Obamacare and Set Theory

Obama and the supporters of Obamacare seem flummoxed by the way polls show people favoring various provisions of the bill, while hating the bill overall. How, they ponder, can so many people like all these parts of it and not like the whole thing?

To understand that, a bit of basic Set Theory.

I'll oversimplify to make it easy to follow.

On any given provision of the bill, there will be three sets of people -- those who like it, those who hate it, and those who have no opinion. For each provision, we will look at the set of those who like it. So the Set of People Who Like Provision A will just be called Provision A for short.

Obama seems to think that the sets are additive -- that is, The Set of People Who LIke The Whole Bill ought to equal the sum of Provision A + Provision B + Provision C and so on. But if you add Provision A + Provision B + Provision C, etc., you'll get The Set Of People Who Like At Least One Provision of the Bill, not The Set of People Who Like the Whole Bill.

Let me illustrate. It's not to scale, because I'm illustrating a basic point, not trying to get exact numbers here.

So -- here is the Set of People Who Like Provision A:



If you pass a bill that's just Provision A, all these people will like it.

Now, watch what happens when you add The Set of People Who Like Provision B:



The area covered by both circles would be The Set of People Who Like At Least One Provision. It's bigger than Provision A or Provision B. But The Set of People Who Like Both Provision A and Provision B is depicted by the area of overlap. It is smaller than either Provision A or Provision B alone. Mathematically, The Set of People Who Like Both Provision A and Provision B can not be larger than the smaller of the two sets.

Following me?

As you add more provisions, two things happen:



The Set of People Who Like At Least One Provision can grow, but The Set of People Who LIke All The Provisions can't. It can never be bigger than the smallest set. And unless there is 100% overlap between any two sets, the Set of People Who Like All The Provisions will continue to get smaller and smaller as you add more provisions:







You've seen this in real life when you try to get a group of people to agree on what to order on a pizza. In a group of 10 people, 8 may like pepperoni, 9 may like extra cheese, 6 may like sausage, 8 may like onions, 4 may like pineapple, and 1 may like anchovies. That doesn't mean you're going to have 10 people who want a pepperoni, sausage, onion, pineapple, and anchovy pizza with extra cheese. The largest possible number of people who would like a pizza with all those toppings is one -- and that's if the anchovy person also likes pepperoni, extra cheese, sausage, onions, and pineapple. If the anchovy person doesn't like extra cheese, even he won't want a pizza with the works.

And this is how you can get so many people who like one more or more parts of the Obamacare bill, while having only a minority that like the whole thing.