The Proof is in the…Proof: Law in Numbers?
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The Proof is in the…Proof: Law in Numbers?
Now, I don’t “do” math as anyone who knows me knows. Just never been my thing. So, when this post is riddled with math theory problems, forgive me. But, let’s roll with it.
This post is sort of a re-hashing of my earlier post. There, I wondered if constitutional interpretation only makes sense in terms of what you view the purpose of the constitution is. Yesterday, I watched parts of an interesting video from the Brookings Institution. Long story short, the second panelist made a point that to think about constitutional interpretation, you need to think about the role of courts in the constitution. Great point!
So, we need to preface any thoughts of constitutional interpretation with thinking about the role of courts and constitutions.
Wait, that gives me a thought. What are courts and constitutions without LAW? That has to be part of the “equation” too. That equation is where the post gets its title. I will try some theory with numbers and symbols and everything! Here we go!
I am going to use the following premises as uncontroversial “givens”. Maybe they are, maybe they are not. Again, roll with it.
(1) Some things are good and some things are bad.
(2) People have preferences.
(3) People generally take actions because they think the outcome is “better” than the status quo.
More detail.
Premise (1) We don’t have to agree on what is good, bad, or best, but let’s agree they exist.
Premise (2) Game theory likes this and it is intuitive.
Premise (3) If I am sitting on the couch and can’t find the remote, I run a quick cost benefit analysis of the cost of getting up to the benefit of watching a different channel. If benefit is greater than cost, I do it. Legislators vote on a bill because they think that law is better than the status quo in some dimension. Granted, they may have different cost benefit analysis calculi, but they share the fact that they think it is better, or that there is utility in taking said action.
Isn’t this blog about constitutional law and game theory or something? Okay, let’s get down to it. I’ll posit this:
The three legal institutions (law, courts, and constitutions) serve at least 1 function and exist because their existence has a utility greater than the status quo or absence of them.
We’ll call those three institutions I_{1}, I_{2}, and I_{3}. Combined, their justification for existence is dependent on having total utility (Ū) greater than 0. (I use Ū because I want to distinguish it from µ, and 0 represents the status quo, or not having those institutions)
Now, each I also has a little equation to it. Let’s take I_{3}, “law”:
Law, as I defined it, must have at least one unique function, and that function must provide law with a total utility of greater than 0. But, let’s say law has many functions:
Function 1: Law’s expressive function (re:McAdams)
Function 2: Law’s crime control function
Function 3: Law’s liberty protection function
Function 4: Law’s coordinating function
Function 5: Law’s restraining function
Function 6: Law’s norm enforcement function
Etc.
and each of those has a utility (µ) to them. So,
Ū (I_{3})=∑ µ(f_{1}) + µ(f_{2}) + µ(f_{3}) + µ(f_{…})
or “The total utility of law is equal to the sum of the utility of each of the functions of law”. {My use of math symbols and even the word utility might be slightly off, but let’s try it out. We apply this logic to each of the legal institutions creating formulas for each.
{Actually this is kind of what I was getting at by saying that we should look at constitutional interpretation in context of the purpose of a constitution. I singled out the coordinating function and said that if the constitution serves to coordinate, its best method of interpretation is the one that best coordinates. But, Professor Calvert pointed out that there is definitely a restraintist function of constitutions that needs to be factored in.}
So now, I am trying to incorporate all possible functions of each institution for its overall utility calculation. This is relevant in determining optimal outcomes for an interpretation method.
Let’s take two methods of constitutional interpretation and see how their utility functions stack up. How about originalism and living constitution?
Originalism
So we look at all three institutions, law, courts, constitutions.
Let’s give a number to how well originalism serves (maximizes the utility of) each of these functions:
Law
Function 1: Law’s expressive function .3
Function 2: Law’s crime control function .2
Function 3: Law’s liberty protection function .1
Function 4: Law’s coordinating function .1
Function 5: Law’s restraining function .1
Function 6: Law’s norm enforcement function .2
These numbers are basically random. We can and should quibble about them. But not yet. The point is that originalism gets .3 units of utility (or whatever) when it comes to law’s expressive function. We now do that for the other institutions.
Courts
Function 1: Courts’ rule of law function .3
Function 2: Courts’ dispute solving function .4
Function 3: Courts’ power checking function .3
Constitutions
Function 1: Constitutions’ coordinating function .5
Function 2: Constitutions’ restraintist function .5
We now have utility measurements (albeit ones I just made up) for how originalism does for each of the three legal institutions. We could do the same for living constitution. Let’s also put it next to originalism.
Utility Calculations | Originalism | Living Constitution |
Law |
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Function 1: Law’s expressive function | .3 | .2 |
Function 2: Law’s crime control function | .2 | .1 |
Function 3: Law’s liberty protection function | .1 | .5 |
Function 4: Law’s coordinating function | .1 | .1 |
Function 5: Law’s restraining function | .1 | .05 |
Function 6: Law’s norm enforcement function | .2 | .05 |
Courts |
||
Function 1: Courts’ rule of law function | .3 | .2 |
Function 2: Courts’ dispute solving function | .4 | .6 |
Function 3: Courts’ power checking function | .3 | .2 |
Constitutions |
||
Function 1: Constitutions’ coordinating function | .5 | .6 |
Function 2: Constitutions’ restraintist function | .5 | .4 |
Now notice that all of those institution’s total utility adds up to 1 for both originalism and living constitution. I did that on purpose. They don’t necessarily have to be. They could total to 0.1 which is just slightly better than not having them. Or they could even be negative! This is where we can start to quibble.
Objection 1: Fine, I agree with how you rated each interpretation model’s maximization of each function. But not all of these functions are equal! The constitution’s coordinating function is WAY more important that it’s restraintist function! It may be true that originalism has a higher maximization of the restraintist function, but it doesn’t matter because the coordinating function has more utility to begin with! Coordinating is twice as important as restraining, so the utility functions should be 1 and 1.2!
Objection 2: Function 6 of law is actually a bad thing! Norm enforcement is just oppressing minorities! It’s a good thing that living constitution has a low norm enforcing utility function because it is actually a negative number!
Objection 3: One or all of your fundamental premises are wrong! There is no good or bad, everything is relative!
Objection 4: All law is bad! Anarchy is best!
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Let’s step back and recap. Constitutional interpretation and really all jurisprudential thought needs to consider law, courts, and constitutions. Moreover, it needs to consider the functions of each of them. Some models of constitutional interpretation are probably better at fulfilling some functions than others.
When we quibble about constitutional interpretation, I think we are fundamentally (maybe implicitly) talking about the functions of law, courts, and constitutions and how we prioritize them.
That’s the take away thought. What is going to give us the most Ū ? If the constitution were a car, I want to know what kind of interpretation method is going to get us the most miles per gallon- leaded, unleaded, diesel, originalism, living constitution, textualism. I guess the real question is what kind of car are you driving and where do you want to go?
Posted on August 5, 2011, in Uncategorized and tagged calculus, constitutionalism, interpreting, living constitution, math, originalism, utility. Bookmark the permalink. Leave a comment.
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