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Lance Fortnow, Northwestern UniversityIncluding Research With:Kim-Sau Chung, University of MinnesotaNikhil 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 beforeRecommendations
from Friends and Others
Reviews: Zagats, Chicago Reader, Google, Yahoo
Restaurants you’ve walked past
Advertisements
How Do We Not ChooseCarefully 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 ChooseCarefully 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 ChooseCarefully 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.
AwarenessSeveral 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.
LimitationsAwareness 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 AwarenessHalpern ’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 AwarenessInformal 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 DefinitionUniverse is set of finite strings over some
alphabet Σ.Environment E:Σ*Σ* and a context yΣ*
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 EnumerationLevin ’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 yU(x|E,y) = The number of steps until NE(y)
outputs x
EmailFrom: RonenTo: Subject: Referee Request
Please referee this paper.
Attachment: Paper.pdf
Papers to Referee
High Awareness
Papers to Referee
Low Awareness
Non-Monotone AwarenessAs 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…
EmailFrom: LanceTo: RonenSubject: Late Report
You still owe me a referee report.
Papers to Referee
High awareness arosefrom change in context
Context: Email askingabout paper.
High Awareness
Human Memory
You can’t be unaware of what you are unaware of.
Battle for Awareness2003
Awareness Level:Very Low
Awareness Level:High
Battle for Awareness2004
Awareness Level:Low
Awareness Level:High
Battle for Awareness2007
Awareness Level:Medium
Awareness Level:High
Battle for Awareness2008
Awareness Level:High
Awareness Level:High
Battle for Awareness2008
Awareness Level:High
Awareness Level:High
Vote on Iraq War
Mandates on Health Care
Battle for Awareness2008
Awareness Level:High
Awareness Level:High
Change
Experience
Battle for Awareness2009
Awareness Level:Highest
Awareness Level:High
President
Secretary ofState
Why do we have calendars?
OrganizersWhy do we keep Calendars?
Make us aware of needed information when the context arises.
To Do ListsAddress BooksEmail ProgramsDesktop SearchPhoto AlbumsBirthday Reminders
Joint work with Kim-Sau Chung, Minnesota
Simple Example
Defense
Plaintiffs
Document
Give Documentto Plaintiffs
Simple ExampleGive Documentto Plaintiffs andmake them computationallyaware of it.
Defense
Plaintiffs
Document
Laws
Pay $50,000
ExclusioExpressio 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 MPHLaw in Florida
Cannot carry concealed weapon.People carried guns out in open.
Rules and StandardsRules: Very specific laws with limited
interpretationTax CodeThree Strikes
Standards: Broadly defined laws that judges interpretReckless drivingPerjury
Someone could follow the letter of a rule but break spirit of law.
Judges may not interpret standard as the legislature intended.
LoopholesLegislature 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-ChicagoVery Preliminary
Decision Making Lots of possible stores:
CostShipping: Time and
CostReliabilityMethods of PaymentReturn Policy
Playstation 3 - Google Search.mht
Role of AdvertisingIncreases 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 SearchClassic 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 SearchOur ModelFor a company C
pC = Probability of click-through conditioned on no click-throughs in earlier slots. Independent of slot.
vC = Value per click
Click-through raterCi = 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 QuestionsWhat 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 ModelUnder 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.
ConclusionsDeveloped new model of Computational
AwarenessComputation 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.
ApplicationsLegal: Possible explanation for loopholes. E-Commerce: Leads to new models of sponsored
search.