Anonymous yes–no voting with abstention and multiple levels of approval

Symmetric (3,2) simple games serve as models for anonymous voting systems in which each voter may vote “yes,” abstain, or vote “no,” the outcome is “yes” or “no,” and all voters play interchangeable roles. The extension to symmetric (j,2) simple games, in which each voter chooses from among j ordered levels of approval, also models some natural decision rules, such as pass–fail grading systems. Each such game is determined by the set of (anonymous) minimal winning profiles. This makes it possible to count the possible systems, and the counts suggest some interesting patterns. In the (3,2) case, the approach yields a version of May's Theorem, classifying all possible anonymous voting rules with abstention in terms of quota functions. In contrast to the situation for ordinary simple games these results reveal that the class of simple games with 3 or more levels of approval remains large and varied, even after the imposition of symmetry.     

A Primer on Logistic Growth and Substitution: The Mathematics of the Loglet Lab Software

This article describes the mathematics underlying the Loglet Lab software package for loglet analysis. “Loglet analysis” refers to the decomposition of growth and diffusion into S-shaped logistic components, roughly analogous to wavelet analysis, popular for signal processing and compression. The term “loglet” joins “logistic” and “wavelet.” Loglet analysis comprises two models: the first is the component logistic model, in which autonomous systems exhibit logistic growth. The second is the logistic substitution model, which models the effects of competitions within a market. An appendix describes the current status of the software.     

Tax revenues, fiscal corruption and “shame” costs

In this paper we explore tax revenues in a regime of widespread fiscal corruption in a static framework. We prove that the relationship between the tax rate and tax revenues depends on the relevance of the “shame effect” of being detected in a corrupt transaction. In countries with a “low shame” effect, tax revenues grow as the tax rate increases. Moreover, there is a critical tax rate where the growth rate of tax revenues begins to reduce. In countries with a high “shame effect” tax revenues increase up to a threshold value and then decrease.     

Can Japan succeed in “Chigyo-ka” (intelprise-formation)?

There are two aspects in today's information revolution that started in the late 1970s. The first is an aspect referred to as “the third industrial revolution,” which triggers the transition to the “21st century system of Industrialization.” The information revolution in this sense brings the creation of new “breakthrough industries (new multimedia industries).” And the second aspect of the information revolution possesses the characteristics of both a technological revolution and a social revolution and brings about the arrival of the third phase of the historical evolutionary process of the modern civilization, which proceeds through three phases, namely “militarization, industrialization, and then informatization.”If the bearers of modern industrialization are a “group of enterprises” that have been engaged in the race in order to gain “wealth” (generalized means of exchange/exploitation power), and if these enterprises' activities have been exercised in the world market where their products have been sold, then it is appropriate to call the bearers of informatization a “group of intelprises.” They will be engaged in the race to gain “wisdom” (generalized means of persuasion/induction power), then stages of their activities can be called a “global intelplace” where “sharables,” that is, information and knowledge, will be disseminated. And now, toward the 21st century, the third phase of modernization, which can be called the “informatization/intelprise formation” or the “wisdom game” (intellectualism), is about to begin.Japan's “ie society (a society based on the ie principle—literally, it means “house” but here it is interpreted as cultural principle for organizing a society), which has been going through the process of evolution on the Japan Archipelago, has developed a network-based organization with little stratification within its infrastructure. In this sense, Japanese society can be characterized as a “network-oriented society” in which intelprises and an intelplace in the broad sense have functioned as the essential components of the society since Middle Ages. In general, an intelplace and intelprises that operate actively within this framework serve as the flexible bases for different types of social relations and institutions, such as states and markets and eventually integrate these into the society to a certain extent. In fact, it took place quite regularly during the modernization “in the narrow sense,” or Westernization of Japanese society after the Meiji Restoration. There exist some problems, however. Some of the characteristics found in Japanese society may become obstacles to activities aimed at the sharing and promotion of information and knowledge in the global intelplace and Japanese participation in the “wisdom game.” Badly needed are serious efforts for Japanese intelprise-formation to reduce these obstacles as much as possible.     

Exact arbitrage, well-diversified portfolios and asset pricing in large markets

For a market with an atomless continuum of assets, we formulate the intuitive idea of a “well-diversified” portfolio, and present a notion of “exact arbitrage”, strictly weaker than the more conventional notion of “asymptotic arbitrage”, and necessary and sufficient for the validity of an APT pricing formula. Our formula involves “essential” risk, one based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets.     

A model of “coupled” technology transfer : A logistic curve approach

This article presents a mathematical model relating to the technology transfer problem. The origin of the problem stems from the existing trade-offs between the strategies of “technological progressiveness” and “static efficiency” employed by firms or countries defined as “leaders” and “followers,” respectively. The formulation of the model is based on the assumption that the technological development of a firm or a country follows a logistic growth curve when related to a specific technology. During the process of a “coupled” technology transfer, the development of the follower changes and its behavior is described by a first order nonhomogenous deferential equation. Different scenarios of the “coupled” technology transfer between the leader and the follower are being discussed.     

The analysis of a price war strategy under market demand growth

We use the finite repeated Prisoners' Dilemma game model herein to discuss how firms choose their optimal strategy under a price war with market demand growth. This model has two players: one is an R-type player and the other is a TFT-type player. Each player has two strategies to choose from: a preemption strategy and a “wait” strategy. Our results indicate that: (i) if the probability that the opponent is an R-type (TFT-type) player is high, then the time when the opponent adopts a preemption strategy will be early (late); (ii) Market demand growth is an incentive for cooperation among firms; (iii) if the market demand growth rate is high, then the R-type player will not have an evolutionary advantage. We use the competition between cell phone manufacturing firms Nokia and Motorola in China as an example. When Nokia is an R-type player and adopts a preemption strategy, Motorola should preferably use a preemption strategy rather than a “wait” strategy. However, as a TFT-type player, this will benefit Motorola under the situation of market demand growth.     

