How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

That’s the familiar self-contradicting position we see in polls: We want to cut! But we also want each program to keep all its funding! How did we get to this impasse? Not because the voters are stupid or delusional. Each voter has a perfectly rational, coherent political stance. But in the aggregate, their position is nonsensical. When you dig past the front-line numbers of the budget polls, you see that the word problem isn’t so far from the truth. Only 47% of Americans believed balancing the budget would require cutting programs that helped people like them. Just 38% agreed that there were worthwhile programs that would need to be cut. In other words: the infantile “average American,” who wants to cut spending but demands to keep every single program, doesn’t exist. The average American thinks there are plenty of non-worthwhile federal programs that are wasting our money and is ready and willing to put them on the chopping block to make ends meet. The problem is, there’s no consensus on which programs are the worthless ones. In large part, that’s because most Americans think the programs that benefit them personally are the ones that must, at all costs, be preserved. (I didn’t say we weren’t selfish, I just said we weren’t stupid!) The “majority rules” system is simple and elegant and feels fair, but it’s at its best when deciding between just two options. Any more than two, and contradictions start to seep into the majority’s preferences.