Eye for an eye: why return only nine out of ten blows

About 3,750 years ago, a king of Babylon had a rule carved into a black stone more than two meters tall that we still repeat today: if a man puts out another man’s eye, let his own eye be put out. In 1980, an American political scientist used computers to find the hidden flaw in that rule. Applied to the letter, it may never end.

The king was Hammurabi. The political scientist, Robert Axelrod. Almost four millennia lie between them, and the same question: when someone hurts you, how much should you give back?

What is the eye for an eye principle (lex talionis)

The eye for an eye principle, known in law as lex talionis or the law of retaliation, holds that punishment should be equal to the harm caused. The Latin talio comes from talis: “such”, “alike”. Harm like the harm received. No more, no less.

Everyone knows its most famous formula: an eye for an eye, a tooth for a tooth.

An eye for an eye, a tooth for a tooth: from Hammurabi to the Bible

The stone in the Louvre

One of its oldest records is in the code of Hammurabi, king of Babylon, carved around 1750 BC on a stele about 2.25 meters tall. It was found at Susa, in present-day Iran, between 1901 and 1902, and is now on display at the Louvre Museum.

Its law 196 reads, in the museum’s own translation: “If a man put out the eye of another man, his eye shall be put out.”

But Hammurabi’s eye for an eye came with fine print. The penalty depended on who the victim was:

• If the eye belonged to another free man of the same rank, an eye for an eye (law 196).
• If it belonged to a commoner, the payment was one mina of silver (law 198).
• If it belonged to someone else’s slave, the payment was half the slave’s price (law 199).

The three versions in the Bible

The formula reappears in the Hebrew Bible, in three places:

• Exodus 21:23-25: “life for life, eye for eye, tooth for tooth, hand for hand, foot for foot, burning for burning, wound for wound, stripe for stripe”.
• Leviticus 24:19-20: “breach for breach, eye for eye, tooth for tooth”.
• Deuteronomy 19:21, with the same formula.

A rule for taking revenge, or for holding it back?

Today “an eye for an eye” sounds like revenge. But lex talionis is usually interpreted the other way round: as a limit. For an eye, an eye. Not a life, not an entire family. Against retaliation without measure, it set a ceiling.

Axelrod calls it a crude form of justice. And he points out something important: when there is a central authority that enforces the rules, punishment can fit the crime without having to be as painful as the crime itself. The problem arises when there is nobody above, and the parties themselves have to punish each other.

The hidden problem: the echo

Axelrod is famous for the computer tournaments he organized around 1980, in which programs written by experts faced each other in the repeated prisoner’s dilemma. The winner was a strategy called TIT FOR TAT, named after the old phrase for paying back like with like: cooperate at first, then copy whatever the opponent did last. It is, in essence, an eye for an eye.

What gets told less often is what happened when that strategy met someone slightly sneaky.

A program that defected only now and then

Among the entries was a program called JOSS. It was almost identical to the winner, with one small change: 10% of the time it defected even when the other side had cooperated. It tried to slip in a small advantage every so often.

Axelrod published a game between the two, move by move:

1. Moves 1 to 5: both cooperate.
2. Move 6: JOSS defects out of the blue.
3. Move 7: TIT FOR TAT punishes. JOSS, which had gone back to cooperating, responds to that punishment by defecting in turn.
4. From then on, a single defection bounces back and forth endlessly: one punishes on the even moves and the other on the odd ones.
5. Move 25: JOSS slips in another defection and a second echo begins.
6. The two echoes overlap and, from that point on, both defect on every move until the end.

Result: 241 points for JOSS and 236 for TIT FOR TAT. JOSS won by a hair. And both came out losing.

When a single defection can set off a long string of recriminations and counter-recriminations, both sides suffer.

