The Curves of Social Cost

In the comment thread of my post on Why is the Second Amendment different from all other rights, frequent commenter A.J. Sutter makes an interesting point about the relationship between liberty and government. In The Constitutionality of Social Cost, I describe the relationship between individual liberty and the power of the state as inversely related:  “Securing liberty is inversely proportional to the power of the state to order society.”

Though A.J. disagreed with the general premise of my argument, he contended that, in theory, a different curve would represent the relationship between liberty and the power of the state: “Maybe the relationship is more like an inverted parabola, where there’s an optimal level of state power that maximizes the security of my liberty.” To illustrate these points, I plotted these two curves (plus another one I’ll explain in a moment).


First, a disclaimer. I don’t purport that social constructs like liberty or state power are easily reducible to plots on a graph. I also put aside for the moment what the equations, and values of these curves are (I leave everything in general percentages). I create this plot for the sole purpose of comparing the relationships between these different views of liberty and government.

The X-Axis represents the power of the state. Assume X=0% is effectively the state of nature, true anarchy, where there is no government. X=100% is a totally repressive state where the government controls all aspects of society (think 1984, except worse). The Y-Axis represents individual liberty. Assume Y=0% reflects a state with no individual liberty (a person cannot do anything with the permission of someone else, presumably the state). Assume Y=100% reflects a anarchist utopia where a person can do anything she wishes.

Curve 1 (Blue), reflects an inverse relationship. This is the relationship I describe in the Constitutionality of Social Cost. As the power of the state increases, individual liberty decreases. Where there is no government, there is 100% liberty. Contrariwise, when the state has 100% power over the people, there is no liberty. This model assumes that liberty, as well as the power of the state, can equal 100%, rather than simply approach 100% (similar to a limit approaching, but not reaching a number). Similarly, this model assumes that liberty, as well as the power of the state can equal 0%.

Curve 2 (Red), depicts the inverted parabola (I think) A.J. described. When the power of the state is equal to zero, there is no individual liberty. Likewise, when the power of the state is equal to 100%, there is no individual liberty. This model assumes that liberty can never be greater than some optimal level less than 100% (say 50% for simplicity’s sake), and that quantity of liberty can only be secured with a certain amount of government power less than 100% (again, say 50% for simplicity’s sake). This model assumes that the power of the state can be equal to 0% or 100%. The optimal balance of liberty and the power of the state occurs at L2.

Curve 3 (Green), depicts a hyperbola. A hyperbola is distinct from a parabola (and a line), in that the curve never touches the axes (it is asymptotic to the X and Y axes). On this curve, both individual liberty and the power of the state can never equal 0% or 100%. Beyond this fact, the hyperbole is similar to the inverse relationship–when government approaches 0%, liberty approaches 100%; when government approaches 100%, liberty approaches 0%. This model will never permit liberty=100 or government=100.

These three curves represent, very generally speaking, three different philosophies of liberty and government (I apologize for my gross oversimplifications. I make them solely to illustrate this point. I do not think they are particularly accurate as applied to individuals).

Curve 1, broadly stated, is the idealistic libertarian position. The less government that is imposed, the more individual liberty you have. This view fetishizes a world without government as a Utopia that will maximize individual liberty (think Galt’s Gulch). Likewise, this view fears a world where increasing statism diminishes individual liberty, up to a point where that liberty is equal to zero.

Curve 2, broadly stated, is the progressive, position. This view fears a world with no individual liberty, but sees two possible routes to that dystopia. First, in agreement with both mainstream and idealistic libertarians (see intersection L3), in a world with 100% government, there would be no individual freedom. Think of any dystopian novel you have ever read (1984, Brave New World, etc.) and that is a world that both progressives and libertarians fear. Second–and here the libertarians and progressives depart–in a world without any government, there can be no individual liberty. This view requires that some government exist to secure rights.

A.J. provides a very good example to illustrate Curve 2. Assume the liberty interest is the right to have sex with whomever one chooses. AJ writes, this example “may seem like the epitome of an individual liberty, but have I really ‘secured’ this if I’m in danger of being lynched by a mob that disapproves of my choice of partner? (to choose another historical example).”

