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An efficient distributed protocol for collective decision-making in combinatorial

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Title: An efficient distributed protocol for collective decision-making in combinatorial


1
An efficient distributed protocol for collective
decision-making in combinatorial domains
CMSS Feb. 20-21, 2012
Minyi Li Intelligent Agent Technology Group
Centre for Computing and Engineering Software
Systems (SUCCESS) Swinburne University of
Technology Melbourne, Australia
2
Motivation and problem setting
  • Society
  • Voters (agents)
  • Alternatives
  • Domain
  • Candidates
  • Problem
  • Choice of one among several Candidates
  • Selection criterion

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
3
Selection criteria
  • Majority rule
  • Majority rule for elections with only two
    candidates which the candidate preferred by more
    than half the agents is the winner.
  • Condorcets Method
  • The Condorcet candidate or Condorcet winner of
    an election is the candidate who, when compared
    with every other candidate, is preferred by more
    than half of the agents (winner in pair-wise
    comparison). 
  • Condorcets Paradox

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
4
Selection criteria
  • What to do when there is no (weak) Condorcet
    winner
  • Smith set the smallest non-empty set of
    candidates in a particular election such that
    each member beats every other candidate outside
    the set in a pair-wise election.
  • The Smith set provides one standard of
    optimal choice for an election outcome.
  • Minimax (Simpson) selects the candidate for whom
    the greatest pair-wise score for another
    candidate against him is the least such score
    among all candidates.
  • May possible choose a Condorcet loser (is a
    candidate who can be defeated in pair-wise
    competition against each other candidate).
  • Smith/minimax chooses a minimax candidate from
    the Simith set.

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
5
Combinatorial Vote
  • When the domain is huge, and variables are
    interdependent
  • Unrealistic to assume linear orders are given by
    the individual agents
  • Exhaustive pair-wise comparison in the entire
    alternative space becomes impractical.
  • Decompose rules or issue by issue voting may
    produce undesirable outcomes, and might be
    impossible.
  • Individual outcome comparison might be very
    difficult.

An efficient distributed protocol for collective
decision-making in combinatorial domains
Page 5
CMSS 2012
6
Combinatorial Vote
  • Possible solution
  • To find reasonable restrictions on the preference
    structures so that sequential voting still
    preserves desirable properties
  • Design good algorithms to compute the winner for
    the combinatorial vote problem, by
  • Utilizing the structures of the preferences work
    on the preference language directly.
  • Avoiding pair-wise comparison as much as possible
  • Choose from a small subset of alternatives (it
    might be easy to detect that some alternatives
    are not socially optimal)

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
7
The proposed protocol MDTreeS/M
  • Basic principles
  • Allow partial vote with optimistic strategy
  • A partial vote is a proposal on an assignment
    over a subset of variables in the domain
  • In each iteration of the protocol, different
    agents may vote for assignments on different
    subset of variables
  • A partial vote can be extend only if it received
    more than half of the agents proposal
  • The agents continue to propose and extend partial
    assignment until all variables are assigned
  • Allow regret of partial choice
  • The agent is not required to stick with and
    extend one partial assignment (or even a complete
    assignment) if there is something else better!

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
8
The framework
  • Majority decision tree (MDTree)
  • A k-ary tree (k is maximum domain size) with
    depth m (m is the number of variables)
  • Root begin at depth 0 with an empty assignment
  • Each level assigns possible values to a single
    variable the order
    following which the variables will be
    assigned is randomly chosen.
  • Each node at level p (pltm) in a MDTree
    represents a unique assignment to a subset of
    variables
  • Open node 1) a leaf node at level p (pltm) 2) a
    majority of agents have proposed on
  • Open node will be expanded automatically for
    further consideration.
  • Winning node 1) a leaf node at level m a
    majority of agents have proposed on
  • Winning node will no longer be feasible for
    making proposal on.

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
9
The framework
An efficient distributed protocol for collective
decision-making in combinatorial domains
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10
The framework
  • Best possible alternative
  • At each node of the negotiation tree (represents
    a partial assignment), each agent has a best
    possible alternative (BPA), i.e., an optimal
    outcome with the variable values in the partial
    assignment being fixed.
  • e.g.
  • BATCD Strategy to proposed on a node that
    optimistically can give him the best!
  • Feasible nodes for an agent i 1) a leaf node
    2) not a winning node 3) agent hasnt proposed
    on that node.

An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
11
The process of negotiation
  • From a broad view, during the negotiation
    process, the agents first try to identify a
    socially prefer winning node by iteratively
    making proposals. Then, they try to converge to
    that node unless there is something better
    (socially more preferred)!
  • The detailed process
  • Step 1 Each agent proposes on a node, unless
  • He has proposed on every node.
  • Nothing will be better for him than the chosen
  • If all the agents stop making offers, the
    process ends and returns the current chosen
  • Step 2 Expanding open nodes.
  • If there exists no winning node, go back to Step
    1.
  • Step 3 Choose a Smith/Minimax solution among
    the winning nodes.
  • Go back to Step 1.

An efficient distributed protocol for collective
decision-making in combinatorial domains
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12
An example
An efficient distributed protocol for collective
decision-making in combinatorial domains
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13
Experiment and evaluation
  • Experiment Setting
  • 2-12 variables 5 and 15 agents
  • Preferences SLO-SCP-net (Soft constraint
    Lexicographic Ordering)
  • Carmel Domshlak, Steven David Prestwich,
    Francesca Rossi, Kristen Brent Venable, and Toby
    Walsh. Hard and soft constraints for reasoning
    about qualitative conditional preferences. J.
    Heuristics, 12(4-5)263285, 2006.

In these experiments, for each number of agents
and variables, in more than 998 cases, the
final decision chosen by MDTree-S/M protocol is
the Smith/Minimax solution.
An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
14
Property of the protocol
  • Desirable properties
  • Satisfies Smith criterion
  • The final decision chosen is sufficiently close
    to the Smith/Minimax solution (experimentally
    evaluated)
  • Enables distributed decision-making and works
    under incomplete information setting
  • The amount of dominance testing needed from each
    agent, as well as the number of pair wise
    comparisons required is significantly less
  • It is sufficiently general that it is applicable
    to most preference representation languages in
    combinatorial domain
  • Future Work
  • Other voting rules, Copeland, range voting
  • Develop more accurate algorithms.

An efficient distributed protocol for collective
decision-making in combinatorial domains
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15
Thank you Questions?
An efficient distributed protocol for collective
decision-making in combinatorial domains
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CMSS 2012
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