Game theory | Cooperative games
The Banzhaf power index, named after John F. Banzhaf III (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights are not necessarily equally divided among the voters or shareholders. To calculate the power of a voter using the Banzhaf index, list all the winning coalitions, then count the critical voters. A critical voter is a voter who, if he changed his vote from yes to no, would cause the measure to fail. A voter's power is measured as the fraction of all swing votes that he could cast. There are some algorithms for calculating the power index, e.g., dynamic programming techniques, enumeration methods and Monte Carlo methods. (Wikipedia).
Weighted Voting: The Banzhaf Power Index
This video explains how to find the Banzhaf power index in a weighted voting system. Site: http://mathispower4u
From playlist Weighted Voting
Banzhaf Power Index Notes & Practice
Notes and guided practice on using the Banzhaf Power Index to evaluate how much power is possessed by each player in a weighted voting system.
From playlist Discrete Math
Math for Liberal Studies - Lecture 2.9.2 The Banzhaf Power Index
This is the second video for Math for Liberal Studies Section 2.9: Power Indices, and the last video for Unit 2: The Mathematics of Voting. In this video, I discuss another power index -- the Banzhaf power index. This is another way of measuring the effective power of voters in a weighted
From playlist Math for Liberal Studies Lectures
Math for Liberal Studies: Banzhaf Power Index
In this video, we learn how to compute the Banzhaf power index for each voter in a weighted voting system. For more info, visit the Math for Liberal Studies homepage: http://webspace.ship.edu/jehamb/mls/index.html
From playlist Math for Liberal Studies
Measuring Power in the Electoral College: Intro to the Banzhaf Power Index
Californians love to complain that their state is the most underrepresented (by population) in the Electoral College. It's true that they have the fewest Electors per million residents, but is this the best way to measure voting power? After all, if, hypothetically, a state had 51% of the
From playlist Summer of Math Exposition Youtube Videos
Physics - Special Relativity (32 of 43) The Lorentz Factor Close-Up
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the Lorentz factor. Next video in the Special Relativity series can be seen at: http://youtu.be/sMBKNmO7aG0
From playlist MODERN PHYSICS 1: SPECIAL RELATIVITY
Physics - Thermodynamics 2: Ch 32.1 Def. and Terms (9 of 23) What is the Gas Constant?
Visit http://ilectureonline.com for more math and science lectures! In this video I will give and explain what is the gas constant and how it was determined. Next video in this series can be seen at: https://youtu.be/8N8TN0L5xiQ
From playlist PHYSICS 32.1 THERMODYNAMICS 2 BASIC TERMS
Watch more videos on http://www.brightstorm.com/science/physics SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► htt
From playlist Physics
Weighted Voting: The Shapley-Shubik Power Index
This video explains how to find the Shapley-Shubik power index in a weighted voting system. Site: http://mathispower4u
From playlist Weighted Voting
From playlist Mathematics of Power
Math Explorations Ep12, Banzhaf power index (Feb 11, 2022)
This is a recording of a live class for Math 1015, Mathematics: An Exploration, an undergraduate course for non-technical majors at Fairfield University, Spring 2022. The major topics are voting, gerrymandering, and graph theory. Handouts and homework are at the class website. Class web
From playlist Math 1015 (Mathematical Explorations) Spring 2022
How to tell the difference between the leading coefficient and the degree of a polynomial
👉 Learn how to find the degree and the leading coefficient of a polynomial expression. The degree of a polynomial expression is the highest power (exponent) of the individual terms that make up the polynomial. For terms with more that one variable, the power (exponent) of the term is the s
From playlist Find the leading coefficient and degree of a polynomial | expression
From playlist Mathematics of Power