Positive-Sum / Zero-Sum / Negative-Sum Situations


Brad Spangler

October 2003

What These Terms Mean

Zero-sum, positive-sum, and negative-sum are all game theory terms that refer to the outcomes of a dispute or negotiation. They refer to the actual amount of wealth (money, land, vacation time) -- measurable rewards -- that each party receives. Though similar, these terms differ from the terms "win-win, win-lose, and lose-lose" which refer to wins or losses relative to expectations.[1]

In a zero-sum situation, it is impossible for one party to advance its position without the other party suffering a corresponding loss. If one side gets $1,000 more, that means the other side gets $1,000 less. The wins and losses add up to zero. These situations typically arise in distributive bargaining cases where a "fixed pie" must be divided between the parties. For example, if two departments are splitting up a fixed amount of money, the more one gets, the less available to the other. Or, if there is only one job, one person will get it and the other person will not. (One job won and one job lost equals zero.)

Peter Woodrow discusses his work designing a dispute resolution system for East Timor land tenure conflicts.

"Positive-sum" outcomes are those in which the sum of winnings and losses is greater than zero. This becomes possible when the size of the pie is somehow enlarged so that there is more wealth to distribute between the parties than there was originally, or some other way is devised so everyone gets what they want or need. This can be done in a variety of ways. Extra funds might be obtained from an outside source allowing both departments to meet their budgets. Or it might be done with integrative bargaining, where different interests are negotiated to meet every sides' needs. For example, one department might agree to take over some of the jobs of another department that it could do at a lower cost. This would make up for some of the lost money, even though the absolute amount of money was not expanded. The more different interests that are on the table for discussion, the more likely a positive sum solution can be worked out.

The most difficult problems are negative-sum situations, where the pie is shrinking. In the end, the gains and losses will all add up to less than zero. This means that the only way for a party to maintain its position is to take something from another party, and even if everyone takes his or her share of the "losses," everyone still loses in comparison to what they currently have or really need. This type of situation often sparks serious competition.

Morton Deutsch talks about Deutsch's "first commandment of conflict:" know what kind of conflict you are in.

However, negative-sum disputes are not always lose-lose because if the parties know the pie is shrinking, it is possible their expectations will be low. A perfect example of a negative-sum dispute is the allocation of budget cuts within an organization. In this case, each department expects to have some funds taken away, but whether the outcome is a win or loss depends on how much money a particular branch gets in comparison to what they expected to have cut from their budget. So, if a branch was expecting to get a 30 percent cut and they only got cut 20 percent, which would be a win, even in a diminishing resource situation.

[1] Most of the material for this essay was drawn from Heidi Burgess and Guy Burgess. Encyclopedia of Conflict Resolution (Denver: ABC-CLIO, 1997), 306-307 and 309-310, and from discussions with Heidi and Guy. <http://www.amazon.com/Encyclopedia-Conflict-Resolution-Heidi-Burgess/dp/0874368391>.

Use the following to cite this article:
Spangler, Brad. "Positive-Sum, Zero-Sum, and Negative-Sum Situations." Beyond Intractability. Eds. Guy Burgess and Heidi Burgess. Conflict Information Consortium, University of Colorado, Boulder. Posted: October 2003 <http://www.beyondintractability.org/essay/sum>.

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