The Power of Non-Zero
Game theory was the invention of one of the most brilliant minds of the twentieth century, John von Neumann (1903–1957). A child prodigy, he went on to make original contributions to mathematics, economics, statistics, computing, and physics. One of his fascinations was decision-making under conditions of uncertainty, in fields as far removed from one another (or perhaps not) as poker, economics, and the logic of deterrence in war.
Before von Neumann, the dominant models in microeconomics tended to be displayed in graphs charting such factors as supply and demand, marginal cost, and marginal utility. Where the lines crossed, there was equilibrium. That was where production and consumption, or selling and buying, evened out. It was as precise and beautiful as a Bach sonata.
But life tends not to be like that. Rarely do we find total information, perfect competition, and unblemished rationality. Moreover, economic variables are often not specifiable in advance. The effect of one person’s decision may well depend on how other people react to it. That is how bluffing works in poker. It is also how major financial decisions operate. The effectiveness of a rise or reduction in interest rates on the part of a central bank will depend on how the market reads it. If it generates confidence, it may well achieve its objectives, but if it is seen as an act of panic, it may prove counterproductive. Von Neumann’s father was a senior banker, and the son had absorbed some of the complexities of such decisions by listening to his family’s dinnertime conversations. He knew that existing models of decision-making failed to account for this level of complexity, in which the outcome is determined not only by what I do but also by how you react to what I do.1A not-dissimilar idea was developed by George Soros, who called it “reflexivity.” Soros’ principle is that how people react to a situation depends on how they interpret the situation. The biblical narrative that best exemplifies this is the story of the spies (Num. 13–14).
That was the basic insight on which game theory was based.
One of the simplest and most important distinctions in game theory is between zero-sum and non-zero-sum games. Zero-sum games are ones in which one person’s gain is matched by the other person’s loss. Either I win and you lose, or you win and I lose. Non-zero games are those in which the sum of the gains and losses is more, or less, than zero. It may be that both sides win or that both lose. What is fascinating is that the sages of the Talmud were well aware of this, and spelled it out in halakhic principles such as zeh neheneh vezeh neheneh, “both sides gain” (Kiddushin 22b), or zeh neheneh vezeh lo ḥaser, “one side gains but the other does not lose” (Bava Kamma 20b).
The idea is hugely important because it opens the way to creative forms of conflict resolution. A classic example is set out in our parasha. The Israelites were on the last stage of their journey to the Promised Land. They had arrived at the east bank of the Jordan, within sight of their destination. Two of the tribes, Reuben and Gad, who had large herds and flocks of cattle, felt that the land they were currently on was ideal for their purposes. It was good grazing country. So they approached Moses and asked for permission to stay there rather than take up their share in the land of Israel. They said: “If we have found favour in your eyes, let this land be given to your servants as our possession. Do not make us cross the Jordan” (Num. 32:5).
Moses immediately saw the dangers in this proposition. The two tribes were putting their own interests above those of the nation as a whole. They would be seen as abandoning their fellow Israelites at the very time they were needed most. There were wars to be fought if the people were to inherit the land. As Moses put it to the tribes: “Are your brothers to go to war while you stay here? Why would you discourage the Israelites from going over into the land the Lord has given them?” (Num. 32:6–7).
The proposal was potentially disastrous. Moses reminded the men of Reuben and Gad what had happened when the spies demoralised the people. The result of that one episode was to condemn an entire generation to die in the wilderness and to delay the eventual conquest by forty years. “And here you are, a brood of sinners, standing in the place of your fathers and making the Lord even more angry with Israel. If you turn away from following Him, He will again leave all this people in the wilderness, and you will be the cause of their destruction” (Num. 32:14–15). Moses was blunt, honest, and confrontational.
What then followed is a model of non-zero negotiation. The Reubenites and Gadites accepted the justice of Moses’ concerns, and proposed a compromise. Let us make provisions for our cattle and our families, they said, and we will then accompany the other tribes across the Jordan. Not only will we fight alongside them, we will go ahead of them. We will not return to our cattle and families until all the battles have been fought, the land has been conquered, and the other tribes have received their inheritance. We will gain by having good land for our cattle, and the nation as a whole will not lose because we will be in the army, in the front line, and we will stay until the war has been won.
Moses recognised that they had met his objections. He restated their position to make sure he and they both understood the proposal and were ready to stand by it. He extracted from them agreement to a tenai kaful, a double condition, both positive and negative: If we do this, these will be the consequences, but if we fail to do this, those will be the consequences.2See Gittin 75a.
He left them no escape from their commitment. The two tribes agreed. Conflict had been averted. The Reubenites and Gadites achieved what they sought, while the interests of the other tribes had been secured. It was a classic non-zero, win-win negotiation.
