A Theory of Discrete Hierarchies as Optimal Cost-Adjusted Productivity Organisations

Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d'\^etre has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that strikes a balance between the benefits of group productivity and the costs of communication for coordination. By maximising a generic representation of the output of a hierarchical organization with respect to its design, the optimal configuration of group sizes at different levels can be determined. With very few ingredients, a wide variety of hierarchically ordered complex organisational structures can be derived. Furthermore, our results rationalise the ubiquitous occurrence of triadic hierarchies, i.e., of the universal preferred scaling ratio between $3$ and $4$ found in many human and animal hierarchies, which should occur according to our theory when production is rather evenly contributed by all levels. We also provide a systematic approach for optimising team organisation, helping to address the question of the optimal `span of control'. The significantly larger number $\sim 3-20$ of subordinates a supervisor typically manages is rationalised to occur in organisations where the production is essentially done at the bottom level and in which the higher levels are only present to optimise coordination and control

Non rivalry and complementarity in computer software

In this paper we contend that – contrary to what argued by a vast part of the literature – computer software and, more in general, digital goods (i.e. symbolic strings on an electronic medium with some eco- nomic value) do not present the characteristics of a public good as they do not suffer from lack of rivarly and excludability any more than other durable goods which are regularly allocated on competitive markets. We argue instead that the “market allocation problem” – if any – with digital goods does not arise from their public nature but from some pe- culiar characteristics of the production technology. The latter presents the nature of a typical problem solving activity as far as the produc- tion of the first unit is concerned, this means that innovative activities in computer software are characterized by high degrees of interdepen- dencies, cumulativeness, sequentiality, path dependence and, more in general, sub-optimality arising from imperfect problem decompositions. As far as the production of further units is concerned, we observe in- stead high (but not infinite) expansibility and perfect codification (lack of any tacit dimension) which make diffusion costs rapidly fall. Given such claims, we argue that a standard “Coasian” approach to property rights, designed to cope with the externalities of semi-public goods may not be appropriate for computer software, as it may decrease both ex-ante incentives to innovation and ex-post efficiency of diffusion. On the other hand the institutional definition of property rights may strongly influence the patterns of technological evolution and division of labor in directions which are not necessarily optimal.Intellectual property; hierarchies; innovation; software; digital goods

A survey of clustering methods

In this paper, I describe a large variety of clustering methods within a single framework. This paper unifies work across different fields, from biology (numerical taxonomy) to machine learning (concept formation). An important objective for this paper is to show that one can benefit by a knowledge of research across different disciplines. After describing the task from a set of different viewpoints or paradigms, I begin by describing the similarity measures or evaluation functions that form the basis of any clustering technique. Next, I describe a number of different algorithms that use these measures, and I close with a brief discussion of ways to evaluate different approaches to clustering

Division of Labor, Organizational Coordination and Market Mechanism in Collective Problem-Solving

This paper builds upon a view of economic system and individual economic organization as problem-solving arrangements and presents a simple model of adaptive problem-solving driven by trial-and-error and collective selection. The institutional structure, and in particular its degree of decentralization, determines which solutions are tried out and undergo selection. It is shown that if the design problem at hand is complex (in term of interdependencies between the elements of the system) then a decentralized institutional structure is very unlikely to ever generate optimal solutions and therefore no selection process can ever select them. We also show that nearly-decomposable structures have in general a selective advantage in terms of speed in reaching good locally optimal solutions.Theory of the firm, Vertical and horizontal integration, Computational complexity

Committees, Hierarchies and Polyarchies

This paper examines optimal decision making under three different organizational forms: committees, hierarchies, and polyarchies. Focus is on the trade-off between errors of rejecting good projects versus errors of accepting bad projects, and on the trade-off between gains from more extensive evaluations of projects versus costs of evaluation. The authors characterize the optimal sizes of these organizations (as well as the optimal level of consensus in committees), and then analyze how these optima change under different organizational environments. They also analyze the influence of organizational environment on the relative performance of these alternative organizational forms