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
.
موضوع الدرس
Prove that
Determine the following groups
Homz(QZ) Hom = (Q13,Z)
Homz(Q), Hom/z/nZ, Qt
for neN-
(2) Every factor group of
adivisible group is divisble.
• If R is a Skew ficald (aring with
identity and each non Zero element is
invertible then every R-module is free.
A: Tan Latitude / Tan P
A = Tan 04° 30'/ Tan 77° 50.3'
A= 0.016960 803 S CA named opposite to latitude,
except when hour angle between 090° and 270°)
B: Tan Declination | Sin P
B Tan 052° 42.1'/ Sin 77° 50.3'
B = 1.34 2905601 SCB is alway named same as
declination)
C = A + B = 1.35 9866404 S CC correction, A+/- B:
if A and B have same name - add, If
different name- subtract)
=
Tan Azimuth 1/Ccx cos Latitude)
Tan Azimuth = 0.737640253
Azimuth
=
S 36.4° E CAzimuth takes combined
name of C correction and Hour Angle - If LHA
is between 0° and 180°, it is named "west", if
LHA is between 180° and 360° it is named "east"
True Azimuth= 143.6°
Compass Azimuth = 145.0°
Compass Error = 1.4° West
Variation 4.0 East
Deviation: 5.4 West
A: Tan Latitude / Tan P
A = Tan 04° 30'/ Tan 77° 50.3'
A= 0.016960 803 S CA named opposite to latitude,
except when hour angle between 090° and 270°)
B: Tan Declination | Sin P
B Tan 052° 42.1'/ Sin 77° 50.3'
B = 1.34 2905601 SCB is alway named same as
declination)
C = A + B = 1.35 9866404 S CC correction, A+/- B:
if A and B have same name - add, If
different name- subtract)
=
Tan Azimuth 1/Ccx cos Latitude)
Tan Azimuth = 0.737640253
Azimuth
=
S 36.4° E CAzimuth takes combined
name of C correction and Hour Angle - If LHA
is between 0° and 180°, it is named "west", if
LHA is between 180° and 360° it is named "east"
True Azimuth= 143.6°
Compass Azimuth = 145.0°
Compass Error = 1.4° West
Variation 4.0 East
Deviation: 5.4 West
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