Competing Ballot Propositions

I have occasionally written about vote-counting protocols.

Onondaga County is to the west of me. Syracuse, NY, is their major city. Members of the county legislature currently have term limits of 12 years. Twelve years is three terms. They are currently arguing about term limits for the County Executive, of 12 or 16 years. The Democrats support the former, and the Republicans support the latter. The County Executive is currently a Republican.

The County Executive has proposed a curious set of ballot initiatives, leaving it up to the voters. One initiative will set a term limit of twelve years. Another will set a term limit of sixteen years. If neither initiative gets a majority of votes, the County Executive will continue to serve without a term limit. If both pass, the one with more votes will prevail.

I do not know if any precedent exists in New York State for dueling ballot initiatives, and, apparently, some argument exists among the county legislature about this question. I suspect the results of votes on California ballot initiatives have posed some such challenge of interpretation.

How to draw district lines and how to count votes is an interesting mathematical question. This question is often entangled with racism in the United States, both in ensuring white supremacy and in fighting it.

Was There A Communist State In Paraguay In The Seventeenth And Eighteenth Century?

People have been organized in diverse ways in many societies across time and space. A communist state existed for a century and a half in Paraguay in the seventeenth and eighteenth century. I doubt many socialists today want this degree of regimentation. This state extended into Argentia and Brazil.

The Jesuits, formally named the Society of Jesus, is a religious order in the Catholic church. The Guarani are an indigenous people in South America.

The Jesuits agreed with the Spanish king, in 1609, to found communities along the Parani River. These communities, called 'reductions', were each organized around a mission. Each was ruled by a cacique, that is, a Guarani chief, under the direction of the Jesuits. Collectively, these missions were eventually called the Rio de Plata missions. They reached a population of almost 150,000 in 30 missions in 1732.

Life in these reductions was regimented under the 1689 General Rules of the Missions. Land was farmed communally, with crops and cattle introduced by the Jesuits. There were also individual fields, albeit with inefficient farming. As with life in a monastery, mornings began with hymns and mass, and many feast days were celebrated. Meals were communal. The Jesuits provided education to the children, as you might expect.

I note above that the population under Jesuit guidance grew to a large extent. Original contact between Europeans and the indigenous people resulted in the spread of deadly, contagious diseases. The Jesuits moved a good portion of the population in the missions twice. The Jesuits armed the population to fend off neighbors who tried to kidnap people to force into slavery. The Guarani thereby had militias. Eventually, the Jesuits moved some communities to more remote areas. Portugal gained territory in Brazil in the Treaty of Madrid in 1750. The Jesuits moved some communities out of Portuguese territory.

This experiment in a theocratic communism came to an end in 1767. Spain expelled the Jesuits from the Americas. This expulsion had more to do with European politics than anything going on in these missions.

Naturally, Jesuits put this history in a good light.

References

• Massimo Livi-Bacci and Ernesto J. Maeder 2004. The missions of Paraguay: the demography of an experiment. Journal of Interdisciplinary History xxxv(2): 185–224.
• Philip Caraman. 1976. The Lost Paradise: The Jesuit Republic in South America. [I have not read this. The title is evocative.]
• Paraguay: The Noble Ruins of Paradise.

Two Ways To Think About Fixed Capital

1.0 Introduction

This post presents two approaches to fixed capital. The first emphasizes power and convention. It emphasizes that the 'money world', as Mason and Jayadev (2026) put it, is not a direct reflection of physical properties of production. The second is much closer to a determined model, with one degree of freedom.

I have at least one previous post, more abstractly on these themes

2.0 Depreciation as Accounting Conventions and Mediated by the Exercise of Power

Robert Paul Wolff points out that how overhead costs are allocated is a political exercise in many firms. Two managers on the same level might each be in charge of the production of a specific product. Suppose these products are produced in the facility. Each manager wants upper management to see that they are making the most profits for the company. In is in the interest of each to see that as much of possible of the overhead for running the facility is applied to their rival's department.

A given machine might be used in multiple production processes, resulting in the production of different products. The allocation of overhead costs here follows the above logic.

Sometimes (many times?), no fact of the matter exists for how to allocate costs. As I understand it, the Generally Accepted Accounting Principles (GAAP) includes different conventions for depreciation. Some models I have seen assume radioactive decay so to speak. Tax law specifies what can be allowed.

3.0 Depreciation and the Economic Life of Machines as an Aspect of Prices of Production

Another way of thinking about fixed capital is as in Sraffa (1960). Enough equations are given for prices to be determined, corresponding to a given wage or rate of profits. The data include inputs and outputs, in disaggregated physical terms, for all combinations of ages of machines. These detailed specifications are not based solely on the age, but the entire history of each machine.

Alessandro Roncaglia showed, back in the 1970s, that a countable infinity of equations can arise when production processes can require inputs of combinations of machines. The theory of pure fixed capital includes assumptions that rule out this possibility.

Sraffa derives the formula for an annuity from his treatment of a machine of constant efficiency. But the analysis generalizes. This approach is in tension with the first approach.

4.0 Conclusion

I will continue exploring mathematical puzzles. I like to think that Sraffa presents the elements of an alternative theory, not just an immanent critique of 'neoclassical' theory. The analysis points outside itself.

Reference

• Mason, J. W. and Arjun Jayadev. 2026. Against Money. University of Chicago.

