Equal Margins?

By: Jonathan Seidel

Tic for tat and eye for an eye: the meaning of compensation.

The YouTuber Veritasium made a video about the origins of game theory and its impact on life. In it he observed that tit for tat was the most optimizing strategy but is it so literal? 

Veritasium opened with the arms build up between the US and the SU. He summed up their strategy as defecting each time. The way game theory works as Axelrod endorsed was via a computer simulation. Working on the famous prisoner’s dilemma strategies were to play against one another consecutively. 3 points for cooperation, 5 points for defecting alone and 1 point for both defecting. Each strategy played head to head. After the competition Axelrod dubbed some nice and others nasty. Some that wished to cooperate and others to deceive. Taking a nasty one who tried to deceive the nice one. If the opponent was a total goody two shoes the nasty one would come on top but if they played a strategy that responded by periodically they would lose.

After all the strategies playing against one another tit for tat came out on top. Tit for tat cooperated until it was deceived. Once doing so, it would deceive. Ironically if the nasty one never wished to cooperate than after being deceived once tit for tat would lose that round if the nasty one never intended to concede but the score wouldn’t be so high and this nasty strategy may have won the battle but would lose the war. Overall tit for tat responded to provoke and would then cooperate for the rest. Overall, the nice strategies remained in the top half and even generationally won out. Nice strategies do finish first. Yet nice is contextual. Only nice until provoked. Once provoked tit for tat must settle the score. Showing it can push back and play professionally. 

Veritasium argued that an important distinction must be made between noisy and no noise. No noise everything is smooth but with noise tit for tat may make a grave error. Historically this almost took place when SU believed the US had shot ballistic missiles at them almost beginning WW3. Thankfully the officer in charge dismissed the possibility. Having faith it was an error to which it was. This sort of noise occurs all the time. Gossip and lies spread like wildfire. Skepticism peers at every corner. This is where Veritasium makes a note of tit for two tats. If someone bumps you, you don’t immediately bump them back. You trust it was an accident and ignore but if it happens a second time you give them a look or tell them to stop hoping that will stop them a third time then you retaliate. 

With lashon hara the immediate reaction is to ignore. The gossip is forbidden to listen or spread it. Gossip is wicked even though true. It is not a matter of correct but right and wrong. Truth is irrelevant when disparaging another. Here value takes priority and its priority is to ignore the information. A person may attempt to provoke you with gossip. This is different than someone insulting you as this information is about someone else. Tit for tat doesn’t exist in the same manner since the evil is about a third party. Yet the gossip is like a heat seeking missile recalibrating the receiver’s perception of the third party and therefore ought to be rejected outright. 

Lashon hara isn’t a direct insult so it doesn’t fit the parameters of a head to head competition. The noise is whether the opponent insulted you or hurt your friend. This in part of gossip. As someone is mentioning the ills of another about you. Here it works as in tit for tat the apparent insulted could hurl insults back or refuse to speak to this person. Now there is no cooperation because a middleman either erred or lied. In this case gossip does make an entrance here. This is indirect but follows the historical case of ballistic missiles. Technology confirmed a US attack and even some of the officer’s man encouraged a response but he decided to trust his enemy. They wouldn’t do that therefore I will wait. Only after his own potential demise would there be retaliation. That is guts.

Noise in game theory contributes to not cooperation but faith. Faith is the basis of conversation. Cooperation is confided in. Only cooperate if you believe the other will reciprocate. One had to extend their hand. Take that leap hoping the other will respond in kind. Yet everyone needs to be realistic. Don’t be gullible. People will try to manipulate do not let them. Therefore if they strike, strike back. If you don’t they will continue to assault you. Ignoring doesn’t answer the problem. Turning the other cheek doesn’t stop the bully only shoving the bully down does. The aggressor will only stop when the defender reciprocates. Revenge is frowned upon but at times necessary. Someone punches you punch back. Don’t let them pummel you because you’re a saint. 

Famously Maimonides codifies that it is forbidden for a Jew to take revenge. Yet this seems to contrast to goel ha’adam. How can these two be reconciled? Nahmanides adds a caveat to revenge. There is a difference between payback and pushback. Revenge for Nahmanides is when there is no debt owed. The case in Yoma is you didn’t let me use your sickle so I won’t let you use mine. Maimonides then differentiates this from holding a grudge which lamenting here you can use my sickle even though you didn’t let me use yours. This pairs with Nahmanides’ view that revenge is a zero sum game. The example in Yoma codified by Maimonides has nothing to do with reciprocation but unnerved agony. There is nothing to gain except to inform the other of their apparent treachery.

