CPS Notes Lecture 6 – September 27, 2006
I.
The Power of Institutions—
a)
Institution: set of rules, which has systematic forms of incentives and
disincentives attached to those rules
II. How do we know what we want as a group? What our interest, or preference set, is?
This is the subject for the lecture today
a)
Everything we do today based on Rationality Assumption—preferences are
consistent, ordered, and trasitive
III. Condorcet, 1743-1794
a)
French mathematician who came up with Game Theory
b) How do groups make decisions is the subject of Game Theory, and Condorcet
studied this
c)
Condorcet’s Paradox
i)
Let’s imagine an extremely simple society with 3 players in it
(1) Player I
A > B > C
(2) Player II
B > C > A
(3) Player III
C > A > B
(a) There is no rule here for figuring out what society wants, so no answer
with first of all specifying some rule for deciding how we know what
this society wants
(b) One rule you can use is to prevent some groups, or players, from
expressing their preferences in order to find out what other groups
want
(4) 1
st
Decision Rule: You can pair up particular preferences so let’s do this
(Pairwise Voting)
(a) 1
st
Round: A vs. B = 2 votes for A (I, III), 1 vote for B (II)
(b) 2
nd
Round: B vs. C = 2 votes for B (I, II), 1 votes for C (III)
(c) 3
rd
Round: C vs. A = 2 votes for C (II, III), 1 vote for A (I)
(5) For preference ranking: A > B > C > A > B > C…. this breaks transitivity
(a) This voting rule is known as
Condorcet Cycle
(6) 2
nd
Decision Rule: Run-off voting
(a) 1
st
Round: A vs. B = 2 votes for A (I, III), 1 vote for B (II)
(b) 2
nd
Round: B vs. C = 2 votes for B (I, II), 1 votes for C (III)
(c) Run-Off: A vs. B = 2 votes for A (I, III), 1 vote for B (II)
(d) So A Wins!!!!
(7) 3