Saturday, December 31, 2016

Welcome

I study economics as a hobby. My interests lie in Post Keynesianism, (Old) Institutionalism, and related paradigms. These seem to me to be approaches for understanding actually existing economies.

The emphasis on this blog, however, is mainly critical of neoclassical and mainstream economics. I have been alternating numerical counter-examples with less mathematical posts. In any case, I have been documenting demonstrations of errors in mainstream economics. My chief inspiration here is the Cambridge-Italian economist Piero Sraffa.

In general, this blog is abstract, and I think I steer clear of commenting on practical politics of the day.

I've also started posting recipes for my own purposes. When I just follow a recipe in a cookbook, I'll only post a reminder that I like the recipe.

Comments Policy: I'm quite lax on enforcing any comments policy. I prefer those who post as anonymous (that is, without logging in) to sign their posts at least with a pseudonym. This will make conversations easier to conduct.

Friday, December 09, 2016

Basic Commodities and Multiple Interest Rate Analysis

I have a new working paper on the Social Science Research Network:
Abstract: This paper considers the application of multiple interest rate analysis to a model of the production of commodities by means of commodities. A polynomial, for the characteristic equation of the augmented input-output matrix, is used in defining the rate of profits in such a model. Only one root is found to be economically meaningful. No non-trivial application of multiple interest rate analysis is found in the analysis of the choice of technique. On the other hand, multiple interest rate analysis can be used in defining Net Present Value in an approximate model, in which techniques are represented as finite series of dated labor inputs. The product of the quantity of the first labor input and the composite interest rate approaches, in the limit, the difference between the labor commanded by and the labor embodied in final output in the full model.

I am proud of some observations in this paper. Nevertheless, I think it tries to go in too many directions at once. It is also longer than I like. It may seem, at first glance, to be longer than it is. I have ten graphs scattered throughout.

Michael Osborne cannot deny that I have taken his research seriously. He needs somebody with more academic credibility than me to write on his topic, though.

This is one paper where I would mind being shown to be wrong. I did not find any use for more than one eigenvalue of what I am calling the augmented input-output matrix. If somebody can find something useful, along the line of multiple interest rate analysis, to say about all eigenvalues, I would be interested to hear of it.

Tuesday, December 06, 2016

Bifurcations In Multiple Interest Rate Analysis

Figure 1: Three Trinomials
1.0 Introduction

Typically, in calculating the Internal Rate of Return (IRR), a polynomial function arises. The IRR is the smallest, non-negative rate of profits, as calculated from a root of this function. The other roots are almost always ignored as having no economic meaning.

Michael Osborne, as I understand it, is pursuing a research project of investigating the use of all the roots of such polynomial functions that arise in financial analysis. A polynomial of degree n has n roots in the complex plane. I have noticed that the roots, other than the IRR, for examples that might arise in practice, can vary in whether they are real, repeating, or complex.

Bifurcation analysis, as developed for the study of dynamic systems might therefore have an application in multiple interest rate analysis. (This post is not about a dynamic system. I do not know how many of these results are about the theory of equations, independently of dynamical systems.) On the other hand, Osborne typically presents his analyses in terms of complex numbers. So I am not sure that he need care about these details.

2.0 An Example

Table 1 specifies the technology to be analyzed in this post. This technology produces an output of corn at the end of one specified year. The production of corn requires inputs of flows of labor in each of the three preceding years (and no other inputs). The labor inputs, per unit corn output, are listed in the table.

Table 1: The Technology
Year
Before
Output
Labor Hired
for Each Technique
1L1 = 0.18 Person-Years
2L2 = 4.468 Person-Years
3L3 = 0.527438298 Person-Years

Let a unit of corn be the numeraire. Suppose firms face a wage of w and a rate of profits, r, to be used for time discounting. Wages are assumed to be advanced. That is, workers are paid at the start of the year for each year in which they supply flows of labor. Accumulate all costs to the end of the year in which the harvest occurs. Then the Net Present Value for this technology is:

NPV(r) = 1 - w[L1(1 + r) + L2(1 + r)2 + L3(1 + r)3]

The NPV is a third-degree polynomial. The wage can be considered a parameter. Figure 1, above, graphs this polynomial for three specific values of this parameters. In decreasing order, wages are 11/250, 11/500, and 2/250 bushels per person-years for these graphs.

