Computer Science and the Socio-Economic Sciences

1
Computer Science and the Socio-Economic Sciences
Fred Roberts, Rutgers University
2
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

3
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

4
CS and SS Outline

• CS and Consensus/Social Choice
• 2. CS and Game Theory
• 3. Algorithmic Decision Theory

5
CS and SS Outline

• CS and Consensus/Social Choice
• 2. CS and Game Theory
• 3. Algorithmic Decision Theory

6
CS and Consensus/Social Choice

• Relevant social science problems voting, group
  decision making
• Goal based on everyones
• opinions, reach a consensus
• Typical opinions
• first choice
• ranking of all alternatives
• scores
• classifications
• Long history of research on such problems.

7
CS and Consensus/Social Choice
Background Arrows 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
8
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. Kemeny-Snell
medians are having surprising new applications
in CS.
John Kemeny, pioneer in time sharing in CS
9
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.
10
CS and Consensus/Social Choice
a1 a2 a3 Fish Fish Chicken Chicken Chicken Fi
sh Beef Beef 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.
11
CS and Consensus/Social Choice
a1 a2 a3 Fish Chicken Beef Chicken Beef Fish
Beef Fish Chicken Three medians a1, a2, a3.
This is the voters paradox situation.
12
CS and Consensus/Social Choice
a1 a2 a3 Fish Chicken Beef Chicken Beef Fish
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.
13
CS and Consensus/Social Choice
a1 a2 a3 Fish Chicken Beef Chicken Beef Fish
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.
14
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.

15
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 computationally
  tractable

16
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

17
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.

18
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.

19
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.
20
Large Databases and Inference
Example Bacterial Promoter Sequences studied by
Waterman (1989) RRNABP1 ACTCCCTATAATGCGCCA TNA
A GAGTGTAATAATGTAGCC UVRBP2
TTATCCAGTATAATTTGT SFC
AAGCGGTGTTATAATGCC Notice that if we are looking
for patterns of length 4, each sequence has the
pattern TAAT.
21
Large Databases and Inference
Example Bacterial Promoter Sequences studied by
Waterman (1989) RRNABP1 ACTCCCTATAATGCGCCA TNA
A GAGTGTAATAATGTAGCC UVRBP2
TTATCCAGTATAATTTGT SFC
AAGCGGTGTTATAATGCC Notice that if we are looking
for patterns of length 4, each sequence has 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.
23
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.
24
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.
25
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.
26
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 ?ik-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 are important in modern molecular
biology.
27
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
  travel-related websites
• Sequential decision making Next query or
  information access depends on prior responses.

28
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.

29
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

30
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

31
Electronic Voting

• Issues
• Correctness
• Anonymity
• Availability
• Security
• Privacy

32
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

33
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

34
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.

35
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.

36
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

37
Software Hardware Measurement

• Hardware Measurement

BENCHMARK
E
F
G
H
I
417 83 66 39,449 772
244 70 153 33,527 368
134 70 135 66,000 369
P R O C E S S O R
R
M
Z
Data from Heath, Comput. Archit. News (1984)
38
Software Hardware Measurement

• Normalize Relative to Processor R

BENCHMARK
E
F
G
H
I
417 1.00 83 1.00 66 1.00 39,449 1.00 772 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
P R O C E S S O R
R
M
Z
39
Software Hardware Measurement

• Take Arithmetic Mean of Normalized Scores

Arithmetic Mean
BENCHMARK
E
F
G
H
I
417 1.00 83 1.00 66 1.00 39,449 1.00 772 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
P R O C E S S O R
1.00
R
1.01
M
1.07
Z
40
Software Hardware Measurement

• Take Arithmetic Mean of Normalized Scores

Arithmetic Mean
BENCHMARK
E
F
G
H
I
417 1.00 83 1.00 66 1.00 39,449 1.00 772 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
P R O C E S S O R
1.00
R
1.01
M
1.07
Z
Conclude that machine Z is best
41
Software Hardware Measurement

• Now Normalize Relative to Processor M

BENCHMARK
E
F
G
H
I
417 1.71 83 1.19 66 .43 39,449 1.18 772 2.10
244 1.00 70 1.00 153 1.00 33,527 1.00 368 1.00
134 .55 70 1.00 135 .88 66,000 1.97 369 1.00
P R O C E S S O R
R
M
Z
42
Software Hardware Measurement

• Take Arithmetic Mean of Normalized Scores

Arithmetic Mean
BENCHMARK
E
F
G
H
I
417 1.71 83 1.19 66 .43 39,449 1.18 772 2.10
244 1.00 70 1.00 153 1.00 33,527 1.00 368 1.00
134 .55 70 1.00 135 .88 66,000 1.97 369 1.00
1.32
P R O C E S S O R
R
1.00
M
1.08
Z
43
Software Hardware Measurement

