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model_thinking.4
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Model Thinking
==============
https://www.coursera.org/modelthinking/class/
Section 4 - Intro to Decision Making
====================================
how people make decisions
how people should make decisions
multi-criterion models
spatial models
decision making under uncertainty
these models have two uses
normative - make us better at deciding
positive - predict the behavior of others
two broad classes of models
multi-criterion
lots of dimensions
choose one alternative vs another
e.g. feature comparisons
probabilistic
uncertainty of outcomes
how to balance risk vs reward
e.g. graph feature X vs feature Y
how far is each choice from the ideal point?
making decisions under uncertainty
don't know how the features will unfold
decision trees
decision trees can also tell us the value of information
Multi-criterion Decision Making
-------------------------------
feature comparison chart - criteria vs options
list allof your criteria
which alternative wins for each criteria?
criteria O1 O2
---------------------------
C1 X
C2 X
C3 X
two approaches
qualitative - simple criterion count
for each criterion, best option gets a point
rank based on # of points
quantitative - weighted criterion count - some criteria mean more than others
add a multiplier (M) to each criterion
for each criterion, best option gets M points
rank based on # of points
Popup quiz
Q - Joanne considered two cameras. Here are their relevant specifications. Camera A: Weight 8 ounces, Memory 12 MB, 5X Zoom, 2 inch screen Camera B: Weight 6 ounces, 10 MB memory, 4X Zoom, 1.5 inch screen What can we say about Joanne's decision making approach?
She uses quantitative methods and cares about zoom
She uses qualitative multi criterion decision making
She's irrational
She uses a quantitative approach and cares a lot about having a light camera
Assuming that less weight, more memory, more zoom power, and a bigger screen are better, then Camera B wins on three of the four criteria Therefore, she must use a quantitative model and care a lot about weight.
[This is either
wrong - since no weights are given, it is qualitative
missing info - the weights were not included]
Spatial Choice Models
---------------------
measuring distance from an ideal point
on a single dimensional scale, or
a multi-dimensional space
single dimension
make a scale mapping range of values for the criterion
place each alternative on the scale based on its score/value for the criterion
hot/cold, left/right, etc
there is an ideal point on the scale
best choice is the alternative closest to the ideal point
Development/applications of the model
Hotelling's location model
Down applied this to how people vote
map candidate on a left vs right scale
d1 = distance between voter and candidate 1
d2 = distance between voter and candidate 2
Gelman - Supreme Court conservativity
not just a simple ranking - adds in data
map conservativity score (Y-axis) for each participant (SC Justice)
do this for multiple points in time (each SC session) on X-axis
Multi-dimensional mapping
burger attributes
attribute ideal O1 D1 O2 D2
----------------------------------------------------
cheese 2 2 0 2 0
patties 2 2 0 1 1
tomatoes 2 0 2 2 0
catsup 4 3 1 3 1
mayo 4 4 0 4 0
pickles 4 6 2 4 0
these attributes would be modeled as six dimensions
a vector of length 6
list each criterion and its ideal value/score
for each alternative
score the alternative at each criterion (O1, O2)
calculate the difference (absolute value) from ideal for each criterion (D1, D2)
sum the differences as the distance from the ideal
best choice (closest to ideal) is lowest sum
use this normatively e.g. to determine who to vote for
positions on issues
use this positively to infer some person's ideal point e.g. burgers example
if someone chose O1, then we can infer that
they prefer two patties, or
they don't like tomatoes, or
they really like pickles, or
some combination of these
(ignore criteria where there is no difference among alternatives)
Development/applications of the model
dw-nominate mapping members of Congress on 2D L/R plane
(Additional thoughts)
you can also weight each ideal
this is a one-dimensional representation on n-dimensional space
each criterion is added as another dimension
e.g. cars - speed vs comfort
there is an ideal point in this multi-dimensional space
use this model to decide what to buy, who to vote for...
how close are the alternatives to the ideal point?
normative
apply the models to data
where are SC Justices or Members of Congress ideologically? (across one or more dimensions)
determine people's product preferences based on purchasing decisions
positive
popup quiz
Q - Jim has spatial preferences over ice cream cones. He cares about the height of the cone in inches and the number of scoops. He chooses a three scoops on a four inch cone over either a double scoop on a seven inch cone or four scoops on a two inch cone, Which of the following could be his ideal point? (assume that he computes the distance from each option to his ideal point).
3 scoops, 5 inch cone
1 scoop, 8 inch cone
2 scoops, 4 inch cone
11 scoops, 3 inch cone
crit ideal O1 O2 O3
scoops 3 2 4
cone 4 7 2
A - He prefers (3,4) to (2,7) and (4,2). If his ideal point were (3,5), his distance to (3,4) would be 2 [this is wrong, the distance from (3,4) to (3,5) is 1]. His distance to (2,7) and (4,2) would be much larger. So (3,5) is possible. (1,8) is not possible as it's closer to (2,7). He would have chosen the two scoops on the seven inch cone. By similar logic (2,4) is possible, but (11,3) is not. If his ideal point was (11,3), he'd have chosen (4,2)
Probability: The Basics
-----------------------
Decision making under uncertainty
need to consider probabilities of criteria, outcomes
probability -the odds of something happening
3 axioms of probability
1) 0 ≤ P ≤ 1
Probability of an outcome is in the range [0,1]
if something can't happen, P = 0
if something is certain to happen, P = 1
2) Σ P = 1
Sum of all possible outcomes equals one
have to make a distinction between outcomes and events
an outcome is an individual thing that can happen
an event is a subset of outcomes
3) A ⊆ B ⇒ P(B) ≥ P(A)
If event A is a subset of event B, the probability of B is greater than the probability of A
e.g. flippng a coin
A = {H}, B = {H,T}
P(A) = 0.5, P(B) = 1
3 types of probability
1) classical probability - all possible outcomes are known, and equally likely
we know why a probability is what it is
dice, coins, cards, lotteries
P(a) = F/N
e.g. roll a die
P(4) = 1/6, P(even) = 3/6, P(odd) = 3/6
2) Relative Frequency - # possible outcomes (n) is so large that we cannot know all of them
we count occurrences of an event within a sample
P(a) = observed f / observed n
e.g. are there more words that begin with r, or that have ras the 3rd letter?
e.g. will it rain on June 7th?
look up weather for last 100 years
P(rain) = F/100 - (F = # times it rained on June 7th)
requries an assumption that nothing has changed over that period of time
3) Subjective probability
a) estimates based on guessing
!!! observe the three axioms when guessing !!!
(Axiom 2 might not have applied in the student example,
unless we were told that one of the choices was the correct answer)
b) estimates determined via models
e.g. will housing prices go up this year?
guess - 30%
popup quiz
Q - If you flip a fair coin and roll a six sided die, what's the probability of getting neither a HEAD or a 3?
5 out of 12
1 out of 6
4 out of 12
1 out of three
A - This means that you have to get a tail (probability 0.5) and get something other than a three (probability 5/6). Therefore we have to multiply those two events and we get 5/12. You can also get this answer by enumerating all possibilities and counting up al the cases where you have a tail and no three. These are T1,T2, T4, T5, and T6.
Decision Trees
--------------