© 2014 Networking for Information Communications and Energy Lab. Why does Wikipedia even work? Prof. Hongseok Kim Sogang University, EE Networked Life: 20 Questions and Answers (M. Chiang, Princeton University)

2 What is Wikipedia ?  Wiki »As a noun, wiki means “ a website that allows anyone to add, delete or revise content by using a web browser”  Pedia »The suffix pedia comes from Greek and means learning or a collection. It is used in the word “Encyclopedia” which means a collection of general knowledge.

3 Wikipedia  Started in 2001, convergence of three forces Wiki collaboration Open software Online Knowledge sharing  By 2011, 3.75 million US articles and 19 million worldwide articles are presented.  Works well: large, comprehensive, quite accurate  Abuses sometimes: misinformation, mistakes, missing info.

4 Reasons for Success  Free Networking effect and tipping phenomenon in usage  Any subject might be written if policies are followed. V NOR NPOV  Reputation system  Editorial system Voting Bargaining

5 Three core policies on Wikipedia  Verifiability (V) »Each key point or data in an article must be externally verifiable, with link to the primary source for verification by readers.  No Original Research (NOR) »This is to prevent people from using Wikipedia as a publication venue of their new results  Neutral Point of View (NPOV) »The basic rule is that a reader must not be able to tell the bias of the author in reading through Wikipedia article. »E.g. Contentious political, social, and religious topics

6 Reputation System  Rating systems for articles »Each article can be rated on a 1-6 grade scale. »There is a hierarchy of Wikipedia communities and debates among contributors who cannot come to an agreement will be put forward to a group of the most experienced editors.  Decision making process Rough consensus

7  Two underlying theories: Voting theory »Each contributor has some partially ordered list of preferences, and a threshold on how far the group decision can be away from her own preferences before she vetoes the group decision and thereby preventing the consensus from being reached. Bargaining theory »In bargaining model, the contributors need to reach a compromise, otherwise there would be no agreement. »Each contributor’s utility function, and the default position in the case of no agreement, need to reflect the good-will typically observed in Wikipedia collaboration.

8 Voting profile  Input Preference profiles  Output Voting outcome  Completeness  Transitivity  Loss of information

9 Voting system C = 4, S = 3, V = 2 Thus, C>S>V

10 Voting system  Positional Voting (Borda count) The first position candidate in each list gets M-1 points, the second position one gets M-2 points, and so on, and the last position one gets 0 point. *Example ( Ice cream flavor voting, Chocolate(C), Vanilla(V), Strawberry(S) ) § C > V > S : 4 votes § S > V > C : 3 votes § V > S > C : 2 votes  Pairwise Voting (Condorcet voting) It is an aggregation of binary results from pairwise comparisons. *Example ( Ice cream flavor voting, Chocolate(C), Vanilla(V), Strawberry(S) ) § C > V > S : 4 votes § S > V > C : 3 votes § V > S > C : 2 votes C = 2x = 8 V = 2x = 11 S = 2x3 + 2 = 8 Thus, V>C=S Compare the pairwise comparison C>V = 4, V>C = 5 => V>C V>S = 4+2, S>V = 3 =>V>S S>C = 3+2, C>S = 4 => S>C Thus, V>S>C

11  Pop Quiz »Calculate the Condorcet voting output in case of following: A > B > C C > A > B B > C > A »1) A=B=C 2) A>B>C 3) B>C>A 4) C>A>B 5) No Condorcet voting output

12  Example *Example ( Ice cream flavor voting, Chocolate(C), Vanilla(V), Strawberry(S) ) § C > V > S : 4 votes § S > V > C : 3 votes § V > S > C : 2 votes Plurality = Borda count = Condorcet voting ?

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17 Arrow’s Axioms  Following five statements that sound very reasonable about any voting system.

18 Arrow’s Impossibility Theorem  As soon as we have M = 3 candidates or more, there are none voting system that satisfy all the five axioms. Which axiom ?  Arrow’s theorem states that when it comes to ranking three or more candidates, pairwise comparisons are inadequate. Is voting flawed or our intuition flawed ?  IIA allows cyclic output even when all inputs are transitive.  What additional information do we need? Answer : “possibility result”

19 Possibility results  By replacing IIA with the Intensity form of IIA (IIIA), there are voting systems that can satisfy all the axioms. When we write A>B, we now also have to write down the number of other candidates that sit in between A and B (Intensity). If none, intensity is zero.  The Borda count is a voting system that satisfies all five axioms now.  Pdf 117 begin.

20 Sen’s axioms  Another fundamental impossibility theorem by Sen.  Following four axioms are incompatible:  Decisive voters may impose strong externalities.  Impossible again.. Which axiom ?

21 Counter-Examples (1/2)  Suppose there are N=5 candidates and M=3 voters.  Voter 1 is decisive voter for (A,B) pairwise comparison.  Voter 2 for (C,D) pair.  Voter 3 for (E,A) pair.

22 Counter-Examples (2/2)  Still, remains cyclic.  In cyclic ranking in Sen’s system, each voter suffers strong negative externality from some decisive voter.

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25 Prisoner’s dilemma (Chap 01)

26 Connection to prisoner’s dilemma  Prisoner 1 is the decisive voter on (A,B) and (C,D) pair.  Prisoner 2 is the decisive voter on (A,C) and (B,D) pair.  We have an outcome that contains two cyclic rankings

27 Connection to prisoner’s dilemma

28 Bargaining Theory  Wikipedia editorial decision is bargaining as well as in many other contexts »Each bargaining party has a selfish motivation and yet all the parties want to achieve some kind of agreement. »If no agreement is achieved, then each party goes back to its own disagreement point. »This interaction is studied in cooperative game theory  Nash Axiomatic Approach in 1950s  Rubenstein in the 1980s (Next slide)

29 Bargaining: Interactive offers (1/3) »Suppose there are two people, A and B bargaining over how to divide a cake of size 1. »Why would either person be motivated to accept an offer? In Rubinstein’s model, the price to pay is time. If an agreement is reached at the k-th iteration, a person’s payoff is

30 Bargaining: Interactive offers (2/3)

31 Bargaining: Interactive offers (3/3)

32 Bargaining: Nash bargaining solution (1/4)

33 Bargaining: Nash bargaining solution (2/4)

34 Bargaining: Nash bargaining solution (3/4)  The solution can be the following problem, which maximizes the product of the gains (over the disagreement point) by both A and B, over the set of payoffs that is feasible and no worse than the disagreement point itself:  The solution is called Nash Bargaining Solution (NBS)

35 Bargaining: Nash bargaining solution (4/4)

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