Or, to borrow a passage from my article, Omniveillance, which considers the relationship between the right to privacy (protected by the state) and the right of free speech (individual liberty), there has to be a “dynamic equilibrium between free speech and privacy that can promote the optimal level of expression.”

Privacy and free speech can be thought of as two sides of the same coin. They are complementary, rather than competing, interests.81 When properly balanced, they yield optimal results. To further explore this, it is necessary to visualize two extremes. In a world with no privacy protections and unrestricted free speech rights, where everything can be known about everyone, free expression would suffer. A person would not want to express his true thoughts for fear of embarrassment, ridicule, humiliation, or retribution.82 This fear would result in the ultimate chilling of speech.

However, in an alternate universe with absolute privacy rights and no free speech, there would be a similar outcome. A person would not be able to express his true thoughts, and would have to keep all of his emotions to himself. This restraint would also result in the ultimate chilling of speech. Therefore, rather than existing as competing interests, privacy and free speech complement one another when properly balanced to provide a symmetry to optimize people’s desire to express themselves, and at the same time, minimizes any apprehension that such an expression may cause. Without privacy, people do not comfortably speak candidly.83 Without free speech, people cannot speak candidly. For this reason, society should strive to achieve a dynamic equilibrium between free speech and privacy that can promote the optimal level of expression.

On Curve 2, where the power of the state is equal to zero, individual liberty (sexual autonomy) would also equal zero. What good is this right if the state fails to provide adequate protection to enforce it. In Lockean terms, when people leave the state of nature, they delegate their executive power to the state in order to allow for the protection of certain rights (life, liberty, and property).  In other words, you need some amount of government to achieve some amount of liberty.

Curve 3, broadly stated, is the mainstream libertarian position. Frequently, idealistic libertarians are attacked for desiring that that liberty should equal 100% (anyone can own a nuclear warhead without any regulation!), or government should equal 0% (Sic utero tuo ut alienum non laedas) .

Government can never be equal to 100%. I referenced dystopian novels as examples of 100% governmental power because in reality, such power is impossible. Pick North Korea, East Germany, the Soviet Union, or any totalitarian state. Even with absolute freedom, people still have at least (a greatly limited) freedom of thought. Likewise, government can never equal 0%. Even in the most free societies, certain norms and structures emerge.

What Curve 3 captures is that there will always be some government, and always some liberty. As more government is added, the rate at which liberty exists decreases. Thus, the optimal amount of liberty on this curve is achieved through less government.  But, you need *some* government to protect this liberty. This view, presupposes, that government is not viewed as a good unto itself, but merely a utilitarian means in order to obtain liberty. To put it in Jeffersonian terms, “That to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed.”

(I have some difficulty plotting social conservatives on this plot. In many respects, they view social ordering of individual liberty as a good unto itself, which really blends the X and Y axes. I’ll consider this a bit more later.)

Now, let’s consider the intersecting points.

Curve 1 and Curve 2 intersect at L2. This represents the point, where most libertarians and progressives will agree.. Almost like a Goldilocks point–not too statist, not too anarchist, just the right amount of liberty.

Curve 1 and Curve 3 intersect at L1. Here, both groups find that liberty can be maximized where government is minimal (though liberty never equals 100%, and government never equals 0%).

Curves 1, Curve 2, and Curve 3 all intersect at L3. All groups agree that when government is approaching 100%, individual liberty is effectively 0%.

So, broadly stated, idealistic libertarians want to achieve L1. Progressives want to achieve L2. Mainstream libertarians want to achieve some point along Curve 3. All groups want to avoid L3.

I welcome comments on this plot. As you can tell by this lengthy post, which I spent some time thinking about (and if you ask A.J., I’m sure he’ll probably say I totally missed his point), I heavily rely on blog posts to learn from others, preferably those I disagree with. Through this process, I recognize the shortcomings of Curve 1, which I adopted in my article. I hope to elaborate on this plot in the future works.

My deepest thanks to Militza Machuca Franco and Corey Carpenter for helping me visualize parabolas, hyperbolas, and lines, items which I tried to repress in my memory as soon as I graduated from high school.

Cross-Posted at

You may also like...

