Computer Science and the SocioEconomic Sciences
Fred Roberts, Rutgers University
1
CS and SS
•Many recent applications in CS involve
issues/problems of long interest to social scientists:
preference, utility
conflict and cooperation
allocation
incentives
consensus
social choice
measurement
•Methods developed in SS beginning to be used in
CS
2
CS and SS
•CS applications place great strain on SS methods
Sheer size of problems addressed
Computational power of agents an issue
Limitations on information possessed by
players
Sequential nature of repeated applications
•Thus: Need for new generation of SS methods
•Also: These new methods will provide powerful
tools to social scientists
3
CS and SS: Outline
1.CS and Consensus/Social Choice
2. CS and Game Theory
3. Algorithmic Decision Theory
4
CS and SS: Outline
CS and Consensus/Social Choice
2. CS and Game Theory
3. Algorithmic Decision Theory
5
CS and Consensus/Social Choice
• Relevant social science problems: voting, group
decision making
• Goal: based on everyone’s
opinions, reach a “consensus”
• Typical opinions:
 “first choice”
ranking of all alternatives
scores
classifications
• Long history of research on such problems.
6
CS and Consensus/Social Choice
Background: Arrow’s Impossibility Theorem:
There is no “consensus method” that satisfies
certain reasonable axioms about how societies
should reach decisions.
Input: rankings of alternatives.
Output: consensus ranking.
Kenneth Arrow
Nobel prize winner
7
CS and Consensus/Social Choice
There are widely studied and widely used
consensus methods.
One well-known consensus method:
“Kemeny-Snell medians”: Given set
of rankings, find ranking minimizing
sum of distances to other rankings.
John Kemeny,
pioneer in time sharing
in CS
Kemeny-Snell medians are having
surprising new applications in CS.
8
CS and Consensus/Social Choice
Kemeny-Snell distance between rankings: twice
the number of pairs of candidates i and j for
which i is ranked above j in one ranking and
below j in the other + the number of pairs that
are ranked in one ranking and tied in another.
Kemeny-Snell median: Given rankings a1, a2, …,
ap, find a ranking x so that
d(a1,x) + d(a2,x) + … + d(ap,x)
is minimized.
Sometimes just called Kemeny median.
9
CS and Consensus/Social Choice
a1
Fish
Chicken
Beef
a2
Fish
Chicken
Beef
a3
Chicken
Fish
Beef
Median = a1.
If x = a1:
d(a1,x) + d(a2,x) + d(a3,x) = 0 + 0 + 2
is minimized.
If x = a3, the sum is 4.
For any other x, the sum is at least 1 + 1 + 1 = 3.
10
CS and Consensus/Social Choice
a1
Fish
Chicken
Beef
a2
Chicken
Beef
Fish
a3
Beef
Fish
Chicken
Three medians = a1, a2, a3.
This is the “voter’s paradox” situation.
11
CS and Consensus/Social Choice
a1
Fish
Chicken
Beef
a2
Chicken
Beef
Fish
a3
Beef
Fish
Chicken
Note that sometimes we wish to minimize
d(a1,x)2 + d(a2,x)2 + … + d(ap,x)2
A ranking x that minimizes this is called a
Kemeny-Snell mean.
In this example, there is one mean: the ranking
declaring all three alternatives tied.
12
CS and Consensus/Social Choice
a1
Fish
Chicken
Beef
a2
Chicken
Beef
Fish
a3
Beef
Fish
Chicken
If x is the ranking declaring Fish, Chicken
and Beef tied, then
d(a1,x)2 + d(a2,x)2 + … + d(ap,x)2 = 32 + 32 + 32 =
27.
Not hard to show this is minimum.
13
CS and Consensus/Social Choice
Theorem (Bartholdi, Tovey, and Trick, 1989;
Wakabayashi, 1986): Computing the Kemeny
median of a set of rankings is an NP-complete
problem.
