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George Bush, Competitive Bayesian MDPs With Influence, and “Blying”. Theodore T. Allen, Ph.D. Associate Professor Industrial, Welding & Systems Engineering. Ronald Reagan. "We did not--repeat, did not--trade weapons or anything else for hostages, nor will we," – Reagan, November 1986

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george bush competitive bayesian mdps with influence and blying

George Bush, Competitive Bayesian MDPs With Influence, and “Blying”

Theodore T. Allen, Ph.D.

Associate Professor

Industrial, Welding & Systems Engineering

ronald reagan
Ronald Reagan

"We did not--repeat, did not--trade weapons or anything else for hostages, nor will we," – Reagan, November 1986

"A few months ago, I told the American people I did not trade arms for hostages. My heart and my best intentions still tell me that's true, but the facts and the evidence tell me it is not." – Reagan, March 1987

  • Was Reagan a “liar” in November 1986?
definitions and goals
Definitions and Goals

Lying – (noun) saying something one believes to be false with the intention to deceive

Truthiness – (noun) the quality of stating concepts or facts one wishes or believes to be true, rather than concepts or facts known to be true (Colbert)

Blying – (noun) the act of communicating beliefs unlikely to be true selected for benefit (Allen)

“You take the blue pill…you wake up in your bed and believe whatever you want to believe.” – Morpheus Character, The Matrix

  • How might blying be modeled using data-driven decision (3D) theory? Insights?
blying examples
Blying Examples
  • My kid is the best kid in the world.
  • “I never intended to deceive.” – Nick Saban
  • Presidential debate (Drum 2004):

Bush # verifiably untrue statements = 18

Kerry # verifiably untrue statements = 11

  • Would anyone here make 11 verifiably untrue statements in a debate?
  • Can these mathematical models explain why “bliars” rise to the top?
blying examples1
Blying Examples

“A Chicago welfare queen had 80 names, 30 addresses, 12 Social Security cards, and collected benefits for four nonexistent deceased husbands, bilking the government out of over $150,000." Reagan over 5 years.

She actually used two different aliases to collect $8,000. Reagan continued to use his version even after... (Allen et. al, 2003)

Reagan’s believed probability queen existed ~ 1.0

Ted’s believed probability queen existed ~ 0.0

  • Today’s focus is on cases in which beliefs are generally less extreme.
outline
Outline
  • Introduction to “blying”
  • Example: supply-side economics
  • Review of Competitive Markov Decision Processes (MDPs)
  • Influence mechanisms
  • Bayesian updating
  • Liars versus bliars
  • Conclusions
allen research group
Allen Research Group

Optimal Design of Search Engines – Ning Zheng, Nilgun Ferhatosmanoglu

Optimal Design of cDNA Microarray Experiments – Nilgun Ferhatosmanlogu

Optimal Design of Experiments for Genetic Network Identification – Cenny Taslim

Meso-Analysis of Six Sigma Projects – Jason Schenk

Quantitative Resilience and Estimation – Jason Schenk

Multi-Fidelity Inverse Engineering with Nano-Technology Applications – Ravishankar Rajagopalan

Bias in Experimental Planning and Analysis – Shih-Hsien Tseng

Recent publications

Design of experiments (how to collect data for data-driven decisions) Technometrics, JQT, JRSSC, J Global Opt.,…

supply side example
Supply Side Example

Facts

i. Top tax rates

ii. Per capita growth rates

iii. Inequality history

Top 5% earners – income, assets, taxes

iv. Deficit history

Modeling

Real Gross Domestic Product (GDP) – Total value of goods and services in 2000 US currency

tax rates and per capita growth
Tax Rates and Per Capita Growth

From eh.com

  • Major adjustments in 1981-1986, 1993, 2001
  • Sample correlation +0.01
inequality history
Inequality History

From

Census Bureau

  • In 1998, top 5% owned 59% wealth, paid 57% taxes
  • Highest inequality of any “advanced industrialized nation”
supply side example1
Supply Side Example

“(My administration will) retire nearly $1T in debt over the next 4 years…the largest debt reduction ever.”– President Bush, 2000

From treasury department

Federal Debt in Trillions

$6T owed to US citizens

Mostly top 5% earners

Money that would

have been taken was borrowed back.

