The mathematics of relations
A set is a collection of objects, called its elements, or
members.
Examples:
the set of all dogs
the set of students in this class
the set comprising the numbers 1, 2, and 3
Typically, we use uppercase Roman letter A, B, ., S,
9/2/2014
Risk, Choice, and Rationality
Philosophy 325 A1
Welcome to the Course!
University of Alberta
September 3, 2014
An introduction to decision theory
Decision Theory: theory of instrumental rationality
Introduction to
PHIL 325 A1
The general study
9/4/2014
Risk, Choice, and Rationality
Philosophy 325 A1
How Decision Theory Can be
Controversial
University of Alberta
September 5, 2014
Newcombs Problem: You walk into a room with
two boxes on a table. One is transparent, and you can
see it contains $1
9/7/2014
Risk, Choice, and Rationality
Philosophy 325 A1
Decision Problems & Matrices
A decision problem is defined by:
University of Alberta
September 8, 2014
1. A set of alternative acts you can perform
2. A set of possible outcomes these acts can resu
9/14/2014
Principles that require interval utility to be coherently /
consistently stated:
Risk, Choice, and Rationality
Philosophy 325 A1
Let (between 0 and 1) represent the importance of getting
the best outcome and let (1- ) represent the importance
9/11/2014
Interval Utility
Risk, Choice, and Rationality
Philosophy 325 A1
Interval utility: a numerical measure of an agents
preferences, which includes information about the strength
of her preference for one outcome over another, in relation
for her p
9/9/2014
Decision Principles with Ordinal
Utility
Risk, Choice, and Rationality
Philosophy 325 A1
University of Alberta
September 10, 2014
Decision under uncertainty: no clear expectations
about probabilities of states that determine the
outcomes of our
An Introduction to Decision Theory
MARTIN PETERSON
Royal Institute of Technology, Sweden
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.,.,.~.;., CAMBRIDGE
:
UNIVERSITY PRESS
.
CAMBRIDGE
UNIVERSITY
PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo,
Delhi, Dubai, Toky
An Introduction to Decision Theory
MARTIN PETERSON
Royal Institute afTechnology, Sweden
)
/
I
I
UCAMBRIDGE
:;
UNIVERSITY PRESS
.
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo,
Delhi, DubaL Tokyo, Mexico
An Introduction to Decision Theory
MARTIN PETERSON
Royal Institute of Technology, Sweden
)
I
I
.,.,.~.;., CAMBRIDGE
:
UNIVERSITY PRESS
.
CAMBRIDGE
UNIVERSITY
PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo,
Delhi, Dubai, Toky
9/17/2014
Risk, Choice, and Rationality
Philosophy 325 A1
Decision Making Under Risk
Decision under risk: decision maker has relatively clear
expectations about probabilities of states that determine
outcomes of acts
University of Alberta
September 17, 2
9/18/2014
Paradoxes of Expected Utility
Risk, Choice, and Rationality
Philosophy 325 A1
Standard principle for decision making under risk:
University of Alberta
September 19, 2014
Principle of Maximizing Expected Utility: The rationality of
an act is a
Siddharth Nair | 1269656
Answer 1:
The role of funding for scientific innovations and development is a very vast and crucial
one, that which could shape the future of a prosperous world or hamper the progress and waste
valuable time and resources due to l
Trade-offs and Social choice
Choice without uncertainty: Trade-offs
Making up your mind can be difficult when the available
options have strengths and weaknesses that trade off
against each other.
In this lecture we will look at some basic principles for
Solutions to assignment 1
1.
Harvey loves Sabrina. Sabrina loves Fred. Jennifer loves Fred. Fred loves himself.
xLy means x loves y
S = cfw_Harvey, Sabrina, Fred, Jennifer
1.1
Based on this information define the relation L on the set S as a set of ordere
2.
Seltens chain store problem. A chain store call it Safe-on-food has a
dominant position in two cities, Edmonton and Calgary. Mickey Mouse from Calgary and
Donald Duck from Edmonton are each considering challenging Safe-on-food. In each
city the situati
Power Point presentations
pdf version of this page
This week we learnt the notion of Interpretation (which parallels the notion of assignment
of truth values in SL) and the notions of quantificational truth, falsity, indeterminacy,
equivalence, consistenc
1. Which pair of strategies from the matrix below should be chosen using iterated
dominance? Why? (4 points)
Player 1
U
M
D
B
L
4,0
1,2
3,-1
0,-2
Player 2
C
0,2
2,0
1,-1
0,1
R
-1,0
-1,1
1,1
0,2
E
0,1
1,3
1,0
2,-1
U
M
D
B
L
4,0
1,2
3,-1
0,-2
Player 2
C
0,2
Allaiss gambles
probability matrix
2500000
0
0.1
0
0.1
A
B
C
D
500000
1
0.89
0.11
0
0
0
0.01
0.89
0.9
desirability matrix
2500000
2500000
2500000
2500000
2500000
A
B
C
D
A
B
C
D
500000
500000
500000
500000
500000
0
0
0
0
0
0 2500000 + 1 500000 + 0 0 = 500
Assignment 3
1.
What would be the mixed-strategy Nash equilibrium for the Serve and Volley game
(coursepack p.100) if the raw player (who returns the service) improved his backhand so that he
returns the service successfully 70% when he both expects it an
Some tricky derivations
There are no precise general patterns that will tell you how to do more difficult
derivations. In the following examples the trick is to introduce new assumptions until you
find some that are helpful.
Peirces law: (AB)A)A
1
(AB)A
2
The formal model of decision making under uncertainty
We start with three sets:
1. a set A of acts that the agent is choosing among
2. a set O of possible outcomes
3. a set S of possible states of the world
An act aA is a function from states of the world
An Introduction to Decision Theory
MARTIN PETERSON
Royal Institute afTechnology, Sweden
)
/
I
I
UCAMBRIDGE
:;
UNIVERSITY PRESS
.
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo,
Delhi, DubaL Tokyo, Mexico