What goes wrong when talks break down

Nonlinear analysis explains how negotiations often fail

SANTA FE, N.M. — Sometimes negotiations appear to be going all right — and then somebody assassinates the High Peace Council chairman. A new way of simulating how groups make decisions combines social psychology and nonlinear mathematics, revealing how forces may unexpectedly conspire to send negotiations off the rails.

The approach captures the unpredictable nature of group decision making and might be used to predict which members of a jury, legislature or corporate board will be supporters or dissenters of a policy, or if consensus is even possible. It may also help explain how Burhanuddin Rabbani, a key figure in negotiations between the Afghan government and the Taliban, ended up the victim of a suicide bomber in September 2011.  

Many methods for assessing how negotiations unfold assume a linear, relatively predictable relationship between the group members’ opinions, their influence on each other and the outcome of the negotiations. These methods can work well for small groups, says policy analyst Hilton Root of George Mason University in Arlington, Va. “But,” he said, “there’s a lot you can’t do with them.”

To capture the complicated turns and twists that occur in many negotiations, University of Washington physicist Michael Gabbay developed a different approach that allows for a traditional linear discussion path but also incorporates nonlinear dynamics, where outcomes can be unpredictable and driven by a seemingly random variable, such as who does the talking first.

Simulating the behavior of decision makers with this technique can suggest tactics — such as not having everyone talk to everyone at the same time — that might make reaching consensus easier, Gabbay reported December 6 at the International Conference on Complex Sciences.

To put the new approach to use, key negotiators are identified and each is assigned a place on a spectrum that reflects some quality relevant to the negotiations. So if the goal is to determine how the Afghan government and insurgent leaders might reach agreement, the spectrum might be hawk on one end, dove on the other. To figure out where Afghan players fit on the spectrum, experts were surveyed as stand-ins for political leaders and asked whether they agreed with statements such as, “partition of Afghanistan should be considered to end the conflict, if necessary,” or “a strong emir with power concentrated in his hands is needed to rule Afghanistan.”

The position each player has on the spectrum can shift subject to three forces: the player’s natural inclinations, the force of the influence of the group and the force of new incoming information. When applied to the Afghan situation, this approach revealed Afghan High Peace Council chairman Rabbani’s key position in the middle of things. He wasn’t an extreme hawk, nor an extreme dove.

Then the players and forces are translated into a mathematical equation and run through a computer simulation, yielding a graph of the possible trajectories of the negotiations. In the Afghan example, such an analysis suggested that Taliban-affiliated actors supported the goal of seizing central state power. This may explain Rabbani’s assassination, Gabbay said. Rabbani’s position suggests he could have succeeded in reaching out to all groups and pushing for peace talks, which would not have aligned with Taliban goals.

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