Lecture 4

Question 1

Note

Answer 1

In decision theory it is preference that is being modelled tf it doesn’t give you an ‘order’ as to what to do

Question 2

Define preference?

Answer 2

A term used in relation to choosing between alternatives

Question 3

What is a preference relation?

Answer 3

A special type of binary relation (basically a set of ordered pairs)

Question 4

What is strict preference?

Answer 4

If x>y

Question 5

What is equivalence/indifference?

Answer 5

x~y (ie. x>=y AND y>=x)

Question 6

What is reversed preference?

Answer 6

x<=y IF y>=x

Question 7

What is strict reverse preference?

Answer 7

xx

Question 8

Suppose V represents >= (ie. it evaluates options in agreement with preference), write this in notation form?

Answer 8

[x>=y V(x)>=V(y)]

Tf >= maximises V (dunno why)

Question 9

What is a weak order?

Answer 9

A ranking of options that allows ties

Question 10

2 main properties of a weak order?

Answer 10

Transitive (if x>=y and y>=z then x>=z)

Complete (for all x,y, x>=y or y>=x)

Question 11

2 other properties of a weak order?

Answer 11

Non-triviality - x>y for some x,y

Reflexivity - for all x, x~x

Question 12

See notes

Answer 12

Newcomb’s paradox (Wikipedia)

See arguments for taking 1 and 2 boxes also

Question 13

What is the maximin rule?

Answer 13

Choosing the act/option whose minimum outcome is the best possible minimum outcome out of all options

Question 14

What is the lethical maximin rule?

Answer 14

When there is a tie of best worst outcomes, we move to compare the second worst outcomes and so on and so forth

If all tie then random selection done between tied options

Question 15

See

Answer 15

Slides 14-19

Question 16

What is maximax rule?

Answer 16

To choose an option whose maximum outcome is the best maximum outcome for all the options

Question 17

What is the optimistic-pessimistic rule?

Answer 17

The rule that considers both maximum and minimum outcomes of act/option A, then evaluates it based on own degree of optimism

Question 18

What is the range of the optimism index and what is the equation to calculate the optimistic-pessimistic rule?

Answer 18

0<=α<=1 (1 being max optimism)

α.max(A)+(1-α)min(A)

Question 19

What is the minimax regret rule?

Answer 19

To choose the option where the maximal regret outcome is the minimum for all the maximal regret outcomes

Question 20

Explain the steps for using the minimax regret rule? (3, and equation, and see table in notes)

Answer 20

1) construct regret table
2) identify maximal regret in each act/option
3) identity which act/option’s regret is minimum

Regret = outcome - max outcome in same column