Lance Fortnow, Northwestern University
Including Research With:
Kim-Sau Chung, University of Minnesota
Nikhil Devanur, Toyota Technological Institute-Chicago
The Big Question
Where should I eat tonight?
7344 Restaurants in Chicago Area
(According to Yellowpages.com)
How Do We Choose?
 Restaurants you have
eaten at before
 Recommendations from
Friends and Others
 Reviews: Zagats, Chicago
Reader, Google, Yahoo
 Restaurants you’ve
walked past
 Advertisements
How Do We Not Choose
 Carefully examine all 7344 restaurants and make
choice that optimizes the expected happiness from
eating there (type and quality of food, atmosphere, …)
 Traditional decision making theory assumes we do
make choices in this manner.
 We have a lack of awareness of most restaurants.
How Do We Not Choose
 Carefully examine all 7344 restaurants and make
choice that optimizes the expected happiness from
eating there (type and quality of food, atmosphere, …)
 Traditional decision making theory assumes we do
make choices in this manner.
 We have a cost of awareness of most restaurants.
How Do We Not Choose
 Carefully examine all 7344 restaurants and make
choice that optimizes the expected happiness from
eating there (type and quality of food, atmosphere, …)
 Traditional decision making theory assumes we do
make choices in this manner.
 We have a computational cost of awareness of most
restaurants.
Awareness
 Several Proposed Definitions
 φ is a logical formula in some knowledge structure
 Fagin-Halpern ’88: General setup used to define explicit
knowledge of φ as having implicit knowledge of φ and
being aware of φ.
 Modica-Rustichini ‘94: Someone is aware of φ if they
either know φ or know they don’t know φ.
 Modica-Rustichini ‘99/Halpern ‘01: Awareness of φ if
they explicitly know φ or they explicitly know they don’t
explicitly know φ.
Limitations
 Awareness of Logical Formulas that have some truth
value in an interpretation of the logical model.
 What is the truth value of “Pizzeria Uno”?
 Binary: Either you are aware of something or you are
not aware of something.
 Can we have a quantitative notion of awareness?
 Consider Awareness as a process.
 Can we have a computational-based definition of
awareness?
Computational Awareness
 Halpern ’01
 It is possible to consider more computationally oriented
notions of awareness. The problem is then to come up
with interesting notions of awareness that have enough
structure to allow for interesting mathematical analysis.
I believe it should also be possible to use awareness
structures to allow for natural reasoning about
awareness and lack of it (so that an agent can reason, for
example, about the possibility that she is unaware of
certain features that another may be aware of). I am
currently working on modeling such reasoning.
Computational Awareness
 Informal Definition
 The amount of unawareness of an object is the time
needed to enumerate that object in a certain
environment and a context.
 A context is a topic like “restaurant”.
 The Environment would consist of ways to find
restaurants including our memories, interactions with
others, guidebooks, “The Internet”, etc.
Formal Definition
 Universe is set of finite strings over some alphabet Σ.
 Environment E:Σ*Σ* and a context yΣ*
 Enumeration Process M, a oracle Turing machine that
on input y with oracle E will enumerate strings x1, x2, …
 The computational unawareness of x with respect to
Environment E, context y and enumeration process M
is the amount of time M uses before it enumerates x,
infinity if x is never enumerated.
Universal Enumeration
 Levin ’71: There is a universal enumeration algorithm
N such that for every M there is a cM such that for all x,
if ME(y) enumerates x in t steps then NE(y) will
enumerate x in cMt steps.
 cM does not depend on E or y.
 The unawareness of x in Environment E and context y
U(x|E,y) = The number of steps until NE(y) outputs x
Email
 From: Ronen
 To:
 Subject: Referee Request
 Please referee this paper.
 Attachment: Paper.pdf
Papers to Referee
High Awareness
Papers to Referee
Low Awareness
Non-Monotone Awareness
 As the environment changes over time, awareness of
an object can drop.
 Much more aware of a restaurant we ate at yesterday
than one we ate at three years ago.
 But we can recover awareness…
Email
 From: Lance
 To: Ronen
 Subject: Late Report
 You still owe me a referee report.
Papers to Referee
High Awareness
 High awareness arose
from change in context
 Context: Email asking
about paper.
Human Memory
You can’t be unaware of
what you are unaware of.
Battle for Awareness
2003
Awareness Level:
Very Low
Awareness Level:
High
Battle for Awareness
2004
Awareness Level:
Low
Awareness Level:
High
Battle for Awareness
2007
Awareness Level:
Medium
Awareness Level:
High
Battle for Awareness
2008
Awareness Level:
High
Awareness Level:
High
Battle for Awareness
2008
Mandates on
Health Care
Vote on Iraq War
Awareness Level:
High
Awareness Level:
High
Battle for Awareness
2008
Experience
Change
Awareness Level:
High
Awareness Level:
High
Battle for Awareness
2009
President
Awareness Level:
Highest
Secretary of
State
Awareness Level:
High
Why do we have calendars?
Organizers
 Why do we keep Calendars?
 Make us aware of needed information when the context
arises.
 To Do Lists
 Address Books
 Email Programs
 Desktop Search
 Photo Albums
 Birthday Reminders
Joint work with Kim-Sau Chung, Minnesota
Simple Example
Give Document
to Plaintiffs
Defense
Document
Plaintiffs
Simple Example
Give Document
to Plaintiffs and
make them
computationally
aware of it.
Defense
Document
Plaintiffs
Laws
Pay $50,000
Exclusio
 Expressio unius est exclusio alterius
 Expression of the one is exclusion of the other
 “One cannot drive over 50 MPH”
 It’s okay to drive at 47 MPH
 Law in Florida
 Cannot carry concealed weapon.
 People carried guns out in open.
Rules and Standards
 Rules: Very specific laws with limited interpretation
 Tax Code
 Three Strikes
 Standards: Broadly defined laws that judges interpret
 Reckless driving
 Perjury
 Someone could follow the letter of a rule but break
spirit of law.
 Judges may not interpret standard as the legislature
intended.
Loopholes
 Legislature may or may not be unaware of future
circumstances.
 Judge is unaware whether legislature was aware of the
current circumstance.
 We create simple model of laws and circumstances.
 We show in this model not only do loopholes occur,
but legislature may purposely leave in loopholes so
that more general unknown circumstances are
properly handled.
Joint work with Nikhil Devanur, TTI-Chicago
Very Preliminary
Decision Making
 Lots of possible stores:
 Cost
 Shipping: Time and Cost
 Reliability
 Methods of Payment
 Return Policy
Role of Advertising
 Increases awareness of brand (store, product, service)
 Changes environment so that we enumerate the brand
earlier.
 Intuitively makes choosing that brand more likely, if
that brand fits the needs of consumer.
 Sponsored Search Advertising
 Increases awareness in context.
Models for Sponsored Search
 Classic Model (Varian)
 For a company C