14
Meta-search and Collaborative
Filtering
Meta-search
• A consensus problem
• Combine page rankings from several search
engines
• Dwork, Kumar, Naor, Sivakumar (2000):
Kemeny-Snell medians good in spam resistance
in meta-search (spam by a page if it causes
meta-search to rank it too highly)
• Approximation methods make this
15
computationally tractable
Meta-search and Collaborative
Filtering
Collaborative Filtering
• Recommending books or movies
• Combine book or movie ratings
• Produce ordered list of books or movies to
recommend
• Freund, Iyer, Schapire, Singer (2003):
“Boosting” algorithm for combining rankings.
• Related topic: Recommender Systems
16
Meta-search and Collaborative
Filtering
A major difference from SS applications:
• In SS applications, number of voters is large,
number of candidates is small.
• In CS applications, number of voters (search
engines) is small, number of candidates (pages)
is large.
• This makes for major new complications and
research challenges.
17
Large Databases and Inference
• Real data often in form of sequences
• GenBank has over 7 million sequences
comprising 8.6 billion bases.
• The search for similarity or patterns has
extended from pairs of sequences to finding
patterns that appear in common in a large
number of sequences or throughout the database:
“consensus sequences”.
• Emerging field of “Bioconsensus”: applies SS
consensus methods to biological databases.
18
Large Databases and Inference
Why look for such patterns?
Similarities between sequences or parts of
sequences lead to the discovery of shared
phenomena.
For example, it was discovered that the sequence
for platelet derived factor, which causes growth
in the body, is 87% identical to the sequence for
v-sis, a cancer-causing gene. This led to the
discovery that v-sis works by stimulating
growth.
19
Large Databases and Inference
Example
Bacterial Promoter Sequences studied by
Waterman (1989):
RRNABP1:
TNAA:
UVRBP2:
SFC:
ACTCCCTATAATGCGCCA
GAGTGTAATAATGTAGCC
TTATCCAGTATAATTTGT
AAGCGGTGTTATAATGCC
Notice that if we are looking for patterns of length
4, each sequence has the pattern TAAT.
20
Large Databases and Inference
Example
Bacterial Promoter Sequences studied by
Waterman (1989):
RRNABP1:
TNAA:
UVRBP2:
SFC:
ACTCCCTATAATGCGCCA
GAGTGTAATAATGTAGCC
TTATCCAGTATAATTTGT
AAGCGGTGTTATAATGCC
Notice that if we are looking for patterns of length
4, each sequence has the pattern TAAT.
21
Large Databases and Inference
Example
However, suppose that we add another sequence:
M1 RNA: AACCCTCTATACTGCGCG
The pattern TAAT does not appear here.
However, it almost appears, since the pattern
TACT appears, and this has only one mismatch
from the pattern TAAT.
22
Large Databases and Inference
Example
However, suppose that we add another sequence:
M1 RNA: AACCCTCTATACTGCGCG
The pattern TAAT does not appear here.
However, it almost appears, since the pattern
TACT appears, and this has only one mismatch
from the pattern TAAT.
So, in some sense, the pattern TAAT is a good
consensus pattern.
23
Large Databases and Inference
Example
We make this precise using best mismatch
distance.
Consider two sequences a and b with b longer than
a.
Then d(a,b) is the smallest number of mismatches
in all possible alignments of a as a consecutive
subsequence of b.
24
Large Databases and Inference
Example
a = 0011, b = 111010
Possible Alignments:
111010
111010
111010
0011
0011
0011
The best-mismatch distance is 2, which is achieved
in the third alignment.
25
Large Databases and Inference
Example
Now given a database of sequences a1, a2, …, an.
Look for a pattern of length k.
One standard method (Smith-Waterman): look for
a consensus sequence b that minimizes
i[k-d(b,ai)]/d(b,ai),
where d is best mismatch distance.
In fact, this turns out to be equivalent to
calculating medians like Kemeny-Snell medians.
Algorithms for computing consensus sequences
26
are important in modern molecular biology.
