User:OrenBochman/WGT/Consensus

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Coordination & Coordination Failures[edit]

Coordination of task requires that agents can agree and locate needed resources within a limited time-frame. While CSCW researchers frequently refer to coordination cost and to communocation costs as setbacks faced by agents articulating collaborative goals, their definitions are to vauge to be quantified. On the other hand Game theory as I originally envisioned it used abstract utility to define costs as well as payoffs but this soon became an barrier to testing the validity of the theory. I have therefore extended the the notion of an abstract utility representing the preferences of agents in a game with a more concrete surrogate. This is a "currency" that might be more conductive for CSCW research.

The currency of interest is (time, information)


I call the inability to coordinate as a coordination failure. How to quantify a such a failure ?

2, 3 & N agent coordination game
with mutually exclusive POV
POV1 POV2
POV 1 3,2 0,0
or[note 1]
POV 2 0,0 2,3
2 agent consensus coordination
POV1 POV2
POV 1 3,2,2 0,0,0
or[note 1]
POV 2 0,0,0 2,2,3
a 3 agent consensus coordination
POV1 POV2
POV 1 3,...,3,2,...2 0,...,0
or[note 1]
POV 2 0,0 2,...,2,3,...3
N agent consensus coordination

The Connection Problem[edit]

It is implicitly assumed that the agents can solve the connection problem[1] meaning that each agent is assumed to be able to locate the other agents who might have capabilities which are necessary for the execution of tasks.

However this is an assumption that should be challenged. One of the most common sources of collabotation failure is the lack of technology to bridge connection problems by suitable networking amongst required social roles as resource owners. The current remedy being used is thematic coordination spaces. These allow agents to locate suitable collaborators. A second remedy used to handle vandalism is to use robots which function in a number of coordination spaces silmultaneously. However while robots are useful for handling specific tasks they are not very good for communication.

Examples for Coordination space are:

  • Article pages (ant path coordination[2] using inline tags)
  • Article talk pages (to coordinate)
  • Page History (to coordinate via editing) - using revert
  • Project Pages
  • Village Pump
  • Community Notice Board
  • Afd
  • Admin Notice boards
  • Comment pages for policy discussions
  • Mailing Lists
  • Irc Channels

These are locations where coordination negotiations take place.

However this assumption is unlikely to be true in the case of a newcomer. For example newcomers are exceedingly [citation needed] rare at AfD and even rarer at Deletion Review WP:DR. this component of the cost can be quantified.

The Consensus Game - Unanimous Decision[edit]

Coordination between two agents is traditionally modelled by Battle of the Sexes. The rules of the game are :

  1. Agents must choose one of a set of mutually exclusive coordination options (e.g. a Point of view in a policy discussion or an opinion/fact to be expressed in an article)
  2. They move simultaneously (or at least without exchanging information)
  3. Each agent has the following preferences:
    1. best is to have Consensus centered on their point of view.
    2. next is to have Consensus centered on another point of view.
    3. worst of all is to not have consensus at all.

The coordination challenge is as follows - they have to rendezvous at a common location. However each is driven by a conflicting personal preference.


Note: A real wiki has infrastructures for messaging (inline and article tagging) and coordination spaces coordination which should empower the agent to always reach consensus - yet in reality coordination failures are common (in some essential scenarios over 50%). Despite the apparent restriction of the model in general this model (and the variant below) can be used to effectively model a very large part of coordination in a wiki.

There are many coordination problems in Wikipedia but a good illustration is what I call the consensus game. This is a situation involving two or more editors attempting to reach consensus. Each agent must contribute a necessary component (technical information, writing skills, language skills, access to paid wall resources, knowledge of policy, user privilege) to reach a new consensus. However if any of a single component is not accounted for than the coordination fails and the only consensus possible is to delete the article. (Cases where editors actively compete are covered under wars of attrition) In this game the preferences for each agents are:

  1. reach (coordinate) a consensus based on their POV.
  2. reach (coordinate) a consensus based on the opposing POV.
  3. return to an old consensus - may often not be an option (e.g. at creation or at AfD).
  4. coordination failure.
  • I call the version shown here as the Consensus coordination between two, three and many members is shown with two option are presented and there is no advantage in returning to the previous consensus. [note 1]
  • Note that in the 3 person version the second player will get a low score in both cases - this naturally models a non involved third agent who benefits from consensus but does nor have a preference. (c.f. conflict resolution)
  • Note that in the N person version there will be additional involved agents coming in who mirror the first/second/third agent. However they can no more force consensus than the case of 3 agents. They also do not posses resources which allow them to bargain for better payoffs in return for joining the coalition.

In many discussions there are several coordination choices (reSome issues are that there are at times more that 2 POV. This makes coordination harder (overall returns smaller).

What is the aspect of Coordination we would need to model:

  1. The cost of establishing a coordination (social) network of agents working in a limited (coordination) space and time possessing the required resources such as:
  • domain knowledge
  • writing skills - good english & knowledge of the manual of style.
  • language skills (translation/verification of foreign language sources.
  • access to scarce research materials - e.g. paid wall resources (New York Times; Highbeam; Web of Science etc).
  • knowledge of policy and norms.
  • user privilege - the ability to edit protected pages
  1. a probability reflecting the scarcity of the agent/resource needed for coordination.
  2. In practice the number of agent seems significant. Two agent are doing 10 more work due to C2. If they are in conflict they can have a coordination failure and require a third opinion. To coordinate a larger group of than two seems to require 10 more work than the case of 2.
  3. some coordination teams also need to form coalitions. This process is defined as agreeing on a payoff allocation based on access to resources. It is usually modelled by a sequence of appeals which can be justified or not. (technical - needs to be explained in laymen's terms).
2, 3 & N agent coordination game
with N mutually exclusive POV
POV1 POV2
POV 1 3,2 0,0
POV 2 0,0 2,3
2 agent consensus coordination
POV1 POV2 POV3
POV 1 3,2,2 0,0,0 0,0,0
POV 2 0,0,0 2,3,2 0,0,0
POV 3 0,0,0 0,0,0 2,2,3
a 3 agent consensus coordination
POV1 POV2 POV3
POV 1 3,2,..,2 0,...,0 0,...,0
POV 2 0,...,0 2,...,2,3,2,...,2 0,...,0
POV 3 0,...,0 0,...,0 2,..,2,3
a N agent consensus coordination

This game has two pure strategy Nash equilibria and one mixed strategies equilibrium. However all the options are suboptimal. A correlated random token could make the mixed strategy ideal - allowing both users to play the pure equilibria options and get equal maximal payoffs. However without such a coordinating device each player will choose his POV more frequently. For the payoffs listed above, each player whom expresses a preference fill opt for the preferred POV probability 3/5. They will miscoordinate with a probability of 13/25 leaving an expected return of only 6/25.

For non involved players the situation is simpler - they will miscoordinate with a probability of 1/2 and have an expected return of 1.

My informal point of view based on recent AfD participation is that there are at least two classes of coordination tasks -

Coordination1 - cost of establishing a (social) network of agents with a set of qualifications (domain knowledge (usually scarce) and policy knowledge) under a space-time constraint (14 days at a AdF page). I'd call this a MicroCosmic Coordination tasks - as it requires creating a social network mixing insiders and outsiders.

Coordination2 - a second class of coordination tasks seems to require a second round of coordination and involve the task of establishing coalitions. This also has a larger communication component. I'd call this a Political Coordination task

Afd discussions - seem to have 2 + modes of closing similar to the Ideas presented by Ayelt Oz in her paper on acoustic separation.[3].

  • Fast (closely related and very similar to CSD) - do not require Micro Cosmic Coordination
  • Slow with a good likelihood of repeated coordination failures - Micro Cosmic failures oft lead to relisting (extending the deadline), while political failures leads to no consensus at closure, multiple Afd of the same article over long timeframes.


Some points still needing more looking into

  • yet another version of the coordination game with N-gaents with a preference fo reaching ever smaller consensus prefered to no consensus at all. (but with equal sized miscoordinated blocks disqualifying each other.
  • repeated participation at Afd discussions leads to ad hoc coalition. These however turning into semi permanent ones.
  • Semi permanent coalitions reduce coordination costs
  • establishment of task related Afd notice boards support longer lasting coalitions by providing coordination discount for locating Afd discussions in related knowledge domains. e.g. PornBio via WikiProject_Deletion_sorting categories - if the categories have enough active participants (low diversity in editors population therefore leads to coordination failure at AfD ).
  • http://www.ri.cmu.edu/pub_files/pub1/shehory_onn_1997_1/shehory_onn_1997_1.pdf

Playing In Turns[edit]

let us consider a couple of variant. we start with a version of the consensus game for Afd where row players nominates deletion and the colum player will want to keep. No Consensus means keep.


Delete Keep
Delte 3,2 0,2
Keep 0,2 2,3
2 agent afd - NC means keep




Refrences & Notes[edit]

  1. R. Davis and R. G. Smith. (1983). "Negotiation as a metaphor for distributed problem solving.". Artificial Intelligence, 20(1) 20 (1): 63–109,.  Unknown parameter |URI= ignored (help); Unknown parameter |month= ignored (|date= suggested) (help)
  2. ant path meta algorithm - inline tags when used correctly provide editors a system of iterative coordinating requirements and changes between domain experts and policy experts using minimal coordination effort.
  3. Oz, Ayelet (5/1/2009). "The Hidden Wikipedia: Wikipedia as a System of Acoustic Separation" (PDF). Harvard Law School. p. 80. Retrieved May 14, 2012.  Check date values in: |date= (help)
  1. a b c d (In case a return to an old consensus is possible this would use the of 1,...,1 in the top right corner.)