How justified Moses’ concerns were became apparent many years later. The Reubenites and Gadites did indeed fulfil their promise in the days of Joshua. The rest of the tribes conquered and settled Israel while they (together with half the tribe of Menashe) established their presence in Transjordan. Despite this, within a brief space of time there was almost civil war.
Joshua 22 describes how, returning to their families and settling their land, the Reubenites and Gadites built “an altar to the Lord” on the east side of the Jordan. Seeing this as an act of secession, the rest of the Israelites prepared to do battle against them. Joshua, in a bold act of diplomacy, sent Pinhas, the former zealot, now man of peace, to negotiate. He warned them of the terrible consequences of what they had done by, in effect, creating a religious centre outside the land of Israel. It would split the nation in two.
The Reubenites and Gadites made it clear that this was not their intention at all. To the contrary, they themselves were worried that in the future, the rest of the Israelites would see them living across the Jordan and conclude that they no longer wanted to be part of the nation. That is why they had built the altar, not to offer sacrifices, not as a rival to the nation’s Sanctuary, but merely as a symbol and a sign to future generations that they too were Israelites. Pinhas and the rest of the delegation were satisfied with this answer, and once again civil war was averted.
The negotiation between Moses and the two tribes brilliantly exemplifies the four principles arrived at by the Harvard Negotiation Project, set out by Roger Fisher and William Ury in their classic work, Getting to Yes.3Roger Fisher and William Ury, Getting to Yes: Negotiating Agreement Without Giving In (London: Random House Business, 2012).
First, Moses separated the people from the problem. He made it clear to the Reubenites and Gadites that the issue had nothing to do with them specifically and everything to do with the Israelites’ experience in the past in the episode of the spies, in which everyone suffered and no one gained. The problem was not about this tribe or that but about the nation as a whole.
Second, Moses and the Reubenites and Gadites focused on interests, not positions. The Reubenites and Gadites were prepared to change their plans for the sake of the nation as a whole, while Moses, in light of this, was willing to retract his opposition. It is striking how different this conflict was from that of Korah and his followers. There, the whole argument was about positions, not interests – about who was entitled to be a leader. The result was collective tragedy.
Third, the Reubenites and Gadites invented an option for mutual gain. By creative thinking, they formulated a proposal that would satisfy both their needs and those of the other tribes.
Fourth, Moses insisted on objective criteria. The Reubenites and Gadites would not return to the east bank of the Jordan until all the other tribes were safely settled in their territories. And so it happened, as narrated in the book of Joshua:
Then Joshua summoned the Reubenites, the Gadites, and the half-tribe of Menashe and said to them, “You have done all that Moses the servant of the Lord commanded, and you have obeyed me in everything I commanded. For a long time now – to this very day – you have not deserted your fellow Israelites but have carried out the mission the Lord your God gave you. Now that the Lord your God has given them rest as He promised, return to your homes in the land that Moses the servant of the Lord gave you on the other side of the Jordan.” (Josh. 22:1–4)
This was, in short, a model negotiation, a sign of hope after the many destructive conflicts elsewhere in the book of Numbers, as well as a compelling alternative to the many later conflicts in Jewish history that had such destructive outcomes. It succeeded not because either side was weak, or used ambiguous words and diplomatic evasions, but because both were honest, principled, and focused on not only what was good for them but also on what was good for the other side. That is the power of non-zero thinking.
Non-zero-sum-ness is more than a mathematical concept. It is fundamental to the theological principle of the dignity of difference and the miracle that unity in heaven creates diversity on earth.4See, for example, Jonathan Sacks, The Dignity of Difference (London: Continuum, 2002), 45–66.
Because we are each finite, limited, and different, what I lack, someone else has. What someone else lacks, I have. Therefore when we come together in collaborative ways, we both benefit. When, to the contrary, we focus on positions, not interests – defining a conflict in win/lose, zero-sum terms – the result is usually violence from which both sides lose.5See on this A. O. Hirschman’s important work, The Passions and the Interests: Political Arguments for Capitalism Before Its Triumph (Princeton, NJ: Princeton University Press, 1977).
The human tendency to do just this is perennial, disastrous, and to be fought against in every generation.6It has to do with a specific set of reactions in the (predominantly male) brain that are sensitive to hierarchy and the role of the alpha male. It tends to dominate in honour-based cultures.
It is by re-conceptualising difference from a source of conflict to one of mutual gain that we become agents for the greatest and hardest-to-achieve divine blessing of all: peace.
Peace is not a world where we are all the same. It is a world in which we use our differences to enlarge our understanding of God and our appreciation of those not like us. It is no accident that Numbers, an anthology of conflicts, moves towards a close with this story of conflict avoided, peace restored.