Skip to main content

Translation of Weighted Voting Concepts to the Boolean Domain: The Case of the Banzhaf Index | Chapter 10 | Advances in Mathematics and Computer Science Vol. 2

This chapter is a tutorial exposition on how to translate concepts of voting systems to the Boolean domain, and consequently on how to use Boolean tools in the computation of a prominent index of voting powers, viz., the Banzhaf voting index. We discuss Boolean representations for yes-no voting systems, in general, and for weighted voting systems, in particular. Our main observation is that non-minimal winning coalitions are related to minimal ones via partial-order structures and also as particular subordinate loops that cover the all-1 cell in the Karnaugh map. We review the method of computing the total Banzhaf indices by the Conventional Karnaugh Map (CKM). Then we extend this method to handle larger problems via the Variable-Entered Karnaugh Map (VEKM). The map methods are demonstrated by two classical weighted voting systems.


Author(s) Details

Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589, Saudi Arabia.

Omar Mohammed Ba-Rukab
Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, P.O.Box 344, Rabigh 21911, Saudi Arabia.

Comments

Popular posts from this blog

Empowerment and Leader Member Exchange towards Organizational Citizenship Behavior Readiness among Government Workforce in Malaysia | Book Publisher International

  State agencies are among the most significant entities that represent the public's needs, and their programmes are essential to a state's and the nation's economic growth and development. State agencies have been rife by public concerns for years, as demonstrated by the Public Complaints Bureau, as problems of inefficiency in service quality and delivery have yet to meet the public's standards. With the support of 15 employees from state agencies on Malaysia's east coast, this study aims to achieve three targets. The first and second objectives are to investigate the ties between leader-member exchange (LMX) and OCB empowerment. The final aim is to define the most significant factors that affect OCB willingness. A total of 288 people took part in the survey, which was conducted using a cluster sampling process. The survey items had achieved the necessary reliability, according to the pilot test results, and some sub-dimensions were renamed after factor analysis.

Re-asserting Cultural Perspectives: Old People and New Ideas in Bole Butake’s Lake God and The Survivors and Sankie Maimo’s Succession in Sarkov | Chapter 10 | Perspectives of Arts and Social Studies Vol. 2

African cultures have undergone transformations from the colonial period to the present, often to the detriment of its cultural evolution and within the larger global community. As it were, colonial education subordinated African communalism and created in its place an anti-African spirit evident in the assimilation of western values. This did not only end up in a kind of cultural betrayal, but also posed as a serious threat to the dignity and identity of the people. Those who fall prey to this kind of cultural imperialism are the young people who are often irrationally carried away by western fashion and modes that they tend to neglect and/or forget their cultural ways of life as they join the race of “progress.” This situation has given rise to a conscious effort by creative writers to re-assert and protect African values while at the same time liberating themselves from the longstanding western effort at suppressing, controlling and dominating their thoughts particularly through n

The Utilization of Agro-Waste: A Nanobiotechnology Point of View | Chapter 10 | Recent Advances in Biological Research Vol. 5

Aims: To review the utilization of agro-waste in the eco-friendly synthesis of nanoparticles and their biomedical, catalytic and industrial applications. Study Design: A review. Place and Duration of Study: This review was carried out in the interim of three weeks exploiting all relevant data, literature and publications where necessary. Methodology: Profound gathering of literatures/publications and reviews were employed with all carefulness and professional courtesy; enough useful information were gathered over time. The introduction emphasizes the dawn of science and technology, when great ideas were still latent later leading to the advent of history changing innovations like the completion of human genome and then the birth of nanotechnology. Although, nanotechnology had been known decades been popularized by Richard Feynman in his talks in the year 1959; and in this present dispensation, nanotechnology has been a solution to many intricate challenges/ t