To put it bluntly, the filibuster has to go. Here is the mathematical reasoning why. Yes, I said math -- don't worry though, it's not the scary math.
Introduction
First, let me specify what I am not talking about. I am not talking after the Jefferson Smith filibuster where a senator holds the floor as long as physically possible. Such filibusters have very real consequences, both political and physical, and I am not concerned about them as long as at the end of the day a simple majority is able to pass legislation.
What I am concerned with is the current ability of a group of 41 senators to prevent the other 59 from passing legislation. When most legislation requires the support of three-fifths of senators, the balance of legislative power in the federal government shifts markedly. This is not intuitively obvious. The filibuster, after all, only raises the necessary level of support by 10% (from 50% to 60%) in a single chamber. Mathematically, though, we can show that this seemingly minor change has a dramatic effect on legislative power and that the resulting balance of power is nowhere near what most of us would consider reasonable for our system of government.
Shapley Value and Two Simple Examples
These results are based on a mathematical concept called the Shapley value. This is not a well-known concept, so a very brief introduction is in order. Anyone who is truly math-phobic or impatient can skip down to the "Balance of Legislative Power" section, but the only math skills you need for this are basic arithmetic and the ability to mix things up (no, really!).
Suppose I decide to start a business with my friends Russ and Hillary. We set up a corporation, and since they are otherwise occupied with their day jobs, they give me extra shares of stock in return for my running the company. I end up with 11 shares and they each end up with 6 shares. If decisions require a simple majority of shares in favor (12 in this case), what proportion of the decision-making power does person have?
There are at least two methods to determine each person's voting power. One method is to calculate the Shapley value for each of us. This requires a few straightforward steps.
First, we write down all the possible ways you can order the three of us. In this case, there are exactly six:
First Person | Second Person | Third Person |
---|
Me | Russ | Hillary |
Me | Hillary | Russ |
Russ | Me | Hillary |
Russ | Hillary | Me |
Hillary | Me | Russ |
Hillary | Russ | Me |
Second, we look at each ordering in turn. We pretend that we are building a voting coalition by adding one person at a time in that order. We figure out which person is the pivotal voter who "tips the balance" and makes the coalition into a winning coalition. That is, we add each person to the coalition in order and see who gives the coalition that critical twelfth vote.
First Person | Second Person | Third Person | Pivotal Voter |
---|
Me | Russ | Hillary | Russ |
Me | Hillary | Russ | Hillary |
Russ | Me | Hillary | Me |
Russ | Hillary | Me | Hillary |
Hillary | Me | Russ | Me |
Hillary | Russ | Me | Russ |
Finally, to determine what each person's share of the overall power is, we divide the number times that the person is the pivotal voter by the total number of orderings. Since each person is the pivotal voter in exactly two orderings, each person's power is 2/6 = one-third.
At first, this result may seem strange. Clearly we have an uneven number of votes, but this strange mathematical process says we have equal power. Luckily this example is simple enough that we can apply a second method: just reason it out directly. A winning voting coalition needs 12 votes, and no one has that many votes alone. Thus, in order to form a winning coalition we always need at least two people. We can check that any coalition of two people is a winning coalition.
Coalition | Number of Votes |
---|
Me + Russ | 11+6=17 (winning) |
Me + Hillary | 11+6=17 (winning) |
Hillary + Russ | 6+6=12 (winning) |
Thus, the three of us are in an equal position since it always takes two of us to form a majority.
If you will indulge me, let us consider a slight variation on our example. Suppose I have 11 votes but Russ and Hillary each have only 5 (instead of 6). Now, a winning coalition needs only 11 votes. Our reasoning says that I can always get my way and that Russ and Hillary can never get theirs, even if the two of them combine forces. Once again, the Shapley value agrees with this assessment.
First Person | Second Person | Third Person | Pivotal Voter |
---|
Me | Russ | Hillary | Me |
Me | Hillary | Russ | Me |
Russ | Me | Hillary | Me |
Russ | Hillary | Me | Me |
Hillary | Me | Russ | Me |
Hillary | Russ | Me | Me |
In every ordering, I am the pivotal voter. My power is 6/6 = 100%.
