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Deep Uncertainty
Lecture 24
November 13, 2023
Review and Questions
Simulation-Optimization
- General approach to decision-making
- Search for approximately “optimal” solutions by evaluating simulation model
- Relies on heuristics (no guarantees about optimality)
- Can be very sensitive to settings and details
Uncertainty and Optimization
Conceptual Assumptions of Optimization
Most optimization frameworks implicitly assume perfect specifications of:
- Model structures/Parameter values
- Decision alternatives
- Probabilities/distributions
Reminder: Bifurcations
Bifurcations occur at thresholds when the qualitative behavior of a system changes.
These thresholds are often associated with a stable state equilibrium transitioning to an unstable one.
Bifurcations and Misspecifications
A Relevant “Quote”
It ain’t what you don’t know that gets you into trouble. It’s what you know for sure that just ain’t so.
– Often attributed to Mark Twain (apocryphal)
How Do We Deal With Misspecification?
If we know something about probabilities: Monte Carlo or decision trees…
What if we don’t?
Deep Uncertainty
What Will CO2 Emissions Be In 2100?
How high do you think CO2 emissions be in 2100?
How High Will CO2 Emissions Be In 2100?
Text: VSRIKRISH to 22333
Why Can’t We Agree?
Future CO2 emissions are dependent on multiple factors which are difficult to forecast:
- economic output
- technological change
- policies and governance
Deep Uncertainty
When there is no consensus probability for an uncertainty, we refer to it as a deep uncertainty.
Another Relevant Quote!
Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns — the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tends to be the difficult ones.
– Donald Rumsfeld, 2002 (emphasis mine)
Translating the Word Salad
- Known Knowns: Certainty
- Known Unknowns: “Shallow” Uncertainty
- Unknown Unknowns: “Deep” Uncertainty or ambiguity
The Ellsberg Paradox
Deep Uncertainty and Decision-Making
“Standard” decision theory assumes people have consistent preferences in the presence of uncertainty, which reflects:
- maximizing some estimation of “losses”;
- under an evaluation of the probabilities of various outcomes.
How do people make decisions under deep uncertainty?
The Two-Urn Game
Consider two urns, each containing 100 balls. Urn A has 50 red, 50 black balls, Urn B is an unknown mix.
You are offered the following bets: - Bet 1A: get \(\$1\) if red ball drawn from Urn A, else \(\$0\). - Bet 2A: get \(\$1\) if black ball drawn from Urn A, else \(\$0\). - Bet 1B: get \(\$1\) if red ball drawn from Urn B, else \(\$0\). - Bet 2B: get \(\$1\) if black ball drawn from Urn B, else \(\$0\).
Do You Prefer Bet 1A or 1B?
Text: VSRIKRISH to 22333
The Ellsberg Paradox (Part 1)
Participants in this experiment were indifferent between 1A and 2A, which is consistent with expected utility theory.
But they also strictly preferred 1A to 1B and 2A to 2B, even though there was no reason to expect that Urn 2 was stacked against them.
Interpretation: People have an aversion to deep uncertainty.
The One-Urn Game
Now there is only one urn, with 30 red balls and 60 (black or yellow) balls (in unknown proportions)
- Bet A: you win \(\$100\) if you draw a red ball;
- Bet B: you win \(\$100\) if you draw a black ball;
- Bet C: you win \(\$100\) if you draw a red or yellow ball;
- Bet D: you win \(\$100\) if you draw a black or yellow ball;
Do You Prefer Bet A or B?
Text: VSRIKRISH to 22333
The One-Urn Game
Now there is only one urn, with 30 red balls and 60 (black or yellow) balls (in unknown proportions)
- Bet A: you win \(\$100\) if you draw a red ball;
- Bet B: you win \(\$100\) if you draw a black ball;
- Bet C: you win \(\$100\) if you draw a red or yellow ball;
- Bet D: you win \(\$100\) if you draw a black or yellow ball;
Do You Prefer Bet C or D?
Text: VSRIKRISH to 22333
The Ellsberg Paradox (Part 2)
Ellsberg found subjects prefer Bet A to Bet B. This is consistent with the Two Urn game: deep uncertainty aversion.
Subjects also preferred Bet D to Bet C. Why is this strange?
Key Takeaways
Key Takeaways
- Misspecification is always a risk when developing a model, but can lead to major errors in the presence of nonlinear systems dynamics.
- Systems can also exhibit deep uncertainties.
- Deep uncertainty increases the risk of misspecification.
- Deep uncertainty can complicate decision-making by leading to inconsistent decisions.
Upcoming Schedule
Upcoming Schedule
Wednesday/Friday: How do we analyze decisions when there is a risk of model misspecification or deep uncertainty?
After Thanksgiving: No class, will schedule 10-minute meetings with teams during class time the week after Thanksgiving to check on project progress. Attendance is required during your meeting.
Assessments
Lab 4: Due Friday
Project: Make sure you check what’s due when!