Given the wage, the IRR is the intersection of the appropriate polynomial with the positive real axis in Figure 1. These IRRs are approximately 101.1%, 175.5%, and 329.5%, respectively. Suppose the economy were competitive, in the sense that capitalists can freely invest and disinvest in any industry. No barriers to entry exist. Then, if this technology is actually in use in producing corn and the wage were the independent variable, the rate of profits would tend to the IRR found for the wage. Profits and losses other than those earned at this rate of profits would be competed away.

The above graph suggests that, perhaps, the NPV for all wages intersects in two points, one of which is a local maximum. I do not know if this is so. Nor have I thought about why this might be. I guess it is fairly obvious that the local maximum is always at the same rate of profits. The wage drops out of the equation formed by setting the derivative of the NPV, with respect to the rate of profits, to zero.

I want to focus on the number of crossings of the real axis in the above graph. Figure 2 shows all roots of the polynomial equation defining the NPV. For a maximum wage, the IRR is zero, and it is greater to the right, along the real axis, for a smaller wage. The corresponding real roots, for the maximum wage, are the greatest and least negative rate of profits along the two loci shown in the left half of Figure 2. For smaller wages, these two real roots lie closer together, until around the middle wage used in constructing Figure 1, only one negative, repeated root exists. For any lower wage, the two roots that are not the IRR are complex conjugates. When the wage approaches zero, the workers live on air and all three roots go to (positive or negative) infinity.

Figure 2: Multiple Rates of Profit for The Technique

This post has presented an example for thinking about multiple interest rate analysis. It is mainly a matter of raising questions. I do not know how the mathematics for investigating these questions impacts practical applications of multiple interest rate analysis.

Thursday, November 17, 2016

The Choice Of Technique With Multiple And Complex Interest Rates

I have expanded this post into a working paper. The abstract is:

Abstract: This paper clarifies the relationships between Internal Rates of Return, Net Present Value, and the analysis of the choice of technique in models of production analyzed during the Cambridge capital controversy. Multiple and possibly complex roots of polynomial equations defining the IRR are considered. An algorithm, using these multiple roots to calculate the NPV, justifies the traditional analysis of a reswitching example.

Michael Osborne, I hope, should find the working paper more constructive than my post.

(I do not know why, when I delete comments or mark them as spam, they still remain in the upper right.)

Saturday, November 05, 2016

Teaching Calculus To Kids These Days?

1.0 Introduction

A couple of years ago I saw somebody in my local library who was obviously tutoring students in mathematics. I cannot recall how or why, but I started a question. He assured me that advanced high school seniors were taught calculus here. But the approach they teach nowadays does not require kids to learn epsilon-delta definitions of limits and continuity. This surprised me. I understand limits are difficult to wrap one's mind around. For one thing, one needs to not think in terms of dynamics, in some sense. And epsilonic definitions are rarely seen as natural to the beginning student.

I have since had similar conversations with a few youngsters. And they did not recall epsilon-delta definitions either. I realize that teaching and student recollection varies. Furthermore, the use of epsilon to represent a small distance in the space of the range of the function is a notational convention. Perhaps, some other symbol was used in their classes (although I doubt it). Furthermore, to engineers and practical-oriented students, they might be more interested in getting to problems with derivatives and integrals. (When I asked C. how his calculus class was, he said, "We're still on limits", which I thought expressed an impatience.)

I wonder about this. I have a theory how some might have justified a change to teaching in calculus since my day, although I can imagine other justifications that do not contradict my ideas below. Anyways, I only intend to raise questions in this post.

2.0 A Potted History of Calculus after Newton

When Newton and Liebniz invented the differential calculus, they had a problem with certain quotients. The slope of secants, drawn for two points on a "smooth" function, might be a well-defined ratio. But what does it mean to take a limit? Sometimes Newton seems to treat a denominator as simultaneously zero and non-zero. And this problem with infinitesimals (or fluxions) is compounded when one starts thinking about second derivatives and even higher orders.

