[Eran]

Did you say the punishment cannot exceed the crime?
What if the rate of reporting, investigating and/ or conviction is very low?
Criminals might find the risk-reward ratio attractive.

Punishment (in the sense of forced restitution) cannot exceed the cost to the victim, plus reasonable enforcement costs.

Nothing else would be just. In particular, punishing somebody more severely than the damage they caused simply because others are also engaged in similar crimes is a gross violation of justice.

Japan has a maximum sentence of 7 years for groping. This isn't because victims suffer intense emotional harm but because the crime is massively under reported and the state wishes to use the potential of a lengthy sentence as a deterrent. If suspected gropers were banned from public transport and other crowded places they may be more cautious.

What do you think?

I think you hit the nail on the head. First, it is clearly unjust to cage somebody for 7 years for the mere crime of groping. That many others engage in groping, and that the crime is under-reported and under-enforcement are ethically irrelevant to the injustice.

However, by privatising currently-public areas such as public transportation and streets, owners of such facilities may condition entrance on a commitment not to grope, with groping leading to (temporary or permanent) expulsion / eviction.

That way (in generally in answering your first question), two goals are achieved without injustice. First, those frequenting such previously-public facilities can be secure in the groping-free nature of such use. Since most people prefer to be free from groping, profit-oriented operators are likely to impose such anti-groping rules (assuming the problem manifests itself).

Second, a deterrence would be created against groping, even if the formal "punishment" (i.e. restitution) is fairly moderate.

Thus while the formal, enforced "punishment" is always monetary and can never exceed the actual damages (plus reasonable costs), the full implication of the crime in terms of society's reaction may well be much harsher, albeit expressed in terms of people's legitimate preference not to associate with the criminal, rather than through the imposition of force on the criminal.

[AFAIK]

In this system would courts compensate all victims of crime equally?
Is "death insurance" a separate entity from life insurance?

What if following a murder conviction the next of kin wish to pursue revenge? Can they kill the guilty party and refund the compensation? Could victims of crimes use their compensation to fund the imprisonment of convicts?

[Eran]

In this system would courts compensate all victims of crime equally?

Courts don't compensate victims, but rather merely publish an opinion as to the amount of restitution due to the victim from his assailant.

Numerous factors will determine that amount, and while I would expect some standardization (as it is easier to rationalize and defend), I wouldn't be surprised if, under special circumstances, different amounts may be awarded.

Is "death insurance" a separate entity from life insurance?

By "death insurance" I take it you mean crime-victim insurance covering loss of life. The two insurance policies (crime-victim and life) have overlapping but not identical coverage. Crime-victim insurance covers all crimes, including those resulting in less than fatal bodily harm, as well, potentially, as crimes against property.

Life insurance covers death from all causes, including accidental, health-related or even suicide.

This is not unusual. Auto insurance covers all car accidents, including fatal ones, thus overlapping with life insurance.

What if following a murder conviction the next of kin wish to pursue revenge? Can they kill the guilty party and refund the compensation?

In analysing this question, we ought to keep in mind that two components of the criminal-justice system. The more "formal" component within which the use of force is authorised to extract restitution from a convicted criminal (but no more), and an "informal" component consisting of the reaction of the rest of society (in my model, largely mediated through insurance companies) to criminal events.

Depending on circumstances, the two sides, formal and informal, may work in different ways, exert different amounts of deterrence, or even partially compensate for each other.

Here are a few examples:
1. The infamous wealthy criminal who enjoys shooting homeless people, can easily afford to pay the restitution payment would find that the informal side quickly arrests his freedom. Since nobody wants to be an accidental murder victim, people have strong preference to living, working, shopping and commuting through areas within which people with known tendency to murder aren't allowed. The criminal may have paid his debt to his victims, but would still be prohibited entry to most developed land areas.
2. The sympathetic murderer, say a battered wife or, as in your question, a heart-broken relative out for revenge. They may be convicted by the formal arm of the law, but either use the restitution money owed them, or even public donations to pay their debt. Since their crime is obviously of a one-of variety, and they are highly unlikely to assault anybody again, their risk to society isn't high, and they are allowed to move freely. People who kill others by accident (and are silly enough not to have carried insurance) may also fall into this category.

Note, however, that your insurance policy will never cover deliberate crimes. If, through pursuing revenge, you cause more harm than you can afford (e.g. by hurting innocent third-parties), you are on your own.

Could victims of crimes use their compensation to fund the imprisonment of convicts?

I don't understand your logic. The compensation is paid in exchange for the restitution rights of the victims. Once paid, the victim no longer has a claim against the criminal - only the insurance company does. If the criminal was himself insured, the two insurance companies will settle. If he is a habitual criminal, he is unlikely to easily get coverage, and may find it difficult to secure housing, employment or credit.

Imprisonment, however, would only apply rarely, to people posing grave and likely risk to society, or those posing flight risk and still owing compensation. Even in these cases, however, the criminal would be able to choose amongst competing facilities, provided only that the facility is willing to take financial responsibility for the consequences of his escape.

[AFAIK]

The imprisonment I envision would be an act of revenge. Perhaps it would be more accurate to use the term hostage or kidnapping.
Could victims of crimes offer their aggressors a debt forgiveness or compensation refund in exchange for a term of imprisonment?
Could victims spend their compensation package imprisoning criminals against their will?

Can criminals redeem themselves by voluntarily entering rehabilitation programs?
How would this influence his ability to attain insurance or continue interacting with others?

[Eran]

Could victims of crimes offer their aggressors a debt forgiveness or compensation refund in exchange for a term of imprisonment?

Of course - any terms agreeable to both sides would work. All crime is private, and nobody is in a position to second-guess such arrangements.

This point pertains only to the formal component of society's response. Informally, other members of society may have their own ideas. For example, while the victim may freely forgive the criminal (in which case no compensation may be collected), others may still prefer to shun the criminal.

Could victims spend their compensation package imprisoning criminals against their will?

No, they couldn't. The compensation marks the end of the legitimate use of force against the criminal. Any further use of force becomes criminal itself.

Can criminals redeem themselves by voluntarily entering rehabilitation programs?
How would this influence his ability to attain insurance or continue interacting with others?

Again, we ought to examine the two sides of the system. In terms of formal restitution, this would be up to the victim (or, very likely, the insurance company that buys his rights) and the criminal (or, often, the insurance company that covers him).

In terms of the informal response, a rehabilitation program may be very helpful. A program with good success record could certainly help past-criminals regain sufficient credibility to rejoin society (which, in practical terms, may simply mean being able to acquire insurance coverage).

[Nunt]

Can criminals redeem themselves by voluntarily entering rehabilitation programs?
How would this influence his ability to attain insurance or continue interacting with others?

Judging from current sentiment it does seem likely that people will be willing to give certain criminals a second chance at an honest life.