Will (Illegal) Immigrants “Cause” Obama to Win Reelection?

A couple weeks ago, I read an interesting article about how illegal immigrants can sway Electoral College votes. As it turns out, the Constitution bases electoral votes off of population counts from the census, which in turn must count all people–citizens, legal immigrants, and illegal immigrants–living in the states. Thus, even though only citizens can vote, states with larger numbers of immigrants receive a disproportionate number of electoral votes.

This has obvious electoral consequences. In particular, California gets hammered. California currently has 55 electoral votes but would drop to 50 if the census only counted citizens. On the whole, traditionally red states tend to gain from the alternative method of counting.

Based on this, the article makes the following causal claim:

If President Obama wins reelection by three or four Electoral College votes next month, the reason may be simple: noncitizens, mostly immigrants, who don’t have the right to vote.

But are immigrants really causing Obama to win reelection? Well, yes, but in a very narrow sense of causation. Presidential campaigns, if nothing else, are extremely strategic. The candidates receive a set of rules and base their strategies off the rules. In such a strategic world, you cannot change the rules and hold strategies as being constant, since the strategies are a function of the rules.

To better understand the relationship, consider the following game. All you have to do is pick A or B. If you pick A, I give you $1. If you pick B, I kill you.

Obviously, you are going to pick A. But that does not mean you prefer A. You just prefer the outcome associated with A. If I were to flip the rules on you and say A leads to your death and B pays you $1, you will suddenly really like B and really hate A.

So now imagine we switched the rules of the election to only grant electoral votes based on citizen population counts. Suddenly, some of Obama’s electoral maps are no longer winning strategies. Will Obama naively continue to pursue those strategies? Certainly not–not anymore than you would continue to select A after I switched A from rewarding $1 to killing you. Obama would spend more time and money in new “must-win” states. Romney would likely follow suit. Obama would probably campaign on different issues. Romney would as well. From here, it is not immediately clear who would win the election, since some red states might switch to blue states due to the new policy offerings and vice versa.

In fact, it is not even clear to me whether Romney would have been nominated or if Obama would have been elected in 2008 under the different set of rules. Indeed, the only clear implication of switching the rules is that both candidates would have selected more conservative policy positions. But this is exactly what you should expect when the median (electoral) voter shifts to the right.

Overall, the original article reflects a common problem with our understanding of causation. James Fearon’s article on counterfactuals is a good reference here. When making a counterfactual argument, his guideline is that a premise A only causes B if in the absence of A we have an absence of B. In other words, when making causal arguments, we must give equal weight to the counterfactual story. What does a world without A look like? If we could still reasonably find that B persists in the absence of A, it is hard to claim that A causes B.

This process isn’t too difficult when players are nonstrategic. But throw in strategic players and you really have to do a lot of work. In fact, game theory has a whole process of calculating such changes called comparative statics. Comparative statics are known for producing brutally counterintuitive results. Below is an example with soccer penalty kicks. Strikers actually aim to their weaker side more often than their stronger side. Weird, right?

Absent learning a lot of game theory and learning how to calculate comparative statics, I suppose the moral of the story is to be very careful when making counterfactual claims and to seriously consider how the entire strategic interaction might change if you alter one of the inputs. Apologies for the somewhat unsatisfying conclusion.

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