Large Databases and Inference
Preferential Queries
• Look for flight from New York to Beijing
• Have preferences for
airline
itinerary
type of ticket
• Try to combine responses from multiple travelrelated websites
• Sequential decision making: Next query or
information access depends on prior responses.
27
Consensus Computing, Image Processing
• Old SS problem: Dynamic modeling of how
individuals change opinions over time,
eventually reaching consensus.
• Often use dynamic models on graphs
• Related to neural nets.
• CS applications: distributed computing.
• Values of processors in a network are updated
until all have same value.
28
Consensus Computing, Image Processing
•
•
•
•
CS application: Noise removal in digital images
Does a pixel level represent noise?
Compare neighboring pixels.
If values beyond threshold, replace pixel value
with mean or median of values of neighbors.
• Related application in distributed computing.
• Values of faulty processors are replaced by those
of neighboring non-faulty ones.
• Berman and Garay (1993) use “parliamentary
procedure” called cloture
29
Computational Intractability of Consensus
Functions
• Bartholdi, Tovey and Trick: There are voting
schemes where it can be computationally
intractable to determine who won an election.
• Computational intractability can be a good thing
in an election: Designing voting systems where
it is computationally intractable to “manipulate”
the outcome of an election by “insincere voting”:
 Adding voters
 Declaring voters ineligible
 Adding candidates
 Declaring candidates ineligible
30
Electronic Voting
• Issues:
Correctness
Anonymity
Availability
Security
Privacy
31
Electronic Voting
Security Risks in Electronic Voting
• Threat of “denial of service attacks”
• Threat of penetration attacks involving a
delivery mechanism to transport a malicious
payload to target host (thru Trojan horse or
remote control program)
• Private and correct counting of votes
• Cryptographic challenges to keep votes private
• Relevance of work on secure multiparty
computation
32
Electronic Voting
Other CS Challenges:
• Resistance to “vote buying”
• Development of user-friendly interfaces
• Vulnerabilities of communication path between
the voting client (where you vote) and the server
(where votes are counted)
• Reliability issues: random hardware and
software failures
33
Software & Hardware Measurement
• Theory of measurement developed by
mathematical social scientists
• Measurement theory studies ways to combine
scores obtained on different criteria.
• A statement involving scales of
measurement is considered meaningful if its
truth or falsity is unchanged under acceptable
transformations of all scales involved.
• Example: It is meaningful to say that I weigh
more than my daughter.
• That is because if it is true in kilograms, then it
is also true in pounds, in grams, etc.
34
Software & Hardware Measurement
• Measurement theory has studied what statements you
can make after averaging scores.
• Think of averaging as a consensus method.
• One general principle: To say that the average score of
one set of tests is greater than the average score of
another set of tests is not meaningful (it is
meaningless) under certain conditions.
• This is often the case if the averaging procedure is to
take the arithmetic mean: If s(xi) is score of xi, i = 1, 2,
…, n, then arithmetic mean is
is(xi)/n.
• Long literature on what averaging methods lead to
meaningful conclusions.
35
Software & Hardware Measurement
A widely used method in hardware measurement:
Score a computer system on different
benchmarks.
Normalize score relative to performance of
one base system
Average normalized scores
Pick system with highest average.
Fleming and Wallace (1986): Outcome can
depend on choice of base system.