rCi = Click-through rate when in position i in list of
advertisers.
vC = Value per click
vC rCi = Value of being in position i.
 vC rCi is independent of advertisers in other slots.
 Sometimes assumed rCi = rC i.
Models for Sponsored Search
 Our Model
 For a company C


pC = Probability of click-through conditioned on no clickthroughs in earlier slots. Independent of slot.
vC = Value per click
 Click-through rate
 rCi = pC j<i (1-pDj) where Dj is the company that wins
bid in position j.
 rCi vC is still value for being in position i. Dependent on
winners in earlier slots.
 Related work by Athey and Ellison.
Research Questions
 What is the best auction mechanism for this setting?
 Truthful.
 Socially efficient.
 Revenue Maximizing.
 Easy to compute.
 Compute equilibrium bids in total and partial
information models.
 Complexity of computing bids in various mechanisms
and information settings.
Testing our Model
 Under different orderings of same companies
 Classic Model

Product of Click-Through rates is fixed (if rCi = rC i)
 Our Model

Sum of Click-Through rates is fixed.
 Both under ideal assumptions.
Conclusions
 Developed new model of Computational Awareness
 Computation not logic based.
 Formal Process-Independent Definition.
 Allows for a gradation of awareness.
 Allows for losing and regaining awareness.
 Seems to fit many intuitive uses of awareness.
 Applications
 Legal: Possible explanation for loopholes.
 E-Commerce: Leads to new models of sponsored search.