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[Solved]: voting scheme for peaceful coexistence

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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?

Asked By : Erel Segal-Halevi

Answered By : Mike Samuel

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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