Lecture 4 Flashcards
Note
In decision theory it is preference that is being modelled tf it doesn’t give you an ‘order’ as to what to do
Define preference?
A term used in relation to choosing between alternatives
What is a preference relation?
A special type of binary relation (basically a set of ordered pairs)
What is strict preference?
If x>y
What is equivalence/indifference?
x~y (ie. x>=y AND y>=x)
What is reversed preference?
x<=y IF y>=x
What is strict reverse preference?
xx
Suppose V represents >= (ie. it evaluates options in agreement with preference), write this in notation form?
[x>=y V(x)>=V(y)]
Tf >= maximises V (dunno why)
What is a weak order?
A ranking of options that allows ties
2 main properties of a weak order?
Transitive (if x>=y and y>=z then x>=z)
Complete (for all x,y, x>=y or y>=x)
2 other properties of a weak order?
Non-triviality - x>y for some x,y
Reflexivity - for all x, x~x
See notes
Newcomb’s paradox (Wikipedia)
See arguments for taking 1 and 2 boxes also
What is the maximin rule?
Choosing the act/option whose minimum outcome is the best possible minimum outcome out of all options
What is the lethical maximin rule?
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
See
Slides 14-19
What is maximax rule?
To choose an option whose maximum outcome is the best maximum outcome for all the options
What is the optimistic-pessimistic rule?
The rule that considers both maximum and minimum outcomes of act/option A, then evaluates it based on own degree of optimism
What is the range of the optimism index and what is the equation to calculate the optimistic-pessimistic rule?
0<=α<=1 (1 being max optimism)
α.max(A)+(1-α)min(A)
What is the minimax regret rule?
To choose the option where the maximal regret outcome is the minimum for all the maximal regret outcomes
Explain the steps for using the minimax regret rule? (3, and equation, and see table in notes)
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
