Duality, Liberty, and Realism in Entangled Political Economy

Abstract

The work concentrates on the implications of the idealistic and the political realism senses of protecting classical liberalism for entangled political economy through the economics framework of duality. While familiar political economy predicts the duality or equivalence of maximizing liberty and of minimizing coercion, we find that this is not the case for entangled political economy. This finding suggests that minimization of coercion is what can (and must) be genuinely solved to protect classical liberalism. This solution hinges on institutional design as opposed to allocative choice. And this solution implies that the relationship between liberty and coercion is itself entangled. Thus the failure of duality is another indication of how entangled political economy differs from more familiar political economy.

Rationalists, wearing square hats,

Thinking, in square rooms,

Looking at the floor,

Looking at the ceiling.

They confine themselves.

To right-angled triangles,

If they tried rhomboids,

Cones, waving lines, ellipses –

As, for example, the ellipses of the half-moon –

Rationalists would wear sombreros.

– Stevens (1923, webbed version)

Models are undeniably beautiful, and a man may justly be proud to be seen in their company. But they may have their hidden vices. The question is, after all, not only whether they are good to look at, but whether we can live happily with them.

– Kaplan (1964), as quoted in Aris (1994: 104)

… all models are wrong, but some are useful.

– Box and Draper (1987: 424)

The authors would like to thank Rosolino Candela, Lorenzo Infantino, Marianne Johnson, Marta Podemska-Mikluch, Richard E. Wagner, participants at the SEF economics seminar series at the University of the Witwatersrand, Johannesburg, and two anonymous referees.

In 2000 or 2001, while a graduate student at the University of Connecticut, Storrs, I (Giampaolo Garzarelli) had a conversation with a young public finance professor about Public Choice and public finance. To my surprise the young professor insisted that Public Choice had been accepted by neoclassical economics, implying with this that Public Choice was good economics being now a subset of neoclassical theory. I suggested that Public Choice could never fully be a subset of neoclassical theory, notwithstanding the fact that Public Choice also employed mathematical and statistical methods, because of the different philosophical starting points of the two research programs (teleological and a-institutional the neoclassical, processual and institutional the Public Choice). He looked at me as if I should not pose myself such ‘nonrigorous’ problems at all. Back then I did not know what I know now, which makes me realize, among other things, that my emphasis should have been more on Constitutional Political Economy than on Public Choice. We also did not have, to the best of my knowledge, entangled political economy – at least as clearly defined as now. Recently, I have come to realize that writing this chapter with Lyndal Keeton and Aldo A. Sitoe represents a subconscious attempt to differently articulate some parts of my original argument that was born from youthful exuberance.

Appendix

Consider a society of N individuals indexed by i = {1, …, N}. There is a bundle of publicly provided goods ${G}^i=\left\{{g}_1^i,\cdots, {g}_N^i\right\}\in {R}_{+}^N$ providing some standard of living ${U}^i\left({G}^i\right)\in {R}_{+}^N$. Let Uⁱ(Gⁱ) measure the level of liberty. Each individual i has an income ${Y}^i\in {R}_{+}^N$ and faces a vector of tax prices ${T}^i=\left\{{t}_1^i,\cdots, {t}_N^i\right\}\in {R}_{+}^N$ for Gⁱ. Each individual i aims to

$$ \underset{G}{\max }{U}^i\left({G}^i\right)\kern1.25em s.t.\kern1.25em {\tau}^i{G}^i={Y}^i, $$

(1)

where τⁱ is the transpose of Tⁱ, τⁱGⁱ = Yⁱ is the coercion constraint, and ${g}_j^i=\frac{Y^i}{t_j^i}-\sum \frac{t_{k\ne j}^i}{t_j^i}$ is the coercion line. The tax ${t}_j^i$ is a measure of coercion: an increase in ${t}_j^i$ increases coercion. An increase in ${t}_j^i$ decreases ${g}_j^i$, Gⁱ, and Uⁱ(Gⁱ). That is to say that an increase in coercion decreases liberty.

The solution to (1) is:

$$ {G}^i={G}^i\left({\tau}^i,{Y}^i\right). $$

(2)

In (2) we have that, for individual i, the optimal quantity of a bundle of publicly provided goods Gⁱ depends on a vector of tax prices τⁱ and income Yⁱ.

Using (1) and (2), we get i’s maximum obtainable liberty, U^i∗, as follows:

$$ {U}^{i\ast }={U}^{i\ast}\left[{G}^i\left({\tau}^i,{Y}^i\right)\right]={V}^i\left({\tau}^i,{Y}^i\right). $$

(3)

Dual to (1) is the following minimization problem:

$$ \underset{G}{\min }{\tau}^i{G}^i={Y}^i\kern1.25em s.t.\kern1.25em {U}^i\left({G}^i\right)={U}^{i\ast }. $$

(4)

The solution to (4) is:

$$ {G}^{i\#}={G}^{i\#}\left({\tau}^i,{U}^{i\ast}\right). $$

(5)

In (5) we have individual i’s optimal quantity of publicly provided goods G^i# stated in terms of the vector of tax prices τⁱ and the maximum attainable liberty U^i∗.

Using (4) and (5) we get the minimum coercion constraint that i needs to obtain U^i∗:

$$ {\tau}^i{G}^{i\#}={\tau}^i{G}^{i\#}\left({\tau}^i,{U}^{i\ast}\right)={Y}^i\left({\tau}^i,{U}^{i\ast}\right). $$

(6)

Using (3) and (5), we have duality as follows:

$$ {G}^{i\#}\left({\tau}^i,{U}^{i\ast}\right)={G}^{i\#}\left[{\tau}^i,{V}^i\left({\tau}^i,{Y}^i\right)\right]={G}^i\left({\tau}^i,{Y}^i\right)={G}^{i\ast }. $$

(7)