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.