places each of our three voting blocs—Republicans, Democrats, and blue-collar independents—at the policy outcomes they prefer when it comes to trade and defense spending. That’s why Republicans are found in the upper right-hand corner as you look at the figure, indicating their support for much freer trade and much higher defense spending. Democrats are on the far left-hand side just below the vertical center. That is consistent with their wanting much less spent on defense and a modest shift in trade policy. Blue-collar independents are found on the bottom right, consistent with their preference for trade protection and higher defense outlays. And, as you can see, there is a point labeled “Status Quo,” which denotes current defense spending and trade policy.
FIG. 2.1. Defense and Trade Policy in the National Interest
By putting the two issues together in the figure I am acknowledging that they are often linked in public debate. The debate generally revolves around how best to balance trade and defense given that there are inherent tradeoffs between them. Free trade, for instance, can imply selling high-end computer technology, weapons technology, and other technologies that adversaries might use to threaten our national security. High tariffs might provoke trade wars or worse, thereby potentially harming national security and prompting arguments to spend more on national defense.
I assume that everyone prefers policies closer to their favored position (that’s where the black dots associated with the Republicans, Democrats, and independents are positioned) to policies that are farther away. For example, blue-collar independents would vote to change the status quo on defense and trade if they had the chance to choose a mix on these issues that was closer to the black dot associated with them—that is, closer to what they want.
To show the range of policy combinations that the blue-collar independents like better than the status quo, I drew a circle (showing only a part of it) whose center is their most desired policy combination and whose perimeter just passes through the status quo policy.6 Anything inside the arc whose center is what blue-collar independents most want is better for them than the prevailing approach to defense spending and trade. The same is true for the points inside the arcs centered on the Republicans and the Democrats that pass through the status quo.
By drawing these circles around each player’s preferred policy mix we learn something important. We see that these circles overlap. The areas of overlap show us policy combinations that improve on the status quo for a coalition of two of the three players. For instance, the lined oblong area tilting toward the upper left of the figure depicts policies that improve the well-being of Democrats and Republicans (ah, a bipartisan foreign policy opposed by independent blue-collar workers). The gray petal-shaped area improves the interests of Democrats and blue- collar independents (at the expense of Republicans), and the bricked-over area provides a mix of trade and defense spending that benefit the Republicans and blue-collar independents (to the chagrin of Democrats).
Because we assumed that each of the three voting blocs is equal in size, each overlapping area identifies defense and trade policies that command the support of two-thirds of the electorate. Here’s the rub, then, when it comes to talking about the national interest. One coalition wants more free trade and less defense spending. Another wants less free trade and less defense spending. The third wants less free trade and more defense spending. So, we can assemble a two-thirds majority for more defense spending and also for less. We can find a two-thirds coalition for more free trade or for higher tariffs or (in the politically charged rhetoric of trade debate) for
