David Ellerman

David Ellerman
University of Ljubljana · Faculty of Social Sciences

PhD

About

261
Publications
67,936
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2,302
Citations
Additional affiliations
January 2019 - present
University of Ljubljana
Position
  • Researcher
September 2005 - December 2015
University of California, Riverside
Position
  • Researcher
September 1993 - September 2003
World Bank
Position
  • Consultant

Publications

Publications (261)
Article
Full-text available
We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an “amount of information,” but, as he pointed out, “no concept of information itself was defined.” Logical entropy provides that definition. Logical entropy is the natural measure of the notion of information bas...
Chapter
This chapter develops the multivariate (i.e., three or more variables) entropies. The Shannon mutual information is negative in the standard probability theory example of three random variables that are pair-wise independent but not mutually independent. When we assume metrical data in the values of the random variable (e.g., a real-valued variable...
Chapter
The purpose of this chapter is to summarize the new foundations for information theory presented in the book and to point out work yet to be done on the topic. The claim is that logical information theory fills the gap left by the Shannon theory of giving a definition of information as being about distinctions, differences, distinguishability, and...
Chapter
In this chapter, all the compound notions of simple, joint, conditional, and mutual logical entropy are defined and then the corresponding notions of Shannon entropy are derived via the dit-bit transform. Moreover, a number of other notions of divergence, cross entropy, and Hamming distance are developed for logical entropy along with the correspon...
Chapter
This chapter is focused on developing the basic notion of Shannon entropy, its interpretation in terms of distinctions, i.e., the minimum average number of yes-or-no questions that must be answered to distinguish all the “messages.” Thus Shannon entropy is also a quantitative indicator of information-as-distinctions, and, accordingly, a “dit-bit tr...
Chapter
This book presents a new foundation for information theory where the notion of information is defined in terms of distinctions, differences, distinguishability, and diversity. The direct measure is logical entropy which is the quantitative measure of the distinctions made by a partition. Shannon entropy is a transform or re-quantification of logica...
Chapter
Full-text available
The transition to density matrices in QM is facilitated by reformulating the ‘classical’ (i.e., non-quantum) results about logical entropy using density matrices. Then the transition to the quantum version of logical entropy is made using the semi-algorithmic procedure of “linearization.” Given a concept applied to sets, apply that concept to the b...
Article
Full-text available
Abstraction turns equivalence into identity, but there are two ways to do it. Given the equivalence relation of parallelness on lines, the #1 way to turn equivalence into identity by abstraction is to consider equivalence classes of parallel lines. The #2 way is to consider the abstract notion of the direction of parallel lines. This paper developm...
Chapter
The Fundamental Myth, that the rights to the (whole) product of production (and the management rights) in a productive opportunity are part and parcel of the ownership of capital (the “means of production”) was introduced and explained in Chap. 1. In this chapter, it is shown how the Fundamental Myth is baked into the simple formulas for the valuat...
Chapter
This chapter develops the formal mathematical treatment of the theory of property rights and contracts in both the descriptive and normative dimensions. The mathematical framework is in terms of vector flows on graphs, but there are two equivalent alternative treatments depending on whether the vectors are all non-negative or are general real vecto...
Chapter
This chapter treats (informally) the sins of omission and commission about property rights and contracts in neoclassical microeconomic theory. The analysis is developed at both the descriptive and normative levels, and then the Fundamental Theory of Property Theory connects the two levels. That theorem is the property theoretic counterpart of the p...
Chapter
This last chapter is devoted to a general description of the descriptive and normative points of jurisprudence that arise when those points are introduced into today’s neoclassical microeconomic theory. These points are contrasted with the usual orthodox or heterodox criticisms of neoclassical economics as being unrealistic since the actual economy...
Chapter
Many of the controversial questions raised by the reintroduction of jurisprudential considerations into economics are also raised in the legal debates about corporations and corporate governance. Hence this chapter delves into the debates about corporations to show how the same issues reemerge in that context.
Chapter
Cost-benefit analysis and wealth-maximization Law & Economics are both based on the Kaldor-Hicks (KH) principle that was developed to bypass the usual notion of a Pareto superior change. In this chapter, the KH principle is shown to be based on a logical fallacy that, in a different context, Paul Samuelson illustrated as the ‘same-yardstick fallacy...
Article