Jack Birner On The Cambridge Capital Controversy

I have been rereading Jack Birner's 2002 book, The Cambridge Controversies in Capital Theory. Birner is an economist of the Austrian school. He probably generally disagrees with me on lots of matters. Torward the start of the introduction, he writes:

"Four decades ago the best minds in economics were engaged in a confrontation which the entire profession followed in the pages of the leading journals almost as if it were a soccer match. It has become customary to distinguish two opposing groups of economists to the debate..." -- Jack Birner (2002: 1)

And he expresses astonishment that the results of this dispute are ignored:

"What I do want to draw attention to is that the conclusions reached in that debate constitute a rare example of a set of formally proven, uncontestable, undeniably true and reliable results in economics... They can be summarized by saying that the K of the production function that modern economists so confidently and fully rely on for their theoretical and empirical work can only be used in conditions where there is only a single, homogeneous capital good. One does not need to have a degree in economics to know that in reality this is not the case. The economy consists of a bewildering variety of buildings, machines, software, skills and ways of organizing production. And as everyone who has filed a corporate tax declaration knows, it is not even possible to give more than a rather inexact estimate of their value. In other words, not only is there no intuitive justification for the use of aggregate, homogeneous K, we have proofs by Nobel-calibre economists assisted by 100 per cent certain mathematical techniques that demonstrate without a shred of doubt that this K cannot and should not be used for the objectives it is currently used for. Nevertheless, economists go about their business as if these proofs did not exist. That some of them are the very same people who produced these proofs earlier makes things even more curious. The fact that production functions with the same aggregate K figure prominently in all current textbooks of macroeconomics is worse than curious: it is deeply worrying." -- Jack Birner (2002: 1-2)

I do not think the situation is different today. I agree with Birner that the overall point of the CCC is not at all clear from the details of the match. The participants were worrying about local details. I think more was at stake than an aggregate theory. I like to emphasize the labor 'market' in my expositions. Fabio Petri, among others, emphasizes mistakes in what the early marginalists thought could be consistently taken as given in their theory.

Birner considers the role of idealizing assumptions in mathematical models. He considers the relations of such ideal models to models that more 'factual', that is, closer to being able to be applied empirically.

The trend, for decades, in the philosophy of science is to be descriptive, to try to understand how specialists in specific disciplines become convinced of their ideas. The CCC poses a problem for the methodologist.

I'm am doubtful about Birner's methodology at points. He draws upon some scholars I like. For example, he draws on Arthur Koestler's The Sleepwalkers: A History of Man's Changing Vision of the Universe. Koestler points out that Copernicus was focused on narrow points. One of the virtues of a geocentric model, for him, was that it got rid of equants. An equant is a circular orbit that has uniform velocity around a point displaced from its center.

Likewise, economists in the CCC were focused on narrow points about, say, Samuelson's surrogate capital and Robinson's pseudo-production function. For Birner, Sraffa and Garegnani were about the only ones awake.

In some sense, Birner does not resolve his problem. He concludes most economists are still asleep.

Socialism Succeeding In Emilia-Romagna

Emilia-Romagna is a region in Italy, north of Tuscany. I have written about its capital, Bologna, before.

About a third of the gross domestic product of Emilia-Romagna is produced by co-operatives. About two thirds of those who reside in Emilia-Romagna participate in co-ops in some ways. (See this article from John Duda.) Apparently, co-ops in Italy go back to the nineteenth century, surviving through the fascists in the twentieth century.

Article 45 of the 1947 Italian constitution promotes co-ops. It states:

The Republic recognises the social function of co-operation of a mutually supportive, non-speculative nature. The law promotes and encourages co- operation through appropriate means and ensures its character and purposes through appropriate checks.

The law safeguards and promotes the handicrafts.

A capability for a worker to take unemployment benefits at once to set up a co-op is one of the provisions of the 1985 Macora law.

A society with a large co-operative segment will have related institutions. Co-ops will market to each other. Scholars, such as Vera Zamagni at the University of Bologna, will study them. Competition among co-ops might be less cut-throat. The study of management and administration at academic institutions will have curriculum supporting co-ops. Mutual banks might be set up to loan to co-ops, and other financial institutions will have more practice in making such loans. Co-ops might set up institutes to perform research into processes and products improving their technology.

The 1986 book, The Second Industrial Divide: Possibilities for Prosperity, by Michael J. Priore and Charles Sabel, is supposed to be of interest on this topic.

Anomalous Switch Points

I have a new working paper at the Centro Sraffa. The abstract follows:

Abstract: This article presents examples of models of rent with decreasing wage frontiers; with unique, square cost-minimizing techniques at a given rate of profits; but without the wage maximization property. Anomalous switch points are highlighted, where an anomalous switch point has properties that contrast with generic switch points in models of circulating capital. This article presents a numeric example of a switch point along a single wage curve, with no other wage curve intersecting at the switch point. Other numeric examples are of switch points in which only the scale, not the operated processes, vary between the cost-minimizing techniques at the switch point. A fake switch point is presented in which prices vary only for goods which are not commodities under the non-cost minimizing technique, also known as ghost commodities.

The Roosevelt Dime And Fluoridated Water: Communist Plots

Franklin Delano Roosevelt died in 1945, and World War II ended with the Japanese surrender in August. Germany had surrendered in May. The Roosevelt dime was introduced in 1946. John Sinnock, an artist at the mint, designed the obverse. His initials are under Roosevelt’s head.

The Soviet Union was the ally of the United States in fighting the fascists. This quickly changed. Somehow anti-communists became convinced that the J. S. on the Roosevelt dime stand for Joseph Stalin. I don't know what advantage the communists were supposed to get out of this plot.

When I first saw Dr. Strangelove, I thought the idea that fluoridated water was a communist plot was quite comic. I did not realize that Kubrick did not make this up. Anti-communists believe this. I do not know if they talk about, "Sapping our precious bodily fluids," as General Jack D. Ripper does in the movie.

I have documented some other stupid stuff anti-communists and anti-Marxists have said.