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Many areas in the world suffer from conflicts between two groups (usually ethnic or religious). For the purpose of this question, I assume that most people of both sides want to live in peace, but there are few extremists who incite hatred and violence. The goal of this question is to find an objective way to filter out those extremists.

Imagine a town with 2 conflicting groups, A and B, each has N people. I propose the following voting scheme (which I explain from the point of view of group A, but it's entirely symmetric for the other group):

  • equality-rule: The number of people in each group must always remain equal.
  • expel-vote: At any time, each person of group A can claim that a certain person of group B is "extremist", and start a vote. If more than 50% of the people in group A agree, then that certain person is expelled from town.
  • counter-vote: To keep the equality-rule, a single person of group A should also leave the town. This person is selected by a vote between the people in group B (i.e. each person in group B votes for a single person in group A, and the one with most votes is expelled from town).

My intuition is that:

  • On one hand, this scheme encourages people to be nice to people of the other group, so that they won't be subject to expel-votes.
  • On the other hand, the equality rule encourages people to think twice before starting an expel-vote, because this will put them in danger of expel in the counter-vote.

[ADDITION] Several questions can be asked about this scheme, for example:

  • Under what conditions does it diverge to a situation where people vote and counter-vote, until the number of citizens in one of the groups reaches 0?
  • Under what conditions does it stabilize on a situation where the two group has more than 0 citizens?
  • Under what conditions, the stable number of citizens is more than half the initial number?

Note that this scheme does not even try to reach an objective measure of "extremism". The only goal is stability.

I would like to know, has this voting scheme has been studied in the past?

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    $\begingroup$ I don't know if it has been studied, but you probably want to wonder what would be the payoff and/or winning. $\endgroup$
    – jmad
    Commented Jun 7, 2012 at 11:40
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    $\begingroup$ Studied with respect to what property? Game theory aside, I am not sure the proposed strategy can fight extremism; even if successful (i.e. almost only and most of the extremists are expelled) it merely moves it out of town. Also, cross-group voting is going to create unnecessary tension (e.g. if B counter-votes a non-extremist of A out of town). Furthermore, you don't assume some voting accuracy: non-extremists may be banished because of politics or petty conflicts, strengthening the extremist factions. $\endgroup$
    – Raphael
    Commented Jun 7, 2012 at 12:14
  • $\begingroup$ Does game theory belong under computer science? I think it doesn't and that this question is off-topic here. Also, this seems more like sociology than game theory: the rules of who is an extremist and what does it mean to “live in peace” are not clearly defined. $\endgroup$
    – svick
    Commented Jun 7, 2012 at 12:15
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    $\begingroup$ @svick: As far as I know, game theory is done by both mathematicians and computer scientists (at least). If this concerns you, please open up a discussion about it on Computer Science Meta. $\endgroup$
    – Raphael
    Commented Jun 7, 2012 at 12:19
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    $\begingroup$ @svick It does, especially algorithmic game theory. I know it has applications in randomized algorithms and online algorithms at least. Even the Gödel Prize was awarded for the foundations of AGT. $\endgroup$
    – Juho
    Commented Jun 7, 2012 at 14:45

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If a person owns property in the town, then when voted out, they presumably forfeit the property. This creates an economic incentive to systematically rob minority groups via things like the Spanish Edict of Expulsion which expelled the community of Jews that had thrived prior to the Reconquista from Spain. Although the decree technically allowed them to sell their possessions (at firesale prices) before fleeing, they were not allowed to take the proceeds with them:

And we likewise give license and faculty to those said Jews and Jewesses that they be able to export their goods and estates out of these our said kingdoms and lordships by sea or land as long as they do not export gold or silver or coined money or other things prohibited by the laws of our kingdoms, excepting merchandise and things that are not prohibited.

Such incentives might be sufficient for cartels to arise. A cartel that can corner the market on readily available portable wealth can combine that control with bloc voting to vote out an identifiable minority group in such a way that they have little option but to liquidate assets through the cartel making the cartel members wealthy.

Any analysis should take into account such incentives. Game theory, since it does not by itself model irrational tendencies like in-group/out-group bias, might have a hard time predicting such things.

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  • $\begingroup$ You mean that, for example, 70% from group A and 70% from group B will form a cartel that will expel the other 30% of each group? $\endgroup$
    – Erel Segal-Halevi
    Commented Jun 10, 2012 at 5:16
  • $\begingroup$ @ErelSegalHalevi, No. I mean a small group of manipulators will form a cartel and use propaganda to convince a larger number from one group to evict a minority by labeling them radical, or by claiming that they should be the ones from their group to leave in order to get radicals from the other group out. $\endgroup$
    – Mike Samuel
    Commented Jun 10, 2012 at 5:26
  • $\begingroup$ One possible solution to this problem is that, in any expulsion vote, one of the people that voted in favor of the expulsion will be selected at random, and expelled as well. Do you think this will solve the problem? $\endgroup$
    – Erel Segal-Halevi
    Commented Oct 20, 2012 at 18:29
  • $\begingroup$ @ErelSegalHalevi, no. Any penalty that aims to prevent this scenario can only work if the cartel organizers are likely to feel a penalty that causes a loss almost as severe as that which they stand to gain. In this scenario a small cartel is manipulating the prejudices of a majority so the chance of any randomly applied penalty affecting a cartel member is relatively small so I'm skeptical that this would really serve as a disincentive. $\endgroup$
    – Mike Samuel
    Commented Oct 20, 2012 at 19:32
  • $\begingroup$ If you assume that a small cartel can influence the majority to act against their own interest, doesn't it go against the democratic idea in general? $\endgroup$
    – Erel Segal-Halevi
    Commented Oct 21, 2012 at 10:23

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