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This paper collects together quotations and extracts from 19th and 20th century thinkers who were little-known for being supporters of workplace democracy.
Chapter
Neoclassical economic theory pays indirect homage to the imputation principle of jurisprudence by giving a metaphorical interpretation of the factor payments according to marginal productivity (MP) in competitive equilibrium so that “each factor gets what it produces.” This chapter does not make the usual criticism for MP theory being unrealistic,...
Chapter
The Arrow-Debreu model of competitive general equilibrium and more recent variants are the highpoints of neoclassical microeconomic theory. They are usually criticized as being unrealistic but the analysis in this chapter is not based on that common criticism. Precisely because the Arrow-Debreu model is so idealized, it is easy to pinpoint the conc...
Chapter
The system of (involuntarily or voluntarily) owning workers was abolished in the mid-nineteenth century, but it was replaced by the system of voluntarily renting, hiring, or employing workers. That system of renting human beings lasted far beyond its institutional ‘shelf-life’ in the twentieth century due to the perception that ‘The Alternative’ wa...
Chapter
Since the middle of the nineteenth century, three types of voluntary contracts, a lifetime master-servant contract, the coverture marriage contract, and the non-democratic constitution (pactum subjectionis) have all been abolished in the advanced democratic countries. Yet conventional classical liberalism and neoclassical economics offer no serious...
Preprint
Full-text available
The purpose of this paper is to abstractly describe the notion of a generative mechanism that implements a code and to provide a number of examples including the DNA-RNA machinery that implements the genetic code, Chomsky's Principles & Parameters model of a child acquiring a specific grammar given `chunks' of linguistic experience (which play the...
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Conventional classical liberalism dumbs down the intellectual history of democratic theory into the question of consent versus coercion. Democracy is then represented as “government by the consent of the governed.” But from Antiquity onward there have been intellectual defenses of autocracy based on consent (the pactum subjectionis) which continue...
Chapter
Conventional classical liberalism poses the fundamental question as “consent versus coercion.” Hence it provides no argument for completely abolishing a truly voluntary contract. Instead classical liberalism promotes greater freedom of contract, a veritable smorgasbord of different voluntary contracts should be available. Yet, in the advanced democ...
Chapter
One of Marx’s biggest blunder was to characterize the private property market economy based on human rentals as “capitalism” and as being based on “private ownership of the means of production.” The mischaracterization of the system was enthusiastically received by the supporters of the human rental system so they could pose as the defenders of pri...
Chapter
The intellectual treatment of slavery or lifetime servitude is typically dumbed-down to the question of coercion versus consent. But from Antiquity, there have been intellectual defenses of contractual slavery that continue to this day. Hence the Abolitionist Movement had to dig deeper than just promote consent over coercion. The deeper tradition o...
Article
This book argues for the abolition of the employment system in favor of workplace democracy and thus escapes the usual capitalism-versus-socialism binary choice by reframing the basic issue as the employment contract, not private property or a market economy. The author repositions the political and economic debate in the lineage of abolitionism...
Book
This book presents an integrated jurisprudential critique of neoclassical microeconomic theory. It explains what is ‘really wrong’ with the theory both descriptively, as well as normatively. The criticism presented is based on questions of jurisprudence, and on neoclassical theory’s sins of omission and commission concerning the underlying system o...
Book
This monograph offers a new foundation for information theory that is based on the notion of information-as-distinctions, being directly measured by logical entropy, and on the re-quantification as Shannon entropy, which is the fundamental concept for the theory of coding and communications. Information is based on distinctions, differences, disti...
Article
Full-text available
We live in the information age. Claude Shannon, as the father of the information age, gave us a theory of communications that quantified an "amount of information," but, as he pointed out, "no concept of information itself was defined." Logical entropy provides that definition. Logical entropy is the natural measure of the notion of information bas...
Preprint
Full-text available
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and...
Article
Full-text available
Purpose This paper will discuss two problems that have plagued the literature on the Ward-Domar-Vanek labor-managed firm (LMF) model, the perverse supply response problem and the horizon problem. The paper also discusses the solution to the horizon problem and the alleged “solution” of a membership market. Design/methodology/approach This is a con...
Article
Full-text available