• Take Arithmetic Mean of Normalized Scores

Arithmetic Mean
BENCHMARK
E
F
G
H
I
417 1.71 83 1.19 66 .43 39,449 1.18 772 2.10
244 1.00 70 1.00 153 1.00 33,527 1.00 368 1.00
134 .55 70 1.00 135 .88 66,000 1.97 369 1.00
1.32
P R O C E S S O R
R
1.00
M
1.08
Z
Conclude that machine R is best
44
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
• ? ?is(xi)

?
n
45
Software Hardware Measurement

• Normalize Relative to Processor R

Geometric Mean
BENCHMARK
E
F
G
H
I
417 1.00 83 1.00 66 1.00 39,449 1.00 772 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
P R O C E S S O R
R
1.00
.86
M
.84
Z
Conclude that machine R is best
46
Software Hardware Measurement

• Now Normalize Relative to Processor M

BENCHMARK
Geometric Mean
E
F
G
H
I
417 1.71 83 1.19 66 .43 39,449 1.18 772 2.10
244 1.00 70 1.00 153 1.00 33,527 1.00 368 1.00
134 .55 70 1.00 135 .88 66,000 1.97 369 1.00
P R O C E S S O R
R
1.17
1.00
M
.99
Z
Still conclude that machine R is best
47
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 not.

48
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.

49
CS and SS Outline

• CS and Consensus/Social Choice
• 2. CS and Game Theory
• 3. Algorithmic Decision Theory

50
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.

51
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 has a Nash
  equilibrium.
• How hard is this to compute?

John Nash Nobel prize winner
52
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

Player 2 strategy
3
2
0
1
0,0 2,-2 2,-2 2,-2
-2,2 1,1 3,-1 3,-1
-2,2 -1,3 2,2 4,0
-2,2 -1,3 0,4 3,3
0
1
Player 1 strategy
2
3
Source Wikipedia
53
Example Nash Equilibrium

• 0-0 is unique Nash equilibrium
• Any other strategy one player can lower his to
  below others and improve.

Player 2 strategy
3
2
0
1
0,0 2,-2 2,-2 2,-2
-2,2 1,1 3,-1 3,-1
-2,2 -1,3 2,2 4,0
-2,2 -1,3 0,4 3,3
0
1
Player 1 strategy
2
3
Source Wikipedia
54
Example Nash Equilibrium

• 0-0 is unique Nash equilibrium
• Any other strategy one player can lower his to
  below others and improve.
• E.g. From 2-2, player 1 lowers his number to 1

Player 2 strategy
3
2
0
1
0,0 2,-2 2,-2 2,-2
-2,2 1,1 3,-1 3,-1
-2,2 -1,3 2,2 4,0
-2,2 -1,3 0,4 3,3
0
1
Player 1 strategy
2
3
Source Wikipedia
55
Example Nash Equilibrium

• 0-0 is unique Nash equilibrium
• Any other strategy one player can lower his to
  below others and improve.
• E.g. From 2-2, player 1 lowers his number to 1

Player 2 strategy
3
2
0
1
0,0 2,-2 2,-2 2,-2
-2,2 1,1 3,-1 3,-1
-2,2 -1,3 2,2 4,0
-2,2 -1,3 0,4 3,3
0
1
Player 1 strategy
2
3
Source Wikipedia
56
Example Nash Equilibrium

• 0-0 is unique Nash equilibrium
• Any other strategy one player can lower his to
  below others and improve.
• E.g. From 2-2, player 1 lowers his number to 1
  (or player 2 lowers his to 1)

Player 2 strategy
3
2
0
1
0,0 2,-2 2,-2 2,-2
-2,2 1,1 3,-1 3,-1
-2,2 -1,3 2,2 4,0
-2,2 -1,3 0,4 3,3
0
1
Player 1 strategy
2
3
Source Wikipedia
57
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
  points, which seems unlikely.

58
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

59
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.

60
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)
61
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 combinations.

62
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.

63
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
  (Cornells experiment)

64
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
65
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 1s Shapley value is 3/7.
• Sum of Shapley values is 1 (since they are
  probabilities)
• Thus, each other shareholder has Shapley value
• (4/7)/6 2/21

66
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.

67
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.

68
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.

69
Multicasting
70
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.

71
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.

72
Bounded Rationality

• Traditional game theory assumption Strategic
  agents are fully rational can completely reason
  about consequences of their actions.
• But Consider bounded computational power.

73
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?

74
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
• ATT uses this to detect fraudulent use of credit
  cards or impending billing defaults
• Other relevant work methods for detecting
  fraudulent behavior in financial systems

75
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

76
CS and SS Outline

• CS and Consensus/Social Choice
• 2. CS and Game Theory
• 3. Algorithmic Decision Theory

77
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

78
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.

79
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

80
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

81
Sequential Decision Making

• Online Text Filtering Algorithms
• We seek to identify interesting documents from
  a stream of documents
• Widely studied problem in machine learning

82
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
  using sequential decision making methods

83
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.

84
Inspection Problems
Follow left branch if ok, right branch if
suspicious.
85
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

86
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).
87
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.

88
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.

89
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
90
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

91
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).

92
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.

93
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.

94
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.

95
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).

96
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.

97
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.

98
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.

99
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.

100
(No Transcript)