A mini-society with five individuals has direct democracy and makes decisions by voting over different alternatives. The voters are labeled 1, 2, 3, 4 and 5, respectively. The mini-society is to decide over three locations for supplying public services and is to vote over various proposals. Three locations are put up for voting, namely A, B and C. The voters have the following preferences (with the operator > indicating "preferred to"): 1: B >C> A, 2: A > B> C, 3: C> B> A, 4: A > C > B. and 5: A>B>C. a) Find the majority voting equilibrium, i.e. the outcome of majority voting over the three locations. b) Which alternative wins with Borda rule? c) Which alternative wins with plurality voting method?
A mini-society with five individuals has direct democracy and makes decisions by voting over different alternatives. The voters are labeled 1, 2, 3, 4 and 5, respectively. The mini-society is to decide over three locations for supplying public services and is to vote over various proposals. Three locations are put up for voting, namely A, B and C. The voters have the following preferences (with the operator > indicating "preferred to"): 1: B >C> A, 2: A > B> C, 3: C> B> A, 4: A > C > B. and 5: A>B>C. a) Find the majority voting equilibrium, i.e. the outcome of majority voting over the three locations. b) Which alternative wins with Borda rule? c) Which alternative wins with plurality voting method?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
1
Transcribed Image Text:A mini-society with five individuals has direct democracy and makes decisions by voting over different alternatives. The
voters are labeled 1, 2, 3, 4 and 5, respectively. The mini-society is to decide over three locations for supplying public
services and is to vote over various proposals. Three locations are put up for voting, namely A, B and C. The voters have the
following preferences (with the operator> indicating "preferred to"): 1: B >C> A, 2: A > B> C, 3: C> B> A, 4: A > C > B, and 5:
A> B>C.
a) Find the majority voting equilibrium, i.e. the outcome of majority voting over the three locations.
b) Which alternative wins with Borda rule?
c) Which alternative wins with plurality voting method?
d) Explain the reason for any differences between the results in a), b) and c).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