7 Responses

  1. Brett Bellmore says:

    As a libertarian, I think curve 2 is closest to reality, but only because it’s impossible to push government power below a certain level. Governments occupy an ecological niche, call it “the gets away with open violence” niche. One of their functions is to keep other institutions, foreign governments, and local proto-governments like the Mafia, from taking that niche away from them.

    So, lower the power of government too far, and while the power of THAT government might be reduced, competition arises, and the sum total of government in a society rebounds. I’m frequently told that, if I don’t like government, I should move to Somalia. But Somalia isn’t at the left side of the curve, it’s near the right, because while any one government in Somalia might not have comprehensive power, might be somewhere near the left end of curve 1, there are a LOT of ‘governments’ in Somalia, and they add up…

    The real issue, as with the Laffer curve, is where we presently are on the curve. Liberals are convinced that, with more powerful government in this country than we’ve ever before experienced, we’re somewhere well down the curve on the left side, and need more government in order to get more liberty. Libertarians that we’re on the right end, and getting steeper fast.

    Partly this conflicting perception is because we define ‘liberty’ differently. Defining “liberty” as including a right to get stuff paid for by other people, and NOT including a right to retain your own stuff if the government wants it, you’re automatically shifted to the right. It’s as though your scale started halfway across the page.

    Oh, and I’d disagree that “All groups want to avoid L3.” You’re leaving out the most important group of all: The people actually running the government. Government power IS their liberty, and they are most assuredly working towards L3, even if they’d deny it.

  2. Shag from Brookline says:

    Brett provides comic relief with his identity of the “real issue, as with the Laffer curve …. ” I view this as a triangulation with a few arcs of a Second Amendment shootout. Just imagine customers lawfully carrying, openly, at a bar discussing “The Constitutionality of Social Cost” and the question arises as to who’s turn it is to buy the next round.

  3. Bruce Boyden says:

    Curve 2 does not strike me as “the progressive position.” (I assume by “progressive” you mean “liberal.”) It’s simply a recognition that there is not much individual liberty in The Lord of the Flies.

  4. A.J. Sutter says:

    Thanks very much for engaging seriously with my comment.

    So I won’t contradict you a second time — I would indeed say you missed my point. (NB: in the spirit of Jeremy Irons’s character in Reversal of Fortune: just kidding.)

    Just a couple of points:

    (1) The choice of a parabola was illustrative. It could have been some other sort of curve with a maximum — e.g. an inverted catenary, 2π’s worth of a cycloid, or more likely something asymmetrical, such as a distribution exhibiting positive or negative skewness.

    (2) If you want to talk about points of intersection, though, the parameters of the curves involved do become quite crucial. E.g., you’ve not only drawn Curve 2 as symmetrical, but you have its maximum at (.5, .5); meantime, Curve 1 has a slope of -1. If Curve 2’s maximum were at a lower level of liberty, or if the curve were asymmetrical, or if Curve 1 had a different slope or intercepts, you’d get very different heuristic results.

    (3) To get back to what was my point: as anticipated, you’re using these figures metaphorically. That’s fine, but it should be clear from (1) and (2), as well as from the various qualifications you rightly include in your post, how many assumptions there are built into doing so, and how shaky are the deductions one can make from the picture. I also agree that it would be difficult — and rather silly — to try to come up with specific equations. So despite the outward appearance of mathematical precision, the actual arguments remain more poetic, albeit in a nerdy sort of way. The question remains what benefit the introduction of this pseudo-precision brings to the discussion. Even your conclusions near the end of the post (where you discuss the intersections) probably could have been reached, in substance, without the mathematical analogies.

    I don’t mean to make a big deal about using diagrams like this in a blog post, where they’re framed as speculative, metaphorical and imprecise. BTW, personally I share a tendency to think all too often in terms of metaphors from math or natural science. But I recognize that such metaphors are rarely illuminating to others, and even more rarely are the appropriate medium of discourse for public debate. Borrowing the authority of quantitative vocabulary and disciplines (costs and other technical concepts from economics, e.g.) by importing that vocabulary into a court’s Constitutional analysis makes me far more uneasy — be several orders of magnitude, let’s say .