Meaningless in sense of measurement theory
Leads to theory of merging normalized scores
36
Software & Hardware Measurement
Hardware Measurement
P R
R
O
C
M
E
S
S
O Z
R
E
417
BENCHMARK
F
G
H
83
66 39,449
I
772
244
70
153
33,527
368
134
70
135
66,000
369
37
Data from Heath, Comput. Archit. News (1984)
Software & Hardware Measurement
Normalize Relative to Processor R
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.00
BENCHMARK
F
G
H
I
83
66 39,449 772
1.00 1.00
1.00 1.00
244
.59
70
.84
153
2.32
33,527
.85
368
.48
134
.32
70
.85
135
2.05
66,000
1.67
369
.45
38
Software & Hardware Measurement
Take Arithmetic Mean of Normalized Scores
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.00
Arithmetic
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.00
1.00 1.00
1.00 1.00
244
.59
70
.84
153
2.32
33,527
.85
368
.48
1.01
134
.32
70
.85
135
2.05
66,000
1.67
369
.45
1.07
39
Software & Hardware Measurement
Take Arithmetic Mean of Normalized Scores
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.00
Arithmetic
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.00
1.00 1.00
1.00 1.00
244
.59
70
.84
153
2.32
33,527
.85
368
.48
1.01
134
.32
70
.85
135
2.05
66,000
1.67
369
.45
1.07
Conclude that machine Z is best
40
Software & Hardware Measurement
Now Normalize Relative to Processor M
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.71
BENCHMARK
F
G
H
I
83
66 39,449 772
1.19
.43
1.18 2.10
244
1.00
70
1.00
153
1.00
33,527 368
1.00 1.00
134
.55
70
1.00
135
.88
66,000 369
1.97 1.00
41
Software & Hardware Measurement
Take Arithmetic Mean of Normalized Scores
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.71
Arithmetic
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.32
1.19
.43
1.18 2.10
244
1.00
70
1.00
153
1.00
33,527 368
1.00 1.00
1.00
134
.55
70
1.00
135
.88
66,000 369
1.97 1.00
1.08
42
Software & Hardware Measurement
Take Arithmetic Mean of Normalized Scores
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.71
Arithmetic
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.32
1.19
.43
1.18 2.10
244
1.00
70
1.00
153
1.00
33,527 368
1.00 1.00
1.00
134
.55
70
1.00
135
.88
66,000 369
1.97 1.00
1.08
43
Conclude that machine R is best
Software and Hardware Measurement
• So, the conclusion that a given machine is best
by taking arithmetic mean of normalized scores
is meaningless in this case.
• Above example from Fleming and Wallace
(1986), data from Heath (1984)
• Sometimes, geometric mean is helpful.
• Geometric mean is
n

 is(xi)
44
Software & Hardware Measurement
Normalize Relative to Processor R
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.00
Geometric
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.00
1.00 1.00
1.00 1.00
244
.59
70
.84
153
2.32
33,527
.85
368
.48
.86
134
.32
70
.85
135
2.05
66,000
1.67
369
.45
.84
Conclude that machine R is best
45
Software & Hardware Measurement
Now Normalize Relative to Processor M
P R
R
O
C
M
E
S
S
O Z
R
E
417
1.71
Geometric
BENCHMARK
Mean
F
G
H
I
83
66 39,449 772
1.17
1.19
.43
1.18 2.10
244
1.00
70
1.00
153
1.00
33,527 368
1.00 1.00
1.00
134
.55
70
1.00
135
.88
66,000 369
1.97 1.00
.99
Still conclude that machine R is best
46
Software and Hardware Measurement
• In this situation, it is easy to show that the conclusion
that a given machine has highest geometric mean
normalized score is a meaningful conclusion.
• Even meaningful: A given machine has geometric
mean normalized score 20% higher than another
machine.
• Fleming and Wallace give general conditions under
which comparing geometric means of normalized
scores is meaningful.
• Research area: what averaging procedures make sense
in what situations? Large literature.
• Note: There are situations where comparing arithmetic
means is meaningful but comparing geometric means is
47
not.
Software and Hardware Measurement
• Message from measurement theory to computer
science:
Do not perform arithmetic operations on
data without paying attention to whether
the conclusions you get are meaningful.
48
CS and SS: Outline
1.CS and Consensus/Social Choice
2. CS and Game Theory
3. Algorithmic Decision Theory
49
CS and Game Theory
• Game theory a long history in
economics; also in operations research,
mathematics
• Recently, computer scientists
discovering relevance to their problems
• Increasingly complex games arise in
practical applications: auctions, Internet
• Need new game-theoretic methods for
CS problems.
