a. Give an example of a weighted voting system with four players and such that the Shapley-Shubik power index of P 1 is 3 4 . b. Show that in any weighted voting system with four players a player cannot have a Shapley-Shubik power index of more than 3 4 unless he or she is a dictator. c. Show that in any weighted voting system with N players a player cannot have a Shapley-Shubik power index of more than ( N − 1 ) / N unless he or she is a dictator. d. Give an example of a weighted voting system with N players and such that P 1 has a Shapley-Shubik power index of ( N − 1 ) / N .
a. Give an example of a weighted voting system with four players and such that the Shapley-Shubik power index of P 1 is 3 4 . b. Show that in any weighted voting system with four players a player cannot have a Shapley-Shubik power index of more than 3 4 unless he or she is a dictator. c. Show that in any weighted voting system with N players a player cannot have a Shapley-Shubik power index of more than ( N − 1 ) / N unless he or she is a dictator. d. Give an example of a weighted voting system with N players and such that P 1 has a Shapley-Shubik power index of ( N − 1 ) / N .
a. Give an example of a weighted voting system with four players and such that the Shapley-Shubik power index of
P
1
is
3
4
.
b. Show that in any weighted voting system with four players a player cannot have a Shapley-Shubik power index of more than
3
4
unless he or she is a dictator.
c. Show that in any weighted voting system with N players a player cannot have a Shapley-Shubik power index of more than
(
N
−
1
)
/
N
unless he or she is a dictator.
d. Give an example of a weighted voting system with N players and such that
P
1
has a Shapley-Shubik power index of
(
N
−
1
)
/
N
.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY