aug 26, 2013 lirong xia computational social choice
TRANSCRIPT
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Aug 26, 2013
Lirong Xia
Computational Social Choice
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• Introduction to the course
– the social choice problem
– course schedule, grading
• Two most important theorems in social choicegoals of
social choice mechanisms
– democracy
– truth
• Examples
– elections
– crowdsourcing
– matching
– resource allocation (we will use this to assign papers)2
Today’s schedule
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“social choice is a theoretical framework for
analysis of combining individual
preferences, interests, or welfares to reach
a collective decision or social welfare in
some sense.”
---Wikipedia
Aug 26, 2013
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Social choice
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Example: Political elections
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> >
> >
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Carol
Bob
Alice
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Social choice problems
R1* R1
Outcome
R2* R2
Rn* Rn
social choice mechanism
… …
Profile
• Agents• Alternatives• Outcomes• Preferences (true and reported)• Social choice mechanism
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• Agents: {Alice, Bob, Carol}
• Alternatives: { , , }
• Outcomes: winners (alternatives)
• Preferences (vote): rankings over alternatives
• Mechanisms: voting rules
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Why this is social choice?
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A very brief history of social choice
Ancient Greece: 4th C. B.C.
13thC.:
BORDA CONDORCET
French revolution: 18th C.
Modern: 20th C.
PLATO
LULL
ARROW
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“Computational social choice is an
interdisciplinary field of study at the
interface of social choice theory and
computer science, promoting an exchange
of ideas in both directions.”
---http://www.illc.uva.nl/
COMSOC/
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Computational social choice (COMSOC)
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Computational thinking + optimization algorithms
CSSocial
Choice
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Social Choice and Computer Science
Strategic thinking + methods/principles of aggregation
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• Not a usual lecture course
– lectures are like academic tutorials
• Try to help with doing research in
– applying (computational) social choice to your
problems
– improving computational social choice
• Participation
– presentations, comments, etc.
– we will use for discussions and
announcements10
Course at a glance
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Schedule of the courseTopics Your work
Part 1: Lectures(10-12 classes)
• Introduction to - social choice- game theory - mechanism design - computation
• Computational social choice
• a few homeworks• prepare for paper
presentation• work on the project START EARLY
Part 2: Students present papers (10-12 classes)
State-of-the-art research topics
Presenter• make slides • present the paper• lead the discussionAudience• ask/answer questions • participate in discussion
Part 3: project presentations (2-3 classes)
Your own projectPresenter: give the talkAudience: enjoy the talk
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• 2 students per team, each team presents 1-2 papers
• When you read the paper, think about the following
questions
– What is the problem?
– Why we want to study this problem? How general it is?
– How was problem addressed?
– Appreciate the work: what makes the paper nontrivial?
– Critical thinking: anything you are not very satisfied with?
• Prepare some “reading questions” for discussion
• More tips on course website12
Paper presentation
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• Very encouraged to find your own topic
• Some quick ideas
– Theory
• design and analyze social choice mechanisms for
topics of your own interest
– Application
• Online voting system for RPI student union elections
• Matching and resource allocation (class slots, dorm
slots)
• Mobile apps for preference handling 13
Project ideas
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• There are 4 awards
– Best theory project
– Best application project
– Best presentation
– Best participation
• NOT bonus grade points
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Awards
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Your final grade
Objective: learning to use
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• After the course, you should
– understand principles and methods in
(computational) social choice
– be able to apply what you learned to your own
research
• More concretely
– get some preliminary results for publication
– develop a real-world preference-handling
system 16
Expectation after the course
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Some applications and social choice mechanisms
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How to design a good social choice mechanism?
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What is being “good”?