• Need new CS methods to solve modern
game theory problems.
50
CS and Game Theory: Algorithmic
Issues
Nash Equilibrium
• Each player chooses a strategy
• If no player can benefit by changing
his strategy while others leave theirs
unchanged, we are in Nash
equilibrium.
• In 1951, Nash showed every game John Nash
has a Nash equilibrium.
Nobel prize winner
• How hard is this to compute?
51
Example: Nash Equilibrium
• 2-player game
• Strategy =
number
between 0 and
3
• Both players
win lower
amount.
• Player with
higher amount
pays $2 to
player with
lower amount
0
Player 2 strategy
2
1
3
0,0
2,-2
2,-2
2,-2
Player 1 1
strategy
-2,2
1,1
3,-1
3,-1
2
-2,2
-1,3
2,2
4,0
3
-2,2
-1,3
0,4
3,3
0
Source: Wikipedia
52
Example: Nash Equilibrium
• 0-0 is unique
Nash
equilibrium
• Any other
strategy: one
player can
lower his to
below other’s
and improve.
0
Player 2 strategy
2
1
3
0,0
2,-2
2,-2
2,-2
Player 1 1
strategy
-2,2
1,1
3,-1
3,-1
2
-2,2
-1,3
2,2
4,0
3
-2,2
-1,3
0,4
3,3
0
Source: Wikipedia
53
Example: Nash Equilibrium
• 0-0 is unique
Nash
equilibrium
• Any other
strategy: one
player can
lower his to
Player 1
below other’s strategy
and improve.
• E.g.: From 2-2,
player 1 lowers
his number to
1
0
Player 2 strategy
2
1
3
0
0,0
2,-2
2,-2
2,-2
1
-2,2
1,1
3,-1
3,-1
2
-2,2
-1,3
2,2
4,0
3
-2,2
-1,3
0,4
3,3
Source: Wikipedia
54
Example: Nash Equilibrium
• 0-0 is unique
Nash
equilibrium
• Any other
strategy: one
player can
lower his to
Player 1
below other’s strategy
and improve.
• E.g.: From 2-2,
player 1 lowers
his number to
1
0
Player 2 strategy
2
1
3
0
0,0
2,-2
2,-2
2,-2
1
-2,2
1,1
3,-1
3,-1
2
-2,2
-1,3
2,2
4,0
3
-2,2
-1,3
0,4
3,3
Source: Wikipedia
55
Example: Nash Equilibrium
• 0-0 is unique
Nash
equilibrium
• Any other
strategy: one
player can
lower his to
Player 1
below other’s strategy
and improve.
• E.g.: From 2-2,
player 1 lowers
his number to
1 (or player 2
lowers his to 1)
0
Player 2 strategy
2
1
3
0
0,0
2,-2
2,-2
2,-2
1
-2,2
1,1
3,-1
3,-1
2
-2,2
-1,3
2,2
4,0
3
-2,2
-1,3
0,4
3,3
Source: Wikipedia
56
CS and Game Theory: Algorithmic
Issues
Nash Equilibrium
• 2-player games: can use linear programming
methods.
• Recent powerful result (Daskalakis, Goldberg,
Papadimitriou 2005): for 4-player games,
problem is PPAD-complete.
• (PPAD: class of search problems where solution
is known to exist by graph-theoretic arguments.)
• PPAD-complete means: If exists polynomial
algorithm, then exists one for Brouwer fixed
57
points, which seems unlikely.
CS and Game Theory: Algorithmic
Issues
Other Algorithmic Challenges
• Repeated games.
• Issues of sequential decision making
• Issues of learning to play
• Other “solution concepts” in multi-player
games: “power indices” (Shapley, Banzhaf,
Coleman)
Need calculate them for huge games
Mostly computationally intractable
Arise in many applications in CS, e.g.,
multicasting
58
Computational Issues in Auction Design
• Auctions increasingly used
in business and
government.
