Giving someone who has been raped, murdered, tortured or enslaved a lump sum of money hardly seems like compensation for their suffering. Yet it’s something that courts, governments and other groups occasionally must do.

On Monday, Japan and Korea announced a decision of this kind, as they reached a historic settlement for wartime atrocities committed more than 70 years ago.

Japan agreed to set up a $8.3 million fund to support 46 surviving South Korean women whom the Japanese military had taken as sex slaves -- so-called “comfort women” -- during World War II. Historians estimate that the Japanese army coerced as many as 200,000 women and girls from occupied countries into sexual slavery, including in South Korea.

The countries described the agreement as a "final and irrevocable resolution" to a dispute that has tattered relations between the U.S. allies for decades. (Whether it actually will mark the end remains to be seen -- this isn't the first time Japan has offered official apologies or compensation.)

The agreement underscores how difficult it is for parties to find common ground over paying for historical injustices.

Monetary reparations are a common way to level the scales between two parties following a historic or moral injustice. Since World War II, Germany has paid nearly $90 billion of reparations to Israel and Jews for stolen property and other atrocities, and it has continued to face claims for payments into this decade. New Zealand paid its native Maori people hundreds of millions of dollars for colonial injustices.

And the United States has made various payments to native American tribes for atrocities and violated treaties, and it paid $20,000 each to around 100,000 Americans of Japanese descent who were interned in camps during World War II. Some have argued -- most notably Ta-Nehisi Coates in a June 2014 cover story for the Atlantic -- that the failure to pay reparations to African Americans for slavery remains an injustice.

In Rwanda, there is an ongoing debate about what compensation is due victims of the 1994 genocide. And over a decade ago, many criticized South Africa's government for approving only $3,900 for each family of apartheid victims.

One of the challenges is the lack of rules to govern reparations. There are few guidelines for how much societies should pay when we decide it’s right to use money to alleviate suffering, and how we set the price for a particular atrocity.

The legal basis for reparations goes back to the beginning of property rights. The philosopher John Locke discusses the right to seek reparations when one man “receives damage” by the transgression of another. And on a smaller scale, courts make these kinds of decisions all the time, awarding monetary settlements to victims who have suffered wrongs like personal injury or slander. 

The justification for giving a victim money is two-fold, says Robin Hanson, a professor who teaches economics and law at George Mason University: Compensating the victim in some way for their losses, and penalizing the perpetrator to try to prevent future crimes.

But the law typically requires identifying specific victims and clear evidence of how they have been harmed, says Hanson. And it has other restrictions, like statues of limitation that limit the period of time in which damages can be collected.

In the case of Japan and Korea, the dispute is more easily resolved because some of the women are still living. When the U.S. compensated Japanese-Americans who it had interned in the Second World War, the money was also given directly to the victim.

Cases where the victims have died and reparations would be given to their descendants – as in the case of American slavery – are much more controversial.

African-Americans have obviously been greatly harmed by the legacy of racial discrimination and slavery. Supporters of reparations argue that that history is still important to the present because wealth and inequality build up over time. This is why African-Americans make 77 cents on a white dollar, but the average black family has only ten cents of wealth for every dollar of wealth an average white family has, according to Dalton Conley, a sociologist at New York University.

But tracking exactly what effect any atrocity has had over generations is still extremely tricky. It requires evaluating a counterfactual that never existed, and it's not clear how the monetary value of reparations should change over decades and generations.

It might seem like more distant relations would be entitled to less compensation. But you could also argue that atrocities like slavery become more costly with time due to the miracle of compound interest. As the economist Tyler Cowen has written, a loss of a billion dollars two hundred years ago turns into $369.4 billion with just 3 percent compounding interest and $17.3 trillion with 5 percent compounding interest.

With slavery, reparations might require transfers of wealth from and to people who are only distantly related to the original perpetrators and victims. Such transfers “could only very crudely track the actual pattern of cause and harm,” writes Hanson.

(Coates points out that many African Americans living today have been directly harmed by Jim Crow laws or housing discrimination, an area in which the argument for reparations is clearer.)

Setting a monetary figure for reparations is also a challenge -- a product of calculating the cost to the victim, estimating any benefits the money is meant to provide, and a lot of negotiation. In Japan's case, the funds will finance and expand a state-run program that provides medical, welfare and other assistance to the victims. A Japanese spokesperson clarified that the money is not a legal settlement.

Many people feel that reparations are just and right in some situations – if only to lend more weight and symbolism to a formal apology, as in Japan and Korea. But the question is where to start, and to stop.

As Cowen writes, much property owned today was once acquired by theft, but it's often impractical and unjust to redistribute it. “Everyone living today, if they go back far enough, can find ancestors who were oppressed and victimized.”

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