supply side example continued
Supply Side Example Continued

Facts

i. Top tax rates → went down a lot

ii. Growth rates → no obvious change

iii. Rich people → got a lot richer

iv. Deficit history → up to $8.4 trillion

  • Models do not prove these facts
  • Models try to describe the decision processes in 1981, 2001, and today
review markov decision processes
Review Markov Decision Processes

State 1 – GDP = $5T

State 2 – GDP = $7T

State 3 – GDP = $9T

State 4 – GDP = $11T

State 5 – GDP = $13T

Xt is state in period t

Period 1

1980

Period 2

1990

Period 3

2000

Player 1 – bottom 95% US

0.2 0.5 0.3 0.0 0.0

0.0 0.2 0.5 0.3 0.0

0.0 0.0 0.3 0.5 0.2

0.0 0.0 0.0 0.3 0.7

0.0 0.0 0.0 0.1 0.9

p1(a11)= = p1(a21)

Action #1 - Top rate ~ 70%

rt1(st,a = 1) = Profit (Action #1) = 0.2  GDP – $1T  t

rt1(st,a = 2) = Profit (Action #2) = 0.17  GDP – $1T  t

Action #2 – Top rate ~ 35%

competitive mdp references
Competitive MDP References
  • Filar, J. and Vrieze, K. (1996) Competitive Markov Decision Processes

- Readable introduction unifying MDPs and the theory of stochastic games

  • Puterman, M. (1994) Markov Decision Processes

- Readable introduction to basic MDPs

  • Brady, J. (2005) Six Sigma and the University: Teaching, Research, and Meso-Analysis

- Shows how Bayesian MDPs help method selection

supply side example2
Supply Side Example

Player 1 only controller, optimal policy is:

  • Recursion:

EUt*(st) = max rt1(st,a) + S p1t(sj|st,a) EUt+1*(sj)

  • Solution – Rate stays 70% always, rich “suffer”
influence mechanism
Influence Mechanism
  • Suppose player 2 can only affect results by influencing player 1’s probabilities
  • = influence parameter

Max {Expected Profits2[p2(a21)]}

p2

Subject to:

Player 2

1*Original or innate beliefs

p1t(sj|st,a) = (1 – a)p1*t(sj|st,a) + ap2t(sj|st,a)

p S where S is set of believable probabilities

influence mechanism continued
Influence Mechanism Continued

Region a scientific minded, impartial, well-informed observer would consider reasonable

What player considers believable

  • “Good politicians” know S well and can believe from the gut any point in it.
  • Learning about R might hurt their ability.

S

R

supply side example3
Supply Side Example

Player 1 after influence:

Bi-product: Depending on a, player 2 (the rich) may have to believe in strong supply-side effect

bayesian updating
Bayesian Updating

Solution for p2(a21)

Using Dirichlet prior, updating probabilities change is too minor to shift solutions → stubborn

Player 2 – richest 5%

0.0 0.2 0.5 0.3 0.0

0.0 0.1 0.4 0.4 0.1

0.0 0.0 0.1 0.6 0.4

0.0 0.0 0.0 0.1 0.9

0.0 0.0 0.0 0.0 1.0

p2(a21) =

State 1 – GDP = $5T

State 2 – GDP = $7T

State 3 – GDP = $9T

State 4 – GDP = $11T

State 5 – GDP = $13T

liars verses bliars
Liars Verses Bliars
  • Is either irrational?
    • Not necessarily
    • Bliars can be maximizing over probabilities → not leading to intransitivity (irrationality)
    • All players maximize expected utility/profits
  • Immediate impacts:
    • Similar (bliar might have higher a)
    • Both generally dominates (larger search space)
  • Future issues:
    • Bliar makes a poor partner on the unexpected
    • Bliar might make easy adversary in some cases
conclusions
Conclusions
  • Phenomenon of “blying”
  • Example: supply-side economics
  • Review of Competitive Markov Decision Processes (MDPs)
  • Can model influence using convex probabilities
  • Bayesian bliars sometimes appear stubborn
  • Bliars probably worse than liars
  • Next time you are starting to call someone a liar consider whether they are a bliar.
2006 us federal budget trillions
2006 US Federal Budget (Trillions)
  • Not much foreign aid, obvious waste
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