The three levels of a retaliation

Axelrod explains why almost nobody sees the problem coming. A decision has three levels of effects:

• The direct one: defecting always earns more points on the move where it happens. Easy to see.
• The indirect one: the other side can punish you. Almost every participant already took this into account.
• The tertiary one: by responding to their punishments, you may be repeating, and even amplifying, your own original defection.

That is where the real cost lies. According to Axelrod, many programs ended up punishing themselves without realizing it: the opponent merely acted as a go-between that delayed the blow by a few moves.

Feuds that last for generations

What on a computer is points, in life is decades. Axelrod recalls that in Albania and the Middle East there are feuds between families that last for generations: every grievance is paid back with another, and every retaliation opens a new cycle. The blows bounce back and forth until the original grievance is lost in the past.

Nobody remembers who started it anymore. Everyone remembers the last blow.

Nine out of ten: Axelrod’s proposal

Against all this, Axelrod suggests a small and very interesting adjustment:

A better strategy might be to return only nine tenths of each blow.

There is still punishment. The other side still has reasons not to defect for free. But each response is a little smaller than the provocation, and the echo fades instead of holding steady.

The example he gives comes straight out of the Cold War. He cites the analyst Richard Betts, who proposed that if the Soviet bloc mobilized troops in Eastern Europe, NATO should respond automatically but in a limited way: one American division for every three Soviet ones. Enough so that the mobilization did not come free. Little enough not to fuel an escalation.

Eternal grudges, the worst of the nice ones

The tournament also had the opposite extreme. A program called FRIEDMAN never defected first, but as soon as the other side defected even once, it never cooperated again. It was a grudge written into code. Of all the “nice” strategies, it scored the worst.

One misunderstanding is enough

Axelrod later repeated the tournament with a very realistic complication: each move had a 1% chance of being misread. A cooperation could be read as a defection, or the other way round.

As expected, there was far more retaliation. The surprise is that TIT FOR TAT was still the best strategy. It got into trouble when a misunderstanding started an echo, but it often got out again thanks to another misunderstanding, because it was willing to cooperate again as soon as the other side did. The less forgiving strategies, once trapped, almost never escaped.

Retaliation, grudges and negotiation

All of this translates directly to life away from computers:

• In a negotiation, a withdrawn concession or a hurtful remark can set off an echo of “well, then neither will I” that nobody remembers starting. It is the logic of the competing conflict style taken to its limit.
• In anger, venting by returning every blow tends to feed the anger rather than put it out, as we explained when writing about catharsis.
• In a team, someone who feels excluded sometimes hits back in ways that look legitimate, as in the case of the meeting that ended up costing millions, which we covered in the article on ostracism.
• In a couple, when each person responds to the other’s last sentence rather than to the underlying problem, the argument can repeat itself without moving forward, something reminiscent of the relationship conflicts that never fully get solved.

Axelrod’s lesson is not “turn the other cheek”. In fact, he argued for responding to a provocation right away. It is subtler than that: respond, yes, but a little less; punish, yes, but leave the door open to cooperating again.

Hammurabi put a ceiling on revenge. Axelrod discovered that, without a judge above, you also need a little margin below.

If you are curious about how you tend to respond when a conflict comes up, you can try our conflict style quiz.

Sources

• Axelrod, R. (2006). The Evolution of Cooperation (rev. ed.; 1st ed. 1984). Basic Books. Chapter 2, “The Success of TIT FOR TAT in Computer Tournaments”; chapter 7, “How to Promote Cooperation”, and chapter 9, “The Robustness of Reciprocity”.
• Code of Hammurabi, laws 196, 198 and 199. Louvre Museum, Department of Near Eastern Antiquities.
• Bible: Exodus 21:23-25; Leviticus 24:19-20; Deuteronomy 19:21.
• Black-Michaud, J. (1975). Cohesive Force: Feud in the Mediterranean and Middle East. Basil Blackwell. (Cited by Axelrod.)
• Betts, R. K. (1982). Surprise Attack: Lessons for Defense Planning. Brookings Institution. (Cited by Axelrod.)