It's still finals week here, but time for a homework assignment. William Riker's The Theory of Political Coalitions. I'd link to it on Amazon, but it is out of print, and they are charging absurd amounts for it, so go ahead and, well, never mind.
Anyway, yes, his name was William Riker.
Game theorists get all the chicks. Man, though, he did not age well. Anywho, one of Commander Riker's more famous books, written shortly before firing on Locutus of Borg, was The Theory of Political Coalitions. Key idea-- the minimal winning coalition. Any game in which policy proposals will be constructed and then voted upon has a variety of coalitions that could potentially be observed, depending on the policy proposals that are put forth. Strategically, though, it doesn't make sense to propose anything that will get any more than the bare minimum that you need to win because then you will be distributing benefits to more people than you need. If the winning threshold is 50%+1, then keep as much as possible for 50%+1. If you do anything to win an extra vote, you are throwing resources away to win that extra vote that you don't need when you could have kept those resources within a smaller coalition. Why share when you don't have to? That's the logic.
Observationally, we rarely see House votes of 218 to 217 (a fully-seated House has 435 members), and plenty of people have tackled that problem. The basic answer is that, when constructing a policy, you always have some uncertainty, so build in some leeway.
I'm going to be referencing Riker a lot as we go through this, but the key problem for the Senate is that the GOP has 52 seats. They can lose two votes, leaving Mike Pence to cast the tie-breaking vote, and still have something pass. The minimal winning coalition argument says that they should lose two votes. That would be Susan Collins and Lisa Murkowski.
I've been saying for a while that they are the key players here, but I think they may be lost votes no matter what, given the Freedom Caucus's demands. Here's the real problem for the GOP. Neither are alone. Collins worked with Bill Cassidy on a competing bill, before the Freedom Caucus ever started on anything, and Murkowski signed a letter along with Rob Portman, Shelley Moore Capito and Cory Gardner saying they hate our Freedom. Caucus bill. If this were a simple Riker problem of managing the minimal winning coalition, then the GOP would just kick Collins and Murkowski out of the coalition by ignoring their demands and be done with it in order to try to keep the Freedom Caucus happy now. Maybe it would work, and maybe it wouldn't, but it isn't that simple. Not after Collins pulled Cassidy into another bill, and not after Murkowski joined with Portman, Garner and Capito.
This is far from over.