Berkeley quickly pointed out these difficulties. I gather he was concerned to argue against the deism - to him, atheism - that often seemed to accompany Newtonian physics and cosmology. Why criticize the mote in your neighbor's eye without first casting out the beam in your own? Anyways, mathematicians recognized Berkeley had a point about calculus. But the mathematics worked in practice and seemed to be extraordinary useful for physics.

So mathematicians struggled for centuries, building an immense structure on what they recognized to be an unsound foundation. They also tried to rebuild the foundations. Cauchy, for example, made some improvements. As far as real numbers and limits are concerned, the decisive work came in the second half of the nineteenth century, with Weierstrass' epsilon-delta definitions and Dedekind's construction of the reals out of sets of rational numbers, known as cuts. Whether this was the answer, or whether this just moved the problems deeper down to questions about sets and logic, was not immediately clear. The work of Cantor, Frege, and Russell are of some importance here. The twentieth century saw intensive exploration of such foundational questions. Anyways, nobody seems to have ever found a contradiction in Zermelo-Fraenkel set theory, even if the absence of such contradictions cannot be proven. ZF set theory, with the axiom of choice in many applications, seems to provide a sufficient foundation for the working mathematician.

I guess that that is how the picture stood around, say, 1960. Newton's own approach to calculus was non-rigorous, but epsilon-delta definitions provide all the rigor introductory students of calculus need. Also, Alfred Tarski had invented something called model theory. Along came Abraham Robinson, who used model theory to develop non-standard analysis. Somehow, nonstandard analysis provides a rigorous justification of infinitesimals. (I wouldn't mind understanding the Löwenheim-Skolem theorem either.)

So maybe it does make sense to teach calculus, without the rigor of epsilon-delta definitions. Keisler wrote a textbook to illustrate the teaching of calculus on the foundations of infinitesimals, maybe easier for the student to understand and justified by the rigor of the advanced abstractions of non-standard analysis. Has this approach, revolutionizing centuries of understanding, won out in introductory calculus classes?

3.0 Other Special Cases in Introductory Teaching

I can think of a couple of other cases where what was in my textbooks in calculus and analysis was superseded, in some sense, in more advanced mathematics. I gather mathematical analysis is often informally defined as what the differential and integral calculus would be if taught rigorously. And Rudin (1976) is a standard introduction to analysis.

Rudin provides an epsilon-delta definition of limits. This definition is more general than you might see in (old?) calculus courses. In such less abstract courses, you might see two definition of limits. One would be for sequences, that is, for functions mapping the natural numbers into the reals. And another would be for functions mapping the real numbers into the real numbers. But Rudin's definition is for functions mapping an arbitrary metric space into (possibly another) arbitrary metric space. One might get the impression that some notion of distance between points is needed to define a limit. But, as was pointed out in the class I took with Rudin as the textbook, a limit of a function is a topological notion.

A common intuition for integration is as of the area under a curve. This notion can be formalized with the Riemann integral, and, for me, this is the first definition I learned. But another definition, Lebesque integration, is taught in classes on measure theory. Lebesque integrals are more general. Some functions have a Lebesque integral, but not a Riemann integral. But, if a function has a Riemann integral, it has the same value for the Lebesque integral.

I offer a suggestion in the spirit of a devil's advocate. Why teach the special case at all in these instances? Why not start with the more general case? Do those who concern themselves with the pedagogy of mathematics selectively advocate the teaching of the more abstract, general case? Is so, how do they choose when this is appropriate?

4.0 Conclusion

Is it now quite common - maybe, in the United States - to teach introductory calculus without providing an epsilon-delta definition of a limit? If so, does common justification of this practice draw on a non-standard analysis approach to calculus? Why should this extremely abstract idea influence introductory teaching, but not other abstractions?

Appendix: Two Definitions of a Limit of a Function and a Theorem

These are from memory, since I do not want to bother looking them up. The proof of the theorem, probably stated more rigorously, was a test question in a course I took decades ago.