The highly mathematical nature of the Arrow-Debreu and other similar models of general equilibrium hide rather than elucidate the nature of equilibrium in a private property market economy where all factors of production may be purchased or rented. It is an empirical commonplace that the Arrow-Debreu model of general equilibrium does not describe t...
Preprint
Full-text available
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the logic of partitions, that is at the same mathmatical level as Boolean subset logic since subsets and quotient...
Preprint
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In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events." Probabilities are introduced for classical events, superposition events, and their mixtures by using density...
Article
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The premise of this paper is that state aid to distressed companies should benefit not only the current owners but also the employees, who are the ones taking personal risks to continue or restart companies. Government aid during the Great Recession was aimed primarily at restoring the status quo. In the current deeper crisis, aid should be designe...
Preprint
Full-text available
Corporations have been getting a bad rap lately. Many blame "corporations" for a litany of ills that, upon closer examination, should be blamed on another institution. Our goal is to analyze a miscellany of fallacies concerning the Citizens United case, corporate personhood, the stakeholder theory, the affected interests principle, and finally endi...
Chapter
Full-text available
Classical liberalism is skeptical about governmental organizations “doing good” for people. Instead governments should create the conditions so that people individually (Adam Smith) and in associations (Tocqueville) are empowered to do good for themselves. The market implications of classical liberalism are well known, but the implications for orga...
Article
Full-text available
Corporations have been getting a bad rap lately. Many blame “corporations” for a litany of ills that, upon closer examination, should be blamed on other institutions. Our goal is to analyze a miscellany of fallacies concerning the Citizens United case, corporate personhood, the stakeholder theory, the affected interests principle, and finally endin...
Article
Full-text available
Preprint
Full-text available
The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theor...
Article
Full-text available
The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theor...
Preprint
Full-text available
The development of the new logic of partitions (= equivalence relations) dual to the usual Boolean logic of subsets, and its quantitative version as the new logical theory of information provide the basic mathematical concepts to describe distinctions/indistinctions, definite-ness/indefiniteness, and distinguishability/indistinguishability. They th...
Article
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions (“dits”) of a partition (a pair...
Preprint
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized using the distinctions (`dits') of a partition (a pai...
Conference Paper
Full-text available
The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theor...
Preprint
Full-text available
Classical liberalism tends to respond to the criticism of any voluntary market contract by promoting a wider choice of options and increased information and bargaining power so that no one would seem to be 'forced' or 'tricked' into an 'unconscionable' contract. Hence, at first glance, the strict logic of the classical liberal free market philosoph...
Article
Full-text available
In her recent book, Private Government, Elizabeth Anderson makes a powerful and pragmatic case against the abuses experienced by employees in conventional corporations. The purpose of this review-essay, says the author, is to contrast Anderson’s pragmatic critique of many abuses in the employment relationship with a principled critique of the relat...
Preprint
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, di¤erences, and distinguishability, and is formalized using the distinctions ('dits') of a partition (a pair...
Article
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized using the distinctions (“dits”) of a partition (a pai...
Article
Full-text available
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of \({\mathbb {C}} \) repl...
Article
Full-text available
In her recent book Private Government, Elizabeth Anderson makes a powerful but pragmatic case against the abuses experienced by employees in conventional corporations. The purpose of this review-essay is to contrast Anderson’s pragmatic critique of many abuses in the employment relation with a principled critique of the employment relationship itse...
Presentation
Full-text available
These are the slides for a talk on new foundations for information theory based on the new logic of partitions, dual to Boolean subset logic. All the Shannon definitions of simple, joint, conditional, and mutual information can be derived by a uniform transformation from the corresponding definitions in logical information theory.
Preprint
Full-text available
There is a fatal logical-methodological fallacy involved in the Kaldor-Hicks principle which analyzes a Pareto improvement into an "efficiency"part and an "equity"part-so that economists can supposedly recommend the efficiency part in their scientific role as economists while leaving the equity part to politicians, moral philosophers, and the like....
