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

1. George Bush, Competitive Bayesian MDPs With Influence, and “Blying” Theodore T. Allen, Ph.D. Associate Professor Industrial, Welding & Systems Engineering

2. 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?

3. 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?

4. 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?

5. 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.

6. Outline • Introduction to “blying” • Example: supply-side economics • Review of Competitive Markov Decision Processes (MDPs) • Influence mechanisms • Bayesian updating • Liars versus bliars • Conclusions

7. 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.,…

8. 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

9. Tax Rates and Per Capita Growth From eh.com • Major adjustments in 1981-1986, 1993, 2001 • Sample correlation +0.01

10. Inequality History From Census Bureau • In 1998, top 5% owned 59% wealth, paid 57% taxes • Highest inequality of any “advanced industrialized nation”

11. 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.

12. 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

13. 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%

14. 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

15. 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”

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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.

23. 2006 US Federal Budget (Trillions) • Not much foreign aid, obvious waste