Definition (Metric Space): Let f be a function mapping a metric space X into a metric space Y. L is a limit of f as x approaches x0 if and only if, for all ε > 0, there exists a δ > 0 such that, whenever the distance between x and x0 is less than δ, the distance between f(x) and L is less than ε.
Definition (Topological): Let f be a function mapping a topological space X into a topological space Y. L is a limit of f as x approaches x0 if and only if for all open sets B in Y containing L, the preimage of B, f-1(B), contains x0.
Theorem: Let f map a metric space X into a metric space Y. Then L is a limit of f as x approaches x0, in the metric space definition, if and only if L is also the limit of f, in the topological space definition, in the topologies for X and Y induced by the respective metrics for these spaces.
References
  • George Berkeley. (1734). The Analyst: A Discourse Address to an Infidel Mathematician... [I never finished this.]
  • H. Jerome Keisler (1976). Foundations of Infinitesimal Calculus, Prindle, Weber & Schmidt. [I barely started this.]
  • Morris Kline (1980). Mathematics: The Loss of Certainty, Oxford University Press.
  • Walter Rudin (1976). Principles of Mathematical Analysis, 3rd edition, McGraw-Hill.

Saturday, October 22, 2016

Multiple And Complex Internal Rates Of Return

Figure 1: One Real and Two Complex Rates of Profit for Alpha Technique
1.0 Introduction

My intent, in this post, is to refute a few lines in Osborne and Davidson (2016). I want to do this in the spirit of this article, while not denying any valid mathematics. Osborne and Davidson have this to say about the numeric example in Samuelson (1968)1:

In other words, when [the Internal Rate of Return] shifts, affecting the capital cost, the product of the unorthodox rates (the duration of the adjusted labor inputs) also shifts such that the overall interest-rate-cost-relationship is linear. This linearity implies that, in the context of this model at least, switching between techniques can happen but reswitching cannot because two straight lines cross only once. Moreover, the relationship between capital cost and the composite interest rate is positive, implying that the neoclassical 'simple tale' that lower rates promote more roundabout technology, is valid when the interest rate is broadly defined.

Samuelson's example is well-established, and it is incorrect to draw the above conclusion from the Osborne and Davidson model. They derive an equation which, when no pure economic profits exist, relates the price of a consumer good to its cost when a certain composite rate of profits is applied to dated labor inputs. This equation is a tautology; the capital cost on the Right-Hand Side of this equation cannot take on different values without the price on the Left-Hand Side simultaneously varying. Thus, however intriguing this equation may be, it cannot support Osborne and Davidson's supposed refutation of reswitching.

2.0 A Model

Consider a flow-input, point-output model of production of, for example, corn. For a given technique of production, let Li, i = 1, ..., n; be the input of labor, measured in person-years, hired i years before the output is produced, for every bushel corn produced. Suppose, for now, that a bushel corn is the numeraire2. Let the wage, w, be given (in units of bushels per person-year), and suppose wages are advanced. Define:

R = 1 + r,

where r is the rate of profits. The cost per bushel produced is:

w L1 R + w L2 R2 + ... + w Ln Rn

Define g(R) as the additive inverse of economic profits per bushel produced:

g(R) = w L1 R + w L2 R2 + ... + w Ln Rn - 1

Divide through by w Ln to obtain a nth degree polynomial, f(r), with a leading coefficient of unity:

f(R) = Rn + (Ln - 1/Ln) Rn - 1 + ... + (L1/Ln) R - 1/(w Ln)

The Internal Rate of Return (IRR), when this technique is adopted for producing corn, is a zero of this polynomial.

3.0 A Composite Rate of Profits

A nth degree polynomial has, in general, n zeros. These zeros need not be positive, non-repeating, or even real. For a polynomial with real coefficients, as above, some of the zeros can be complex conjugate pairs. The IRR is the rate of profits, r1, corresponding to the smallest real zero, R1, exceeding or equal to unity.

r1 = R1 - 1 ≥ 0

The IRR is well-defined only if the wage does not exceed the maximum wage, where the maximum wage is the reciprocal of the sum of dated labor inputs for a bushel corn:

wmax = 1/(L1 + L2 + ... + Ln)

Let r2, r3, ..., rn be the other n - 1 zeros of the above polynomial. As I understand it, these zeros, especially any complex ones, are ignored in financial analysis. Notice that these rates of profits are calculated, given the quantities of dated labor inputs and the wage. One cannot consider different rates of profits without varying the wage or vice versa.

