# Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Tracking Conflict through Page Reverts

#### 2.2. Hidden Markov Models

#### 2.3. Fitting and Characterizing HMMs

#### 2.4. Subspaces, Trapping Time, and Viterbi Reconstruction for HMMs

#### 2.5. Causes of State Transitions

## 3. Results

#### 3.1. Epoch Detection

#### 3.2. Drivers of Conflict Transitions

- How many events are there and what fraction are associated with a transition? (Effectiveness)
- What fraction of transitions are associated with an event? (Explanatory power)
- For those transitions that we can associate with an event, what fraction have the expected effect? (Valence)

#### 3.2.1. Page Protection Events

#### 3.2.2. Anti-Social User Events

#### 3.2.3. Major External Events

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A. Articles in Our Analysis

## Appendix B. Choosing the Number of States in an HMM

**Table B1.**Using AIC and BIC to choose the number of states in a hidden Markov model fit. Here, we take an actual model from our data (the 8-state best fit model for the

`God`page), use that model to generate a new time series of equal length (10,731 samples) and attempt to fit a new model, using either AIC or BIC to select the preferred number of states in a manner similar to Refs. [92,93]. The table lists the fraction of the time this process led to a preferred machine of each size, for the two different penalties. Both AIC and BIC tend to underestimate model complexity; in general, BIC performs worse, significantly underestimating the true number of states. AIC performs better, recovering the correct number of states nearly half the time.

Number of States | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 (Truth) | 9 | 10 |

AIC | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 37.5% | 7.2% | 45.8% | 9.3% | 0.0% |

BIC | 0.0% | 0.0% | 0.0% | 20.8% | 54.1% | 23.9% | 1.0% | 0.0% | 0.0% | 0.0% |

`God`page. We took the derived HMM for this page and used it to generate 96 simulated datasets of equal length to the original. We then ran our fitting code on each of these datasets and compared what happened when we used the AIC and the BIC criteria to select the preferred number of states. Consistent with [92,93], we found that BIC tended to underestimate model complexity, choosing machines significantly smaller than the true number and, in fact, never recovering the true system size. We found, by contrast, that AIC worked better; like BIC, it still often underestimated model complexity, but did so by smaller amounts. Conversely, a small fraction of the time (less than 10%), it preferred a model that was one state more complex than reality.

## Appendix C. Relaxation Time, Mixing Time, Decay Time, Trapping Time

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**Figure 1.**Top panel: Hidden Markov model for cooperation and conflict on the George W. Bush page. States are labeled by the probability of emitting each of the two output symbols; “C” ($P\left(C\right)>0.8$, lighter yellow), “R” ($P\left(R\right)>0.8$, darker blue) or “cr” (otherwise). Edge weights show transition probabilities; the lightest lines, connecting the two subspaces, correspond to probabilities of order ${10}^{-4}$. Despite its complexity, the system is dominated by a transition logic that, on short timescales, confines the system to one of two separate modules with a high density of internal transitions. Bottom panel: below the diagram, as an example of our method, we show the Viterbi reconstruction in the neighborhood of one of the sixteen between-subspace transitions in our data. As the system wanders, during this period, among internal States 5, 9, 3, 8 and 4, it emits the symbols C and R probabilistically depending on which particular state it is in. On 8 November 2004 at 9:11 UTC (Coordinated Universal Time), long runs of cooperation and conflict gave way to more rapid-fire conflict and vandal-repair as the system crossed from the left module to the right, via the bridge between State 5 and State 8.

**Figure 2.**Relaxation time, τ, for the sixty-two pages in our sample (solid line). Times are exceptionally long, an average of 698 steps, and, on average, a factor of 50 times longer than expected for Markov models with similar sparseness (dotted line). The longest trapping times are for the pages associated with the Gaza War, the Russo-Georgian War, and the page describing Wikipedia itself.

**Figure 3.**Distribution of edit rates for type one (high conflict) and type two (low conflict) subspaces. Shown here, as an example, is the spacing between edits on the George W. Bush page. When the system is in the high-conflict subspace, edits occur once every 212 s (median; 3.5 min); in the low-conflict subspace, once every 951 s, or every 16 min. When the system is in the high-conflict subspace, users almost never wait more than a day to take action.

**Table 1.**Hidden Markov models and derived parameters for cooperation and conflict on the ten most-edited pages on Wikipedia. Editing patterns are characterized by high levels of determinism, and long timescale trapping in distinct higher and lower conflict spaces.

**Table 2.**Characteristic motifs of the higher (type one) and lower (type two) conflict subspaces across all 62 pages, ranked by partial-KL (see Ref. [43], Equation 2). The lower-conflict subspace is characterized by long runs of cooperation, but also by long runs of reversion. Conversely, the higher-conflict subspace is characterized by more rapid patterns of alternation between R and C moves.

Size | Type One Motifs | Type Two Motifs |
---|---|---|

2 | CR, RC | CC, RR |

3 | CRC, RCR, RCC, CCR | CCC, RRR, RRC, CRR |

4 | RCRC, CRCR, CRCC, CCRC, RCCR | CCCC, RRRR, RRCC, RCRR, CRRC |

5 | CRCRC, RCRCR, RCRCC, CCRCR, CRCCR | CCCCC, RRCRR, RRRRR, CRRRR, RRRRC |

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DeDeo, S. Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions. *Future Internet* **2016**, *8*, 31.
https://doi.org/10.3390/fi8030031

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DeDeo S. Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions. *Future Internet*. 2016; 8(3):31.
https://doi.org/10.3390/fi8030031

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DeDeo, Simon. 2016. "Conflict and Computation on Wikipedia: A Finite-State Machine Analysis of Editor Interactions" *Future Internet* 8, no. 3: 31.
https://doi.org/10.3390/fi8030031