• Information technology
allows complex auctions
with huge number of
bidders.
• Auctions are unusually
complicated games.
59
Computational Issues in Auction Design
Bidding functions maximizing expected profit
can be exceedingly difficult to compute.
Determining the winner of an auction can be
extremely hard. (Rothkopf, Pekec, Harstad
1998)
60
Computational Issues in Auction Design
Combinatorial Auctions
• Multiple goods auctioned off.
• Submit bids for combinations of goods.
• This leads to NP-complete allocation
problems.
• Might not even be able to feasibly express all
possible preferences for all subsets of goods.
• Rothkopf, Pekec, Harstad (1998): determining
winner is computationally tractable for many
economically interesting kinds of
61
combinations.
Computational Issues in Auction Design
Some other Issues:
• Internet auctions: Unsuccessful bidders
learn from previous auctions.
• Issues of learning in repeated plays of
a game.
• Related to software agents acting on
behalf of humans in electronic
marketplaces based on auctions.
• Cryptographic methods needed to
preserve privacy of participants.
62
Allocating/Sharing Costs & Revenues
• Game-theoretic solutions have long
been used to allocate costs to different
users in shared projects.
Allocating runway fees in airports
Allocating highway fees to trucks of
different sizes
Universities sharing library facilities
Fair allocation of telephone calling
charges among users sharing
complex phone systems (Cornell’s
experiment)
63
Allocating/Sharing Costs & Revenues
Shapley Value
• Shapley value assigns a payoff to each player
in a multi-player game.
• Consider a game in which some coalitions of
players win and some lose, with no subset of
a losing coalition winning.
• Consider a coalition forming at random, one
player at a time.
• A player i is pivotal if addition of i throws
coalition from losing to winning.
• Shapley value of i = probability i is pivotal if
an order of players is chosen at random.
• In such games with winners/losers, called
Shapley-Shubik power index.
Lloyd Shapley
64
Allocating/Sharing Costs & Revenues
Shapley Value
Example: Board of Directors of Company
Shareholder 1 holds 3 shares.
Shareholders 2, 3, 4, 5, 6, 7 hold 1 share each.
A majority of shares are needed to make a decision.
Coalition {1,4,6} is winning.
Coalition {2,3,4,5,6} is winning.
Shareholder 1 is pivotal if he is 3rd, 4th, or 5th.
So shareholder 1’s Shapley value is 3/7.
Sum of Shapley values is 1 (since they are probabilities)
Thus, each other shareholder has Shapley value
65
(4/7)/6 = 2/21
Allocating/Sharing Costs & Revenues
Shapley Value
Allocating Runway Fees at Airports
Larger planes require longer runways.
Divide runways into meter-long
segments.
Each month, we know how many
landings a plane has made.
Given a runway of length y meters,
consider a game in which the
players are landings and a coalition
“wins” if the runway is not long
enough for planes in the coalition.
66
Allocating/Sharing Costs & Revenues
Shapley Value
Allocating Runway Fees at Airports
A landing is pivotal if it is the first
landing added that makes a coalition
require a longer runway.
The Shapley value gives the cost of the
yth meter of runway to a given
landing.
We then add up these costs over all
runway lengths a plane requires and
all landings it makes.
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Allocating/Sharing Costs & Revenues
Multicasting
• Applications in multicasting.
• Unicast routing: Each packet sent from a
source is delivered to a single receiver.
• Sending it to multiple sites: Send multiple
copies and waste bandwidth.
• In multicast routing: Use a directed tree
connecting source to all receivers.
• At branch points, a packet is duplicated as
necessary.
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Multicasting
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Allocating/Sharing Costs & Revenues
Multicasting
• Multicast routing: Use a directed tree
connecting source to all receivers.
• At branch points, a packet is duplicated as
necessary.
• Bandwidth is not directly attributable to a
single receiver.
• How to distribute costs among receivers?