The case in Yoma is a far cry from theft, teasing and even murder. The difference between pushback and payback is demeaning another for their error versus mimicking their hurt to them. While the latter sounds worse, it corresponds to a direct assault rather a perceived one. Retaliation is an affront while reciprocation is merely the balanced effort. The sickle example applies to being punched so don’t punch back but such assault renders reciprocation necessary. Revenge on the Talmudic and Roshonim level is a feeling. It is a grudge and not an action. The whole point of goel ha’adam is permitting the family member to actualize his grievances. The negligent is forced to pay for his mistake. Revenge becomes an avenger not bitter. The punishment is either death or exile where then the avenger can calm himself.

Even Joseph the grand forgiver is only partially forgiving. He deceives the brothers and tests them at every turn. While there may have been altruistic motives, his attitude was clearly one of distaste and spite. He may have forgiven in the end but he enjoyed reciprocating his anger onto them. So by rabbinic literature revenge is prohibited in indirect ineffective situations. While given the biblical narrative as well as rabbinic confirmation revenge is permissible to even the odds to a direct assault. Revenge and retaliation are types of reciprocation: the former is emotional and the latter physical. This is tit for tat. Tit for tat in revenge scenarios is prohibited. Rather the colloquial revenge or reciprocation even if burdened is permissible. Eye for an eye holds up biblically, rabbinically and justifiably metaphorically.

Noise in game theory is take a step further in real world. Noise is not only misheard but emotion. How one reacts to being attacked. Some people are more sensitive than others. Tit for tat for one person will be tit for two tats for another. The strategy is a good model for how not to be a pushover yet some people don’t respond as quickly nor care as much. An insult may hurt less than a punch. A punch from a child may care more than an insult from an adult. While it is subjective to the person it also depends on the variables involved. While cooperation is a better measure if the goal isn’t worthwhile one may not care to be a pushover. If the whole goal is to outwit one another then yes cooperation is the way to go. In the case of life and death working together does remain superior but many situations are regulatory with little impact on life. 

Another important variable is magnitude of the provoke. There isn’t an equal response. If A hits B and B strikes back A may respond again since B hit too hard. A may perceive B’a retaliation as two tats instead one in return. While A started it, if A feels B is unjustified A will hit back and the cycle continues. This is akin to brothers pummeling one another because the light tap was reciprocated with a stronger punch. Each punching harder trying to one up the other. A boxing match with only exhaustion in sight. Being physically or emotionally wronged doesn’t have an equal measure whether due to untranslatable reciprocation or emotional difference. If one side strikes the other will respond and feeling wronged reciprocally will respond again. The mature setting is an understatement that fails to account for the childish notions of instigation. The rule of unprovoked attacks must responded fairly but no one does that because unprovoked ought to stop. A swift response hopes to cease but the aggressor only internalizes it as a challenge. 

In theory, the aggressor ought to never provoke in the first place but again immaturity and selfishness. One side for fun or sorrow attacks the opponent. Wishing to deflect rather than cooperate. The other side responds with deflection to show they will not be pushed over. What counts as deflection a punch or an invasion? A lie or an insult?  The computerized system doesn’t work eloquently when there are other favors involved. The aggressor takes his chances and leaps forward annoying the opponent. The opponent responds harshly. It is no tit for tat but tits for tat. A stronger retaliation than the attack. It isn’t about giving what they did but making sure they never do so again. Cooperation must be responded not in equity but with understanding.

In this regard, the role of compensation does the job. An eye for an eye accomplishes nothing. Both men are without an eye and worse off. Compensation places the debt on the aggressor to own up for his error. He must pay. If the victim can never work again maybe the aggressor ought to pay for the rest of his life or accommodate all his losses. It’s not about the eye itself but conceding to the damage. The rabbinic role was never literal because that would defeat the purpose. There is nothing to gain. Rather compensation ascertains that each understand the situation. A sum makes up for the error. An obligation that furthers future cooperation. The goal of an eye for an eye is not for both to suffer but for the aggressor to repent with his intimation to the other. He initiated the conflict now he must initiate the solution. 

Game theory prioritizes cooperation. Yet immaturity breeds aggression which is justifiably retaliated asymmetrically. The aggressor in his immaturity may grow upset but it the hopefully empathy of the screw up. An understanding that if you strike first you may get hurt double. Equity in damage is dubious. The defector has chosen their side and if they get burnt worse that is their fault for trying to play with the big boys. Until the aggressor ceases his immaturity cooperation is minute and lesson still unlearnt