Fashion statement

We study bilateral matching under private information about agents' characteristics. Assortative matching is the only equilibrium outcome in the absence of private information. When an information friction is present, the matching process can be improved if a payoff-irrelevant variable which we term “fashion” is introduced. Informed agents choose to adopt fashion as a signaling device. If success in matching is observed, other agents can imitate the signal. Thus, for fashion to be useful, it must constantly change. If there are more than two types of agents, both “high” and “low” fashion are needed to facilitate assortative matching.     

Limiting the system and reshaping lifestyles: Solving unemployment by social and technical innovations

We have become used to seeing crises in growth, unemployment, and inflation as purely economic problems that can be overcome by suitable economic and political means. One basic assumption of the following reflection however, is that the above might be only half the picture. To paraphrase a formula of Friedrich Engels, the concern is not “in the first and last instance” with questions of the “economic basis,” but with questions of the current images of human kind, social milieus and lifestyles. Solutions will thus tend to lie in social innovations and reorganization of the System insofar as they complement the new lifestyles.     

Democracy and growth in Africa: Implications of increasing electoral competitiveness

Estimating a 1975–2004 decadal panel data in an augmented production-function framework, the paper finds that indexes of electoral competitiveness exhibit U-shape relationships with GDP growth, implying quite different “intermediate” and “advanced”-level effects of reforms in Africa.     

Increasing returns and the share economy

Under imperfect competition, profit maximization by firms results in the market price exceeding the marginal cost of production; Weitzman terms this “excess supply” Weitzman wishes to replicate in the cost function (in terms of labor) the properties of the revenue function (in terms of output), thus generating “excess demand” for labor. A revenue-sharing scheme will achieve this if and only if there are decreasing returns to scale. Hence increasing returns apparently play no role in Weitzman's analysis.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Topological games at Princeton, a mathematical memoir

The games of the title are “Nash” (or Hex), “Milnor” (or Y), “Shapley” (or Projective Plane) and “Gale” (or Bridg-It) all of which were discovered (or re-discovered) in Princeton in 1948–1949. After giving the basic topological connections, I will discuss more recent ramifications related to computational complexity theory. A recurrent theme will be non-constructive proofs, or how we can know something can be done without having the slightest idea of how to do it.     

Constant per capita consumption paths with exhaustible resources and decaying produced capital

We introduce decay in produced capital and exogenous technical progress to the recent “Solow Model” of Asheim et al. with population growth and observe the possible collapse of the economy given too high a rate of decay. “Enough” technical progress can restore sustainable per capita consumption.     

Imitation processes with small mutations

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,” meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i” to “all play j” is the probability of a transition from the state “all agents but 1 play i, 1 plays j” to the state “all play j”.     

Don’t let your robots grow up to be traders: Artificial intelligence, human intelligence, and asset-market bubbles

Researchers who have examined markets populated by “robot traders” have claimed that the high level of allocative efficiency observed in experimental markets is driven largely by the “intelligence” implicit in the rules of the market. Furthermore, they view the ability of agents (artificial or human) to process information and make rational decisions as unnecessary for the efficient operation of markets. This paper presents a new series of market experiments that show that markets populated with standard robot traders are no longer efficient if time is a meaningful element, as it is in all asset markets. While simple two-season markets with human subjects reliably converge to an efficient equilibrium, markets with minimally intelligent robot traders fail to attain this equilibrium. Instead, these markets overshoot the equilibrium and then crash below it. In addition to firmly establishing the role of trader intelligence in asset-market equilibrium, these experiments also provide insights into why bubbles and crashes are consistently observed in many asset-market laboratory experiments using human subjects.     

Quasi-weightings, Trading, and Desirability Relations in Simple Games

We investigate the problem of simultaneously characterizing various classes of simple games in three different ways: (i) the existence of “quasi-weightings” in which smaller numerical values are assigned to losing coalitions than are assigned to winning ones, (ii) the robustness of “winningness” with respect to trades involving groups of players, and (iii) the acyclicity of certain strict “orderings” that intuitively correspond to the idea of one player being more desirable than another.Journal of Economic LiteratureClassification Number: C71.     

Influence of decision styles on use of decision models

This article discusses how the “decision style” of an administrator influences the adoption and use of particular decision models. Several “interactive” and “analytical” decision models often used to guide decision making are described and critiqued to point out their virtues and deficiencies. Propositions are suggested that contend that “systematic,” “judicial”, “speculative”, and “intuitive” styles have clear-cut preferences for a particular decision model. This model seems to be used, even when another would be more suitable. Effective decision makers are postulated to adapt their styles, or at least to see the benefits of different styles. Mixed-mode models are proposed that seem to simulate the behavior of successful decision makers.     

Computer-assisted panel sessions (CAPS): Review of an experiment in accelerated international teleconferencing

A complex set of telecommunication links was used to permit eight geographically separated expert panels (in Austria, Poland, the Soviet Union, and the United States) to participate in a Delphi-type exercise conducted in connection with an International Institute for Applied Systems Analysis (IIASA) workshop titled “Systems Assessment of New Technology: International Perspectives.” No significant technical difficulties were encountered in creating and using this communication mechanism, but a number of sociopsychological and procedural problems arose that were sufficiently serious to prevent substantively useful results from being obtained. It seems clear, however, that if such an activity were to focus on questions agreed to be worthwhile, with participants and an agenda structure truly suitable for resolving these questions, then a number of relatively minor organizational and informational adjustments should permit “computer-assisted panel sessions” to become a useful tool for international scientific cooperation.