For any complex number z, one can calculate a corresponding real number, namely, the magnitude (or absolute value):

|z| = |zreal + j zimag| = [(zreal)2 + (zimag)2]1/2

where j is the square root of negative one. (I have been hanging around electrical engineers, who use this notation all the time.) Consider the magnitude of the product of all rates of profits associated with the zeros of the polynomial f(R):

| r1 r2 ... rn| = r1 |r2| ... |rn|

One can think of this magnitude as a certain composite rate of profits. Michael Osborne's research project, as I understand it, is to explore the meaning and use of this composite rate of profits in a wide variety of models.

4.0 A Derivation

One can express any polynomial in terms of its zeros. For f(R), one obtains:

f(R) = (R - R1)(R - R2)...(R - Rn)

Or:

f(R) = (r - r1)(r - r2)...(r - rn)

Two equivalent expressions of the polynomial of interest can be equated:

Rn + (Ln - 1/Ln) Rn - 1 + ... + (L1/Ln) R - 1/(w Ln)
= (r - r1)(r - r2)...(r - rn)

The above equation holds for any rate of profits. In particular, it holds for a rate of profits equal to zero. Thus, one obtains the following identity:

1 + (Ln - 1/Ln) + ... + (L1/Ln) - 1/(w Ln) = (-r1)(-r2)...(-rn)

Some algebraic manipulation yields:

(1/w) = (L1 + L2 + ... + Ln) - Ln(-r1)(-r2)...(-rn)

Take the magnitude of both sides. One gets:

(1/w) = (L1 + L2 + ... + Ln) + Lnr1 |r2| ... |rn|

The above equation, albeit interesting, is a tautology, expressing the absence of pure economic profits. For a given technique (that is, set of dated labor inputs), one cannot consider independent levels of the two sides of the equation. Osborne and Davidson's mistake is to fail to notice that the tautological nature of the above equation invalidates their use of this equation to say something about the (re)switching of techniques.

The Left Hand Side of the above equation is the cost price of a unit output, in terms of person-years. The Right Hand Side is the sum of two terms. The first is the labor embodied in the production of a commodity. The second term is the first labor input, from the most distant time in the past, costed up at the composite rate of profits. Somehow or other, that composite rate of profits, as Osborne and Davidson note, expresses something about the number of time periods over which that first input of labor is accumulated and the distribution of dated labor inputs over those time periods. The number of time periods is expressed in the number of rates of profit that go into forming the composite rate of profits. I find how the distribution of labor inputs affects the composite rate of profits more obscure3. I also wonder how the composite rate of profits appears for a technique in which a first labor input cannot be found.

5.0 Numerical Example

An example might help clarify. Suppose labor inputs, per bushel corn produced, are as in Table 1.

Table 1: The Technology
Year
Before
Output
Labor Hired for Each Technique
AlphaBeta
133 Person-Years0 Person-Years
20 Person-Years52 Person-Years
320 Person-Years0 Person-Years

5.1 Alpha Technique

The number of time periods, n, for the alpha technique, is three. The polynomial whose zeros are sought is:

fα(R) = R3 + (33/20)R - 1/(20 w)

The maximum wage is (1/53) bushels per person-years. The above polynomial, not having a term for R2, is a particularly simple form of a cubic equation. Nevertheless, I choose not to write explicit algebraic expressions for its zeros. Instead, consider the complex plane, as graphed in Figure 1, above. The traditional rate of profits is on the half of the real axis extending to the right from zero. The other two zeros are on the rays shown extending to the northwest and southwest. When the wage is at its maximum, the traditional rate of profits is zero and the complex rates of profits are at the rightmost points on those rays, as close as they ever come to zero. For wages below the maximum and above zero, the rates of profits are correspondingly further away from the origin. Figure 2, on the other hand, graphs the traditional and composite rates of profits, as functions of the wage.

Figure 2: Rate of Profits and Composite Rate of Profits for Alpha Technique

5.2 Beta Technique

For the beta technique, the number of time periods, n, is two. The polynomial whose zeros are sought is:

fβ(R) = R2 - 1/(52 w)

For wages not exceeding 1/52 bushels per person-year, the traditional rate of profits is:

r1, β = 1/(52 w)1/2 - 1

The other rate of profits is:

r2, β = -1/(52 w)1/2 - 1

The composite rate of profits is:

r1, β | r2, β | = [1/(52 w)] - 1

The dependence of the composite rate of profits on the wage is clearly visible in the beta technique.

