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# Mathematics could stabilize peace treaties

Game theory might help draw up war settlements.

Less than one in five civil wars end through negotiated settlements. Credit: © GettyImages

A political scientist at the Santa Fe Institute in New Mexico has devised a mathematical method that could help civil-war negotiators to find the most stable peace treaties1.

Elisabeth Wood calculates that a settlement will be stronger and more likely to last if it finds the ideal way to apportion the stakes. For example, if two warring factions each want control of some part of a disputed region, negotiators need to divide the territory in a way that comes closest to satisfying them both.

This doesn't guarantee that neither party will fight on in the hope of gaining more. But it may lead them to decide that further fighting will not substantially improve the eventual outcome.

Wood hopes that her technique could provide a general framework for resolving civil conflicts over power, land or other resources fairly and transparently. At present, dispute is addressed ad hoc. She reckons that her mathematical model offers a way to make progress even if the stakes of the conflict are less obviously divisible.

Some of the worst outbreaks of violence in the late twentieth century have involved civil war, such as in Rwanda, the Balkans and Colombia. Less than one in five civil wars end through negotiated settlements. When an agreement is reached, it is implemented only in around 60% of cases.

Long division

Wood argues that the behaviour of a warring party depends on its beliefs about its opponent. If one party thinks that the other will fight on instead of agreeing a settlement, they may do the same. Wood points out that the way the stakes are distributed in a peace agreement feeds back into these beliefs and may give each side a more positive view of the other.

She uses game theory, a favourite theoretical tool of military and political strategists since the 1950s, to calculate how the probability of each party's decision to fight or compromise changes as the terms of an agreement change. This enables her to find the 'best' terms: those that produce the lowest likelihood of continued hostilities, and the smallest chance that either side will renege on a pact.

Strictly quantitative calculations never satisfy policy people very much Michael O'Hanlon , Brookings Institution

From this analysis, Wood draws up a list of possible obstacles to a robust settlement, and a corresponding list of potential solutions. The importance of rendering the stakes divisible, for example, could entail encouraging the emergence of moderates within negotiating parties who are prepared to countenance sharing rather taking an all-or-nothing attitude.

But bare numbers are always of limited use in the messy arenas of real peace negotiations. Although Wood's model looks fine, says foreign-policy expert Michael O'Hanlon of the Brookings Institution in Washington DC, "strictly quantitative calculations never satisfy policy people very much".

"I suspect the model is too abstract to be of much practical use," admits Wood, who now intends to test how it might apply to real civil conflicts.

## References

1. Wood, E. J. Modeling robust settlements to civil war: indivisible stakes and distributional compromises. 03-10-056, (2003).

Authors

Brookings Institution

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Ball, P. Mathematics could stabilize peace treaties. Nature (2003). https://doi.org/10.1038/news031215-1