Ranking systems: the PageRank axioms

1
Ranking systems the PageRank axioms

• This paper
• initiates research on the foundations of ranking
  systems
• deals with PageRank, the most famous page ranking
  algorithm
• presents a set of simple (graph-theoretic,
  ordinal) axioms that are satisfied by PageRank
  and
• any page ranking algorithm that does satisfy them
  must coincide with PageRank
• bridges the gap between page ranking algorithms
  and the mathematical theory of social choice.

2
Representing and Reasoning with Preferences

• This paper considers
• How to represent and reason with users
  preferences
• Representing preferences binary preference
  relation, CP-nets and its extensions
• Preference aggregation voting rules
• Manipulation of voting rules
• Uncertainty incomplete preferences are given
• How we can elicit preferences efficiently and
  effectively
• Preference elicit focus on resolving the
  relationship between possible winners
• Single-peaked preferences easy to elicit and to
  aggregate

3
Qualitative Decision Theory

• This paper
• Describes a framework for specifying conditional
  desires desire ? if ? and
• Example If I have the umbrella, then I will be
  dry
• Evaluating preference queries would you prefer
  ?1 over ?2 given ?
• Would an agent decides whether she should carry
  an umbrella given that she sees that the sky is
  cloudy?
• Equips an intelligent agent with decision making
  capabilities based on two inputs belief and
  preference

4
Reasoning With Conditional Ceteris Paribus
Preference Statements

• In many domains it is desirable to assess the
  preferences of users in a qualitative rather than
  quantitative way.
• Such representations of qualitative preference
  orderings form an important component of
  automated decision tools
• CP-network (Conditional Preference-network) is a
  graphical model for representing qualitative
  preference orderings

5
Preferences over Sets

• Research on preference elicitation and reasoning
  typically focuses on preferences over single
  objects of interest.
• However, in a number of applications the
  outcomes of interest are sets of such atomic
  objects.
• This paper gives
• An intuitive approach for specifying preferences
  over sets of objects.
• A set-preference specification language is given
• Set-preference statements are represented by a
  TCP-net (tradeoffs-enhanced CP-nets)

6
Propositional belief base merging and some links
with social choice theory

• Belief merging defines the goals (beliefs) of a
  group of
• agents from their individual beliefs (resp.
  goals)
• This paper
• Studies the relationships between two important
  sub-families of merging operators
• Shows some relationships between logical belief
  merging operators and social choice rules

7
Social choice theory, belief merging, and
strategy-proofness

• This paper investigates the link between the
  belief merging and some results in social choice
  theory by
• Providing a consistent set of properties for
  merging
• Showing that there is no Arrow-like impossibility
  result for merging
• Investigating notions of strategy-proofness in
  the context of merging

8
Belief revision, belief merging and voting

• This paper investigates the relationship between
  revision, merging and voting
• Voting There are several conflicting
  demands/preferences and we are looking for a
  collective compromise
• Belief revision There is a theory T and we get
  new information ?, we want to accommodate ? into
  T consistently
• Belief merging We are trying to aggregate
  knowledge bases which together are possibly
  inconsistent.
• Common feature fairness principles are concerned
  when resolve conflicts

9
Representing and Aggregating Conflicting Beliefs

• This paper considers the two-fold problem of
  representing collective beliefs and aggregating
  these beliefs
• proposes modular transitive relations for
  collective beliefs
• describes a way to construct the belief state of
  an agent informed by a set of sources of varying
  degree of reliability
• gives a simple set theory-based operator for
  combining the information of multiple agents
• shows that this operator satisfies desirable
  properties

10
Common Voting Rules as Maximum Likelihood
Estimators

• This paper
• Gives a view on voting rule
• There exists a correct outcome (winner/ranking)
• Each voter's vote corresponds to a noisy
  perception of this correct outcome
• Studies
• Voting rules that can be interpreted as MLEs
  (Maximum Likelihood Estimator)
• Voting rules that cannot be interpreted as MLEs

11
Arrow's theorem in judgment aggregation

• Judgment aggregation How can the judgments of
  several individuals on logically connected
  propositions be aggregated into corresponding
  collective judgments?
• It is related to earlier results in social choice
  theory
• This paper
• proves two impossibility theorems on judgment
  aggregation
• discusses relationship between preference
  aggregation in social choice theory and judgment
  aggregation

12
Judgment aggregation under constraints

• This paper
• make constraints explicit in judgment aggregation
  with
• constraints as propositions that the decisions
  should be consistent with
• discusses some properties of the judgement
  aggregation under constraints
• reviews several general results on judgment
  aggregation in light of such constraints.