5.3 Cost Minimization

Figure 3 graphs the traditional and composite rate of profits, as a function of the wage. In the traditional analysis, the cost-minimizing technique is found by choosing the technique on the outer envelope for the two curves to the left in the figure. Although I do not what meaning to assign to it, one could also form the outer envelope for the two curves on the right, that is, the composite rate of profits. If the (composite) rate of profits is zero, the technique on the outer envelope is the one that intersects the wage axis furthest to the right. This is the technique with the smallest total of dated labor inputs, that is, the beta technique. The outer envelope for both the traditional and composite rate of profits yield the same conclusion.

Figure 3: Wage-Rate of Profits Curves

If one based the choice of technique on the composite rate of profits, one would find the alpha technique preferable for all composite rate of profits above a small rate. This would be a switching example, not a reswitching example. There would only be one switch point, as shown on the diagram. And, by the traditional analysis, it is indeed a reswitching example, with switch points at r1 equal to 10% and 50%. I still see no reason to believe otherwise or to accept a non-equivalent model.

6.0 Conclusion

Although I reject Osborne and Davidson's conclusion about reswitching, I find the concept of the composite rate of profits intriguing. I suspect Osborne is more interested in impacting corporate finance, with the Cambridge Capital Controversy being a by-the-way kind of application. I do not see how the composite rate of profit helps with the analysis of the choice of technique. Osborne (2010) uses the composite rate of profits to clarify the relationship between the Internal Rate of Return and Net Present Value. I like that in my previous exposition of the above example, I applied an algorithm in which both IRRs and NPVs are relevant. I have not yet absorbed Osborne's NPV analysis.

Footnotes
  1. I have an example with reswitching at more reasonable rates of profits.
  2. Osborne and Davidson take a person-year of labor as the numeraire. I do not see anything in this model can depend on which commodity is the numeraire.
  3. Osborne and Davidson state that the composite rate of profits describes the weighted-average timing of labor inputs. Unlike this average, the Austrian average period of production was originally meant to be defined without references to prices.
Bibliography
  • Micheal Osborne (2010). A resolution to the NPV-IRR debate? Quarterly Review of Economics and Finance, V. 50, Iss. 2 (May): pp. 234-239 (working paper).
  • Michael Osborne (2014). Multiple Interest Rate Analysis: Theory and Applications, Palgrave Macmillan [I HAVE NOT READ THIS].
  • Michael Osborne and Ian Davidson (2016). The Cambridge capital controversies: contributions from the complex plane, Review of Political Economy, V. 28, No. 2: pp. 251-269.
  • Paul Samuelson (1968). A summing up, Quarterly Journal of Economics, V. 80, No. 4: pp. 568-583.

Saturday, October 08, 2016

Why Republicans in the USA are "The stupid party"

1.0 Introduction

In 1865, John Stuart Mill, when he was almost 60, was elected to Parliament. He represented the radical wing of the Liberal party. He had been a public intellectual for decades, with lots of books, editorials, and articles for the Tories to draw on in attacking him. Some Tories overreached. This led to the conservative party becoming known as "The stupid party".

2.0 Adventures in Parliament

I find Mill's attitude towards being a Member of Parliament (MP) unusual, albeit consistent with his stated opinions. He was not interested in giving speeches in support of his party's view when many others were willing to do so. He "in general reserved [him]self for work which no others were likely to do." (from his Autobiography. Uncited quotes below are from this book.) He had such opportunities, for few radicals were in Parliament. (Earlier in his life, such a group was known in Britain as the Philosophical Radicals.)

Despite his radicalism, some of his advocacy was in opposition "to what then was, and probably still is, regarded as the advanced liberal opinion". For example, Mill was against abolishing capital punishment and "in favour of seizing enemies' goods in neutral vessels".

But other efforts seem more progressive, when viewed from the standpoint of later times. In a speech on Gladstone's Reform Bill, Mill argued for sufferage of the working class. He also promoted women's sufferage through his parliamentary work. He put out a pamphlet for reforming British rule in Ireland, including "for settling the land question by giving to existing tenants a permanent tenure, at a fixed rent." He joined in an organization that attempted to have British officers in Jamaica prosecuted, in a criminal case. These officers had engaged in killing, flogging, and general brutality, under the pretence of having civilians brought before court-martials.