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Two goals for social choice mechanisms
GOAL1: democracy
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GOAL2: truth
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• Goodness:
– democracy: fairness, efficiency, etc
– truth: accuracy
• Computation: how can we compute the
outcome as fast as possible
• Incentives: what if an agent does not
report her true preferences?20
Challenges
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Recall: social choice
R1* R1
Outcome
R2* R2
Rn* Rn
social choice mechanism
… …
Profile
• Agents• Alternatives• Outcomes• Preferences (true and reported)• Social choice mechanism
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Example1: Political elections
> >
> >
> >
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A profile
Carol
Bob
Alice
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• Agents: {Alice, Bob, Carol}
• Alternatives: { , , }
• Outcomes: winners (alternatives)
• Preferences (vote): rankings over alternatives
• Mechanisms: voting rules
• Goal: democracy
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Why this is social choice?
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• Input: profile of rankings over alternatives
• Output: a single winner
– For each vote R, the alternative ranked in the i-th position gets m-i points
– The alternative with most total points is the winner
• Use some tie-breaking mechanism whenever there is a tie
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The Borda voting rule BORDA LULL
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Example of Borda
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> >
> > Carol
Bob
Alice
Borda
: 2+2+0=4 : 1+1+1=3 : 0+0+2=2Total scores
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• Many other voting rules beyond Borda
will be discussed in the next class
• Which one is the best?
– Hard to compare. Criteria will be discussed in
the next class
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Other voting rules?
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a b
a b c
Turker 1 Turker 2 Turker n
…
> >
Example2: Crowdsourcing
...
.
.
.
....
. ....
. . .
.. .
. .
. .. . .
> ab > b c>
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• Agents: Turkers
• Alternatives: { , , }
• Outcomes: rankings over the pictures
• Preferences: pairwise comparisons
• Mechanisms: Maximum likelihood estimator
• More in the “statistical approaches” class
• Goal: truth 28
Why this is social choice?
a b c
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Example3: School choice
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> >
> >
Kyle
Stan
Eric
> >
> >
> >
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• Agents: students and schools
• Alternatives: students and schools
• Outcomes: matchings between students and schools
• Preferences:
– Students: rankings over schools
– Schools: rankings over students
• Mechanisms: Stable matching (Nobel Prize 2012)
• More in the “matching” class
• Goal: democracy or truth? 30
Why this is social choice?
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> > > > >
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Example4: Resource allocation
1 2 3 4 5 6> > > > >
1 6 2 3 5 4> > > > >
6 5 4 3 2 1
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• Agents: { }
• Alternatives: { }
• Outcomes: allocations of papers to students
• Preferences: rankings over papers
• Mechanisms: sequential allocation
• More in the “fair division” class
• Goal: democracy or truth? 32
Why this is social choice?
1 2 3 4 5 6
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• Given
– n students’ preferences over 2n papers, and
– an order O over the students
• SAO has 2n rounds
– In the first n rounds,
• for each t =1 to n, the t-th student in O selects her
most preferred paper that is available
– In the next n rounds,
• for each t =n to 1, the t-th student in O selects her
most preferred paper that is available 33
Sequential allocation
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Example
> > > > >
1 2 3 4 5 6> > > > >
1 6 2 3 5 4> > > > >
6 5 4 3 2 1
O=>
>
Kyle
Stan
Eric
Step 1 Step 2 Step 3 Step 4 Step 5 Step 6
1 6 5 4 2 3
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• Sounds good
– Efficient: if we have different preferences,
then we will all (almost) get what we want
– Fair: (1st pick, last pick), (2nd pick+2nd to last
pick)…
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Is it a good mechanism?
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• We will use sequential allocation to come up
with an initial assignment of papers
– Each team reports a full ranking over the papers
– The earlier a team reports, the higher it will be
ranked in O
• You will have better chance to pick your favorite paper
• Being the first to report your preferences guarantees
that you are not the first to present (unless you enjoy
it!)36
Sequential allocation for you
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• Expectation: learn how to apply computational
social choice to your own research area
• But be careful and keep in mind the two goals
– democracy
– truth
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Wrap up
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• Sign up at piazza (link on the course
website)
• Brief introduce your background
• Participate in discussions on piazza
– Try to name some other applications of social
choice
– In your applications, will you design a
mechanism to achieve democracy or truth?38
Before the next class