University of California, Irvine
Political Science
Professor Marek Kaminski
Designing Institutions of Democracy
Sample Final
There is a total of 60 points + 6 extra points. The number of points for each problem is
indicated in [brackets]. Numerical calcul
University of California, Irvine
Political Science
Professor Marek Kaminski
Designing Institutions of Democracy
Sample Midterm
There is a total of 40 points + 4 extra points.
The number of points for each problem is indicated in [brackets].
Numerical calc
University of California, Irvine
Political Science
Professor Marek Kaminski
Designing Institutions of Democracy
Sample Midterm
There is a total of 40 points + 4 extra points.
The number of points for each problem is indicated in [brackets].
Numerical calc
7: Apportionment
UNIVERSITY OF CALIFORNIA, IRVINE, Voting and Political Manipulation
Apportionment of seats among districts and within districts
in a Proportional Representation political system
Lecture 7: Apportionment and
Proportional Representation
App
L i ice-lb B V- Q W 6k\ K
V PM Discussion Exercise
There is an Assembly with 10 Seats, N. An election: was held and voters chose among ve Parties.
Support for each party was as follows:
Party A 36%
Party B «~ 299/0
Party C - 170/0
Patty D - 11
University of California, Irvine
Political Science
Professor Marek Kaminski
Designing Institutions of Democracy
Sample Final
There is a total of 60 points + 6 extra points. The number of points for each problem is
indicated in [brackets]. Numerical calcul
Introduction
UNIVERSITY OF CALIFORNIA, IRVINE, Voting and Political Manipulation
Lecture 1: Introduction: What is
social choice?
1
Main empirical domains of social choice
Two most important (at least for us) applications of social choice theory:
voting in
1/26/2016
How to I select a winning alt using
[14
Beer
Wine
Soda
]
[10
Juice
Wine
Soda
]
[8]
Water
Wine
Soda
[16
Milk
Wine
Soda
]
[2]
Soda
Wine
Beer
Juice
Water
Milk
Beer
Water
Milk
Beer
Juice
Milk
Beer
Juice
Water
Juice
Water
Milk
Plurality
Most top vo
2/23/16
What are Quota and divisor method for apportioning seats
How do you calculate how many state/party should get using Halmilton-Hare,
Hagenbach-Bischoff, Jefferson dtlondt and Webster-SL?
What is STV?
(N+1) P
(NP)
(N+2) P
Population
State
Propo H
2/2
Strategic voting
Manipulate an agenda make a given alt win
V1: E D A B C
V2: C A B D E
V3: B E A C D
Managing order: E A D C B (given)
Diagram of game tree
E beats A 2:1
E beats D 2;1
B beats E 2:1
B is the winner
Put a managing order to let A win
3/1/16
What re the different types of coalitions?
How do I calculate the Banzhaf index?
4 senators whether to elect either Trump/Clinton
Senators A, B, C, D
Winning Coals: ABC, ABD, ACD, BCD, ABCD
Minimal winning: ABC, ABD, ACD, BCD
Losing: D, C, B, A
1/19/16
XYZ
XpYpZ
X preferred to Y. Y is preferred to Z
Cycle
XYZ
YZX
ZXY
X beats Y 2:1
Y beats Z 2:1
Z beats X 2:1
(X p Y p Z p X)
Cycle no alternative beats the other alternative
Strong Condorcet winner
Alternative that beats all other alternativ
3/8/16
Banzhaf + S-S index Calculating the power each party has
Calculate the Banzhaf index
Banzhaf = pivotal
of all parties are prvotal
A
B
C
4
4
3
Total = 14
To win = 8+
D
3
1. List out all the coalition
None
1 party
coalition
A
B
C
D
3 Party
Coalit