• One idea: Use Shapley value.
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Allocating/Sharing Costs & Revenues
• Feigenbaum, Papadimitriou, Shenker (2001):
no feasible implementation for Shapley value
in multicasting.
• Note: Shapley value is uniquely characterized
by four simple axioms.
• Sometimes we state axioms as general
principles we want a solution concept to have.
• Jain and Vazirani (1998): polynomial time
computable cost-sharing algorithm
 Satisfying some important axioms
 Calculating cost of optimum multicast tree within
factor of two of optimal.
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Bounded Rationality
• Traditional game theory assumption: Strategic
agents are fully rational; can completely
reason about consequences of their actions.
• But: Consider bounded computational power.
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Bounded Rationality
Some issues:
• Looking at bounded rationality as bounded recall in
repeated games.
• Modeling bounded rationality when strategies are
limited to those implementable on finite state
automata
• What are optimal strategies in large, complex games
arising in CS applications for players with bounded
computational power?
• E.g.: How do players with limited computational
power determine minimal bid increases in an auction
to transform losing bids into winning ones?
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Streaming Data in Game Theory
Streaming Data Analysis:
• When you only have one shot at the
data as it streams by
• Widely used to detect trends and
sound alarms in applications in
telecommunications and finance
• AT&T uses this to detect fraudulent
use of credit cards or impending
billing defaults
• Other relevant work: methods for
detecting fraudulent behavior in
financial systems
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Streaming Data in Game Theory
Streaming Data Analysis:
• “One pass” mechanism of interest in game
theory-based allocation schemes in
multicasting Herzog, Shenker, Estrin (1997)
• Arises in on-line auctions.
Need to develop bidding strategies if only
one pass is allowed
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CS and SS: Outline
1.CS and Consensus/Social Choice
2. CS and Game Theory
3. Algorithmic Decision Theory
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Algorithmic Decision Theory
• Decision makers in many fields (engineering,
medicine, economics, …) have:
Remarkable new technologies to use
Huge amounts of information to help them
Ability to share information at unprecedented
speeds and quantities
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Algorithmic Decision Theory
• These tools bring daunting new problems:
Massive amounts of data are often
incomplete, unreliable, or distributed
Interoperating/distributed decision makers
and decision making devices need
coordination
Many sources of data need to be fused into a
good decision.
• There are few highly efficient algorithms to
support decisions.
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Sequential Decision Making
• Making some decisions before all data
is in.
• Sequential decision problems arise in:
Communication networks
Testing connectivity, paging
cellular customers, sequencing
tasks
Manufacturing
Testing machines, fault
diagnosis, routing customer
service calls
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Sequential Decision Making
• Sequential decision problems arise in:
Artificial Intelligence
Optimal derivation strategies in
knowledge bases, best-value
satisficing search, coding decision
tables
Medicine
Diagnosing patients, sequencing
treatments
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Sequential Decision Making
Online Text Filtering Algorithms
• We seek to identify “interesting” documents
from a stream of documents
• Widely studied problem in machine learning
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Sequential Decision Making
Online Text Filtering Algorithms: A Model
• As a document arrives, need to decide whether or
not to present it to an oracle
• If document presented to oracle and is interesting,
get r reward units.
• If presented and not interesting, get penalty of c
units.
• What is a strategy for maximizing expected
payoff?
• See Fradkin and Littman (2005) for recent work
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using sequential decision making methods
Inspection Problems
• Inspection problem: in what order to
do tests to inspect containers for drugs,
bombs, etc.?
• Do we inspect? What test do we do next?
How do outcomes of earlier tests affect this
decision?
• Simplest case: Entities being inspected need
to be classified as ok (0) or suspicious (1).
• Binary decision tree model for testing.
• Follow left branch if ok, right branch if
suspicious.
• Find cost-minimizing binary decision tree.
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Inspection Problems
Follow left branch if
ok, right branch if
suspicious.
