Decisioi Models - Sections 3 & 4

Aggregation (Lesson 3)

Philip Anderson - Physicist - Nobel Prize Winner - "More is Different"

-  Focuses on looking at systems vice components

-  One molecule of water isn't really wet, it takes many brought together.

Actions

Central Limit Theorem - Add Independent (Uninfluenced by others) Events - Probability Distribution

for Heads and Tails 

   if we have N events ==> mean = N/2

Binomial Distribution - more than 2 options (Not heads and tails)

pN where p is probability of something occurring

Mean = pN

SD  = sqrt(p(1-p)N)

sigma = Standard Deviation = -1 sigma to 1 sigma are seperated by 68%, where there are 2 standard deviations the probability increases to 95%, 3 sigma is 99.75%

Bimodal Distribution

2 peaks in the normal distribution

Six Sigma

Making production processes more predictable

- 3 Sigmas on either side of the mean - < 3.4 in a million

-  Single Rules

-  Family of Rules 

-  Preferences

Cellular Automata Models

Steven Wolfram is the original founder
Four Classes of Behavior in Automata Models

If you use the rules at the top, and start with the first row, then you get the follow-on rows.

  

Normative models - help us make better choices

Positive models - predict behavior of others

Classes of models
Multi-criterion models - selecting a car (many dimensions)

Qualitative Approach  - (create a table that help w/ the decision)(buying a house including sq ft, # bedrooms, # bathrooms, etc) and then filling it in.  Select where each one is better and count them up.

We can now add Quantitative Weights to each of the criteria

Spatial Choice Models
Probabilistic models - when you can compare x and y (fast and comfortable) and how far are we from an ideal point
Ideal Point - select a product closest to your ideal point.
You take the absolute value of the difference ==>  add them up and calc the distance

You can reverse this to explain what we are seeing.

Probability: The Basics
Axiom 1: any probability is between 0 and 1
Axiom 2: Sum of all outcomes is 1
Axiom 3: In an event, if one is a subset of the other, it's probability must be lower than the superset.

Types of probabilities
Classical probabilities (rolling dice, gambling, etc)
Frequency Probability (we look at data and estimate whether it will happen)
Subjective Probabilities (guessing, or using some subjective model)

Decision Trees
Decision Trees - yes/no trees leads to the value of information.  Good for model where there are lots of contingencies.

Scholarship: $5000
200 Applicants
2 Page Essay ($20 cost)
10 Finalists who will have to write a 10 page essay ($40 cost)
                                                 / Win (.1 chance) for 4940
                                  /Essay 2
              /  Selected                \ Lose (.9 chance) for -60
  /Essay                        \ Don't (-20)
X           \ Lose ( -20)
   \Don't start
   





Value of Information -