Bumpei Nakano

Frankl's Conjecture is True for Modular Lattices

Abstract. It is shown that every finite modular lattice L with |L|≥2 contains a join-irreducible element x∈L such that at most |L|/2 elements y∈L satisfy y≥x.

Lower Semimodular Types of Lattices: Frankl's Conjecture Holds for Lower Quasi-Semimodular Lattices

Abstract. We introduce a measure of how far a lattice L is from being lower semimodular. We call it the lower semimodular type of L. A lattice has lower semimodular type zero if and only if it is lower semimodular. In this paper we discuss properties of the measure and we show that Frankls conjecture holds for lower quasi-semimodular lattices: if a lattice L is lower quasi-semimodular then there is a join-irreducible element x in L such that the size of the principal filter generated by x is at most (|L|− 1) /2.

A unified theory of decision principles

Abstract The purpose of this paper is to provide a unified framework to investigate the meanings of decision principles. A decision principle is a guiding rule to define a preference order over the set of alternatives for a given decision problem. Although many decision principles have been proposed as rational ones, it is uniformly agreed that no decision principle is uniformly best and it is an important subject for decision theory to explore the meaning of a decision principle to specify when it is reasonable. This problem has been considered in various ways. This paper, first, characterizes & rational decision principle as a rule which satisfies the two conditions, Pareto consistency and the similarity condition. Pareto consistency has been accepted as an essential condition for a rational decision principle. The similarity condition, which is an original idea of this paper, requires that if two decision problems are structurally similar, then their preference orders induced by a rational decision pri...

A STATIONARIZATION FUNCTOR AND ITS CONCRETE REALIZATIONS

The purpose of this paper is lo investigate a transformation of systems in a category theoretic way and to reveal its structural property by showing that the famous Nerode realization and a well known stationarization operation are concrete realizations of the transformation. There is a well-known stationarization operation which transforms a lime variant tlynamicul model given by z =ƒ(t,z,.x) and y = g(t,z,) into a time invariant dynamical model ([udot],z)= (l.ƒ(u,z,x)) and y=g(u,z) where x, y and z are, respectively, an input, an output and a state variable. The paper integrates the Nerode realization and the above stationarization operation by one transformation and shows that they yield minimal causal stationary models using the category-theoretic treatment of the transformation. The paper demonstrates that the category theoretic consideration is powerful in integrating diversified systems concepts and in disclosing their underlying structures. In particular, a certain structural property of a station...

Characterization of the linear weighted sum decision principle

Abstract Recently the multicriterion decision problem (MCDP) has attracted more and more attention, and many decision principles have been proposed for it, among which the linear weighted sum decision principle is the most widely used. This paper discusses an axiomatic characterization of that principle to find out its essential meaning. Firstly, we give an axiomatic system characterizing it. Secondly, we examine the meanings of the axioms. Thirdly, we try to give a logical explanation of why the linear weighted sum decision principle is so popular by comparing it with other decision principles for the MCDP and for decision making under uncertainty. Finally, we investigate whether or not decision principles for the MCDP are applicable to decision making under uncertainty and vice versa.

An analysis of an incentive problem considering non‐monetary utility

The present paper describes a new approach to the agency model, which is a cybernetic model designed to analyze the situation in which an economic actor (the principal) controls the behavior of another actor (the agent), by including the factor of non‐monetary utility (intrinsic motivation). The new model addresses an incentive problem in an organization. An organization is considered to be a system constituted by the principal and the agent. Two state variables of this system, namely productivity and intrinsic motivation, are the focus of the present study. The effect of these variables on how to offer incentive is analyzed. The following results were obtained: when productivity is high and the strength of intrinsic motivation and uncertainty of output are low, organizations should introduce performance‐based incentive system.

Analysis of the incentive problems considering intrinsic motivation and multiple objectives of the agent

The agency theory has often been employed to discuss the incentive problems. In the standard models, the labourers have been assumed to devote their effort only to the objectives given by the organizations. However, in actual organizations, labourers seem to have individual objectives besides the ones assigned by the organizations. In this paper, a new model considering this individual objective is developed, and the question of how to provide incentives according to non-monetary productivity of the organizational and individual objectives is discussed. From the analysis, it is obtained that when the non-monetary productivity of the individual and the organizational objective are low, introducing the piece rate should be effective.

Design of an incentive system for application in a creative organization

The present paper investigates an incentive problem (the method of providing incentives to members) in creative organizations, such as research and development departments, using a cybernetic model called the agency model. In such organizations, members appear to have their own individual objectives which are different from those defined by the organization, and so significant conflicts can exist. Therefore, the proposed model considers the objective of the individual, which is given no consideration in conventional models, and conflict between the objective of the individual and that of the organization. The principles of incentive system design (the effectiveness of the performance‐based wage system) are entirely different depending on whether the conflict exists.

How to design incentive systems based on the multiple signals from agent's behavior

Agency theory has often been employed to discuss the incentive problems. Holmstrom (1979) noted that if there is a signal from the agents behavior, the principal had a better design of incentive systems by considering this signal. In this paper, a model including intrinsic motivation which is given little considerations in the former models is developed. From the analysis, the following results are obtained: 1) when the agent is highly intrinsically motivated, the principal has to take not only the accurate signal but also the noisy signal into account in evaluating the agents behavior; and 2) when the agent is not intrinsically motivated, the principal has to evaluate the agents behavior based on only the signal which has few noises.