Presentation
Full-text available
Slides from a talk in the School of Social Sciences at the University of Ljubljana Nov. 2017.
Presentation
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Slides from a talk at the Haus der Kunst in Munich.
Article
Full-text available
here is a new theory of information based on logic. The definition of Shannon entropy as well as the notions on joint, conditional, and mutual entropy as defined by Shannon can all be derived by a uniform transformation from the corresponding formulas of logical information theory. Information is first defined in terms of sets of distinctions witho...
Conference Paper
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, di¤erences, and distinguishability, and is formalized as the distinctions of a partition (a pair of points d...
Article
Full-text available
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized as the distinctions of a partition (a pair of points...
Article
Full-text available
John Tomasi’s 2012 book, Free Market Fairness, has been well received. On the dust jacket, Tyler Cowen proclaims it “one of the very best philosophical treatments of libertarian thought, ever” and Deirdre McCloskey calls it a “long and friendly conversation between Friedrich Hayek and John Rawls — a conversation which, astonishingly, reaches agreem...
Article
Full-text available
Much of the recent discussion in progressive circles [e.g., Stiglitz; Galbraith; Piketty] has focused the obscene mal-distribution of wealth and income as if that was "the" problem in our economic system. And the proposed redistributive reforms (e.g., changes in income, wealth, and estate taxes, increased minimum wages, income caps, and universal b...
Working Paper
Full-text available
Given an equivalence relation ~ on a set U, there are two abstract notions of an element of the quotient set U/~. The #1 abstract notion is a set S=[u] of equivalent elements of U (an equivalence class); the #2 notion is an abstract entity u_{S} that is definite on what is common to the elements of the equivalence class S but is otherwise indefinit...
Article
Full-text available
ince the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there...
Working Paper
Full-text available
Logical probability theory was developed as a quantitative measure based on Boole's logic of subsets. But information theory was developed into a mature theory by Claude Shannon with no such connection to logic. But a recent development in logic changes this situation. In category theory, the notion of a subset is dual to the notion of a quotient s...
Article
Full-text available
Following the development of the selectionist theory of the immune system, there was an attempt to characterise many biological mechanisms as being ‘selectionist’ as juxtaposed with ‘instructionist’. However, this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky’s principles-and-parameters (P&P...
Article
Full-text available
Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank tha...
Article
The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in dif...
Article
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there...
Working Paper
Full-text available
The theory of q-analogs develops many combinatorial formulas for finite vector spaces over a finite field with q elements--all in analogy with formulas for finite sets (which are the special case of q=1). A direct-sum decomposition of a finite vector space is the vector space analogue of a set partition. This paper develops the formulas for the num...
Article
Full-text available
The Commons/Green Movement seems to have accepted that the current system is based on the principles of private property, and then has juxtaposed the notion of common property to private property. In fact, the current system is based on violations of the principle on which private ownership is supposed to rest, namely, the principle of people getti...
Article
Full-text available
Category theory has foundational importance because it provides conceptual lenses to characterize what is important and universal in mathematics—with adjunctions being the primary lens. If adjunctions are so important in mathematics, then perhaps they will isolate concepts of some importance in the empirical sciences. But the applications of adjunc...
Article
Full-text available
There is a fault line running through classical liberalism as to whether or not democratic self-governance is a necessary part of a liberal social order. The democratic and non-democratic strains of classical liberalism are both present today* particularly in the United States. Many contemporary libertarians and neo-Austrian economists represent th...
Conference Paper
Full-text available
Recent developments in pure mathematics (category theory) and in mathematical logic (partition logic) have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets (mis-specified as the logic of "propositions") and the logic of quotient sets, equivalence relations, or parti...
Research
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I was asked by a national economics correspondent to give a short version, written in non-technical terms, of the responsibility principle (or labor theory of property) applied to the workplace. This is the “justice in the workplace” argument in a nutshell.
Article
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There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate p...

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