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Sequential Decision Making Problem
Some More Details:
•Containers have attributes, each
in a number of states
•Sample attributes:
Levels of certain kinds of chemicals or
biological materials
Whether or not there are items of a certain
kind in the cargo list
Whether cargo was picked up in a certain port
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Sequential Decision Making Problem
•Simplest Case: Attributes are in state 0 or 1
•State 1 means have attribute and that is
suspicious.
•Then: Container is a binary string like 011001
•So: Classification is a decision function F that
assigns each binary string to a category 0 or 1: A
Boolean function.
011001
F(011001)
If attributes 2, 3, and 6 are present and others are
not, assign container to category F(011001).
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Binary Decision Tree Approach
•Reach category 1 from
the root by:
a0 L to a1 R a2 R 1 or
a0 R a2 R1
•Container classified in
category 1 iff it has
a1 and a2 and not a0 or
a0 and a2 and possibly a1.
•Corresponding Boolean
function F(111) = F(101)
= F(011) = 1, F(abc) = 0
otherwise.
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Binary Decision Tree Approach
•This binary decision
tree corresponds to the
same Boolean function
F(111) = F(101) =
F(011) = 1, F(abc) = 0
otherwise.
However, it has one less
observation node ai. So,
it is more efficient if all
observations are equally
costly and equally likely.
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Binary Decision Tree Approach
•Realistic problem much more difficult:
Test result errors
Tests cost different amounts of money and
take different amounts of time
There are queues to wait for testing
One can adjust the thresholds of detectors.
There are penalties for false negatives and
false positives.
•Challenging problems
for computer science
Gamma ray
detector
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Inspection Problems
• Problem of finding optimal binary
decision tree has many other uses:
AI: rule-based systems
Circuit complexity
Reliability analysis
Theory of programming/databases
• In general, problem is NP-complete
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Inspection Problems
• Some cases of decision functions
where the problem is tractable:
k-out-of-n systems
Certain series-parallel systems
Read-once systems
“regular systems”
Horn systems
• Recent results in case of inspection
problems at ports: Stroud and Saeger
(2004), Anand, et al. (2006).
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• Successful decision making requires efficient
elicitation of information and efficient
representation of the information elicited.
• Old problems in the social sciences.
• Computational aspects becoming a focal point
because of need to deal with massive and
complex information.
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• Example I: Social scientists study
preferences: “I prefer beef to fish”
• Extracting and representing preferences is key
in decision making applications.
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• “Brute force” approach: For every pair of
alternatives, ask which is preferred to the
other.
• Often computationally infeasible.
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• In many applications (repeated games,
collaborative filtering), important to elicit
preferences automatically.
• CP-nets introduced as tool to represent
preferences succinctly and provide ways to
make inferences about preferences (Boutilier,
Brafman, Doomshlak, Hoos, Poole 2004).
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• Example II: combinatorial auctions.
• Decision maker needs to elicit preferences
from all agents for all plausible combinations
of items in the auction.
• Similar problem arises in optimal bundling of
goods and services.
• Elicitation requires exponentially many
queries in general.
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Computational Approaches to Information
Management in Decision Making
Representation and Elicitation
• Challenge: Recognize situations in which
efficient elicitation and representation is
possible.
• One result: Fishburn, Pekec, Reeds (2002)
• Even more complicated: When objects in
auction have complex structure.
• Problem arises in:
 Legal reasoning, sequential decision making,
automatic decision devices, collaborative
filtering.
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Concluding Comment
• In recent years, interplay between CS
and biology has transformed major
parts of Bio into an information science.
• Led to major scientific breakthroughs in
biology such as sequencing of human
genome.
• Led to significant new developments in
CS, such as database search.
• The interplay between CS and SS not
nearly as far along.
• Moreover: problems are spread over
many disciplines.
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Concluding Comment
• However, CS-SS interplay has already
developed a unique momentum of its own.
• One can expect many more exciting outcomes
as partnerships between computer scientists
and social scientists expand and mature.
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