3.0 Considerations on Representative Government

J. S. Mill had long been what we would call a public intellectual. I want to particularly focus on his book with the above title. He gives a qualitative discussion of particular voting games. Mill was for proportional representation, also known then as "personal representation". And Mill recommended Thomas Hare on the topic. Other issues he considered include:

  • Provide multiple votes (a greater weight) to more highly educated members of the electorate.
  • Giving voters multiple votes for distributing in elections for a district that had multiple members to elect to a council.
  • Working class and women's sufferage.
  • The advantages and disadvantages of a secret ballot (as opposed to an open one).
  • The advantages and disadvantages of having a two-stage election (e.g., the electoral college, Senators being elected by a state's legislature.
  • The advantages and disadvantages of an upper house (e.g., the Senate, the House of Lords), under various assumptions about its composition.
  • Whether or not the chief executive should be independently elected (e.g., the President of the United States) or by the legislature (e.g., the Prime Minister in the United Kingdom).
  • How the central government and localities should interact and what should the authority and responsibility of each be.

In short, Mill seems to write about concerns often of interest today in analytical political science, albeit in a qualitative way and grounded in concrete practices in his time.

4.0 Attention and the Aftermath

The Tories in Parliament took advantage of Mill's long paper trail. In debates, they would ask if he wanted to defend some of his previous written statements. Because of Mill's forthrightness, this strategy backfired:

"My position in the House was further improved... by an ironical reply to some Tory leaders who had quoted against me certain passages of my writings, and called me to account for others, especially for one in 'Considerations on Representative Government,' which said that the Conservative party was, by the law of its composition, the stupidest party. They gained nothing by drawing attention to the passage, which up to that time had not excited any notice, but the sobriquet of 'the stupid party' stuck to them for a considerable time afterwards."

Considerations on Representative Government contains this passage:

"...It is an essential part of democracy that minorities should be adequately represented. No real democracy, nothing but a false show of democracy, is possible without it.

Those who have seen and felt, in some degree, the force of these considerations, have proposed various expedients by which the evil may be, in greater or lesser degree, mitigated. Lord John Russell, in one of his Reform Bills, introduced a provision that certain constituencies should return three members, and that in these each elector should be allowed to vote only for two; and Mr. Disraeli, in the recent debates, revived the memory of the fact by reproaching him for it, being of opinion, apparently, that it befits a Conservative statesman to regard only means, and to disown scornfully all fellow-feeling with any one who is betrayed, even once, into thinking of ends."

And that passage has this footnote (which I read as noting the existence of negative partisanship):

"his blunder of Mr. Disraeli (from which, greatly to his credit, Sir John Pakington took an opportunity soon after of separating himself) is a speaking instance, among many, how little the Conservative leaders understand Conservative principles. Without presuming to require from political parties such an amount of virtue and discernment as they that they should comprehend, and know when to apply, the principles of their opponents, we may yet say that it would be a great improvement if each party understood and acted upon its own. Well would it be for England if Conservatives voted consistently for every thing conservative, and Liberals for every thing liberal. We should not then have to wait long for things which, like the present and many other great measures, are eminently both the one and the other. The Conservatives, as being by the law of their existence the stupidest part, have much the greatest sins of this description to answer for; and it is a melancholy truth, that if any measure were proposed on any subject truly, largely, and far-sightedly conservative, even if Liberals were willing to vote for it, the great bulk of the Conservative party would rush blindly in and present it from being carried." (emphasis added.)

I assume Mill's refers to the following statement, in parliamentary debates, as his "ironical reply":

"I did not mean that Conservatives are generally stupid; I meant, that stupid persons are generally Conservative. I believe that to be so obvious and undeniable a fact that I hardly think any honourable Gentleman will question it."
5.0 Conclusion

And so, to this day, the more conservative party in some countries, such as the United States, is sometimes called "The stupid party".

References
  • J. S. Mill (1861). Considerations on Representative Government
  • J. S. Mill (1873). Autobiography of John Stuart Mill