  5. BL1Y says:

    Curve 2 represents the libertarian point of view. You’d be hard pressed to find a libertarian who does not think we need certain government institutions, such as a defensive military, a criminal justice system, traffic regulations, some food and health regulations, public primary education, etc.

    Curve 1 actually represents the anarchist point of view.

  6. I originally put this comment up at, but I’ll add it here too:

    I mostly agree with what you’ve written, and it gets at what I think is one of the serious problems with mainstream libertarian thought: there’s an unnatural conflation of “liberty” and “lack of government involvement.” I tend to agree with curve 2 (and so do most people, at least implicitly): there is some amount of government that is necessary in order to optimize liberty.

    There are two criticisms I’d make:

    1. Most liberals/progressives wouldn’t aim for L2 because they (generally) don’t engage in the kind of value-exclusivity that libertarians do. That is, liberty isn’t the only relevant standard. It might be worth it to sacrifice some liberty in the name of social justice, for instance.

    2. This passage is incorrect: “What Curve 3 captures is that there will always be some government, and always some liberty. As more government is added, the rate at which liberty exists decreases. Thus, the optimal amount of liberty on this curve is achieved through less government. But, you need *some* government to protect this liberty. This view, presupposes, that government is not viewed as a good unto itself, but merely a utilitarian means in order to obtain liberty.”

    That’s actually not captured by curve 3. It doesn’t tell you that some government is necessary to protect liberty (since on that curve less government always equals more liberty) it just tells you that for some unrelated reason, it’s impossible to completely get rid of government. Someone looking only to maximize liberty who buys into curve 3 wouldn’t say “this level of government is good” they would say “government will always exist, but we should do everything we can to weaken it as much as possible.”

    That said, I’ve never met anyone who bought into either curve 1 or curve 3 *and* thought that liberty is the only thing of value that should be optimized. Basically everyone operates on curve 2, and just disagrees about how far along the line the peak is, or thinks that maximizing liberty isn’t the only relevant factor for determining the amount of government.

  7. Bill Potts says:

    Being of a mechanistical frame of mind, I enjoyed reading your post. I think a graphical representation, for those who can interpret it, is a very good way to visualise a complex situation.

    However, it needs a clear understanding of what the axes represent.
    Individual liberty – we may all be free to buy a Lear jet but do not have the means to do so. Even if we all maximised our opportunities we cannot all earn or inherit sufficient wealth. There’s simply not enough of it.

    So is this axis “average” Individual liberty? Do we need a third axis of economic means?

    How do we measure power of the state? What values would you assign to Nazi Germany, Stalinist USSR or Idi Amin’s Uganda?

    Secondly, a pedantic point, curve 1 is not an inverse relationship, curve 3 is.
    If A is proportional to B, then A = kB, where k is the constant of proportionality.
    If A is inversely proportional to B, then A is proportional to 1/B, i.e. A = k/B, where k is the constant of proportionality. Plotted on a graph this is a hyperbola (curve 3).

    As A.J. Sutter says for curve 2 “It could have been some other sort of curve with a maximum” so curves 1 & 3 fall into a general class of decay curves, those decreasing from an initial positive value.

    Exponential decay is equally valid. Further the curves are bounded within a space of 100% liberty & 100% state power. So an inverse relationship cannot be true as the curve ‘breaks out’ of this space when state power is very weak.

    Thirdly, have you considered Catastrophe Theory. One can envisage a reversed ‘S’ curve rather like a smoothed figure ‘2’. Here as the power of the state increased there would be a gradual reduction in liberty until the point of inflection was reached when unable to follow the curve back on itself there would be a catastrophic collapse of liberty down to the tail of the figure ‘2’.
    Subsequent relaxation of state power would see only slight increases in liberty until the state became weak enough to allow a similar abrupt transition to a highly liberated situation.

    If we allow a third dimension, as I mentioned above, this gives a sheet, the undulations of which boggle the mind.

    This is a long winded way of agreeing with A.J. Sutter when he says “it would be difficult — and rather silly — to try to come up with specific equations.”

    Until these concepts can be measured and hence become variables, it is pointless trying to fit them to a curve. One could present convincing arguments for almost any curve. After all, social science is not physics.