If we have two methods that give the same answer, then it is perfectly legitimate to ask why we need the more complex process to calculate Shapley values instead of just reasoning it through. The answer is that reasoning can work fine for very small situations, but for larger situations it gets too difficult. The Shapley value, though, can always be calculated with that same step-by-step process (at least in theory!).
My Methodology
Having just convinced you of the power of the Shapley value, I must now confess that there is one small hitch with the step-by-step process: the number of orderings in some cases is just too large to actually list. We will be considering the President and all voting members of Congress, or 536 people in total. Even if we consider senators to be interchangeable -- after all, one coalition of 60 senators can end a filibuster just as well as a different coalition of 60 senators -- and representatives to also be interchangeable, we still end up with more than a googol different orderings. Suffice it to say, that large of a problem is well beyond our computing ability for the foreseeable future.
There are two alternatives to just mechanically listing every ordering. First, we could use a branch of mathematics called combinatorics to work through the problem. Mathematical gluttons for punishment are welcome to do so. The other alternative is to use simulation, or in effect "poll" the population of orderings, which is what I did in this case.
I used PHP to run through 100,000 generated orderings. I used the same random number seed for each setup, so the only thing I varied was the number of senators needed to pass legislation. Assuming that the random number generator is sufficiently random for our purposes, the margin of error in my results is approximately 0.3%. My program determines which chamber the pivotal member for each ordering is in and then determines the proportion of orderings where each chamber was pivotal.
In each case, if the President is not yet a member of the coalition then 290 representatives and 67 senators are needed to be a winning coalition and override the veto. If the President is a member of the coalition, then only 218 representatives are needed. The number of senators needed to pass legislation when the President is part of the coalition is our dependent variable in this simulation experiment.
The Balance of Legislative Power
Let us first look at the balance of power if only 51 votes (a simple majority) are needed in the Senate. In that case, the House of Representatives has 40% of the power, the Senate has 44% of the power, and the President has 16%. A quick check shows that this seems reasonable -- both chambers are roughly equal, and the President is worth about one-sixth of the votes (presidential support means that only 50%+1 votes are needed instead of two-thirds). Since we are looking at the legislative process, Congress clearly has much more power than the Executive branch. Again, this is reasonable, since Congress can pass laws without the President but not vice versa.
Keep that result in mind: 40% / 44% / 16% for the House, Senate, and President respectively. We are going to compare it to what happens when 60 votes are needed in the Senate. When the filibuster is in place, the balance of power turns out to be 19% / 72% / 9%. In other words, when the filibuster is in place, the Senate has an overwhelming share of the legislative power.
Certainly, the framers were not doing mathematical calculations when they wrote the Constitution. We can picture a range of reasonable values for the balance of power that would serve just as well. However, the filibuster causes a significant distortion of power in favor of the senate.
The Vice President
One factor I have not mentioned thus far is the Vice President. As President of the Senate, the Vice President has the ability to break any ties. As a practical matter, the Vice President will generally agree with the President,
meaning that only 50 votes are needed in the Senate to pass legislation with presidential support. I have skipped this complication because it does not substantially alter the balance of power. If only 50 votes are needed in the Senate, then the balance is 44% / 40% / 17% (does not add to 100% due to rounding) instead of 40% / 44% / 16%.
Political Considerations
Any push to abolish the filibuster is going to face numerous political challenges. First and foremost, members of the minority party are going to suspect that such a move is based on partisan considerations. The only way to deal with such an objection is for opponents of the filibuster to remain steadfast in their opposition regardless of the partisan composition at any given time.
A less obvious problem, though perhaps much more troubling, is that the Senate itself has a vested interest in continuing the filibuster. For the minority party, the benefits are obvious. The majority party, though, benefits in two ways. First, political fortunes wax and wane over time and many members of the majority party expect to eventually be in the minority. Second, even the majority party in the Senate gains power when the filibuster is in place. The filibuster does increase the power of the minority senators, but it also increases the power of the majority senators as well. In effect, the legislative process becomes focused on placating the Senate instead of on balancing the concerns of the three entities (the House, the Senate, and the President).
Critics of the filibuster have attacked it on a variety of grounds in the past. Now we have an additional argument, backed up by mathematics, to add to those criticisms: the filibuster shifts the legislative power in a fundamental and unbalanced way. For the long-term health of our form of government, it needs to be abolished as soon as possible.