Lots of different factors affect compensation for a case, the main one being how bad someone was hurt in the accident, how much were their medical expenses, have the injuries healed or are they ongoing, whether a person has health insurance, time lost from work, and the list goes on. These all factor in to the amount of damages. The second question for compensation is the level of insurance available. If someone has a lot of damages, but the responsible driver did not have much insurance or the injured party did not have his iown insurance, then that could limit the compensation available. How the accident happened can also affect the amount of compensation, someone injured by a drunk driver is likely to receive more compensation than someone injured in a routine accident, even if their injuries are the same.
Those are some main factors, but there are plenty more. Be sure to consult with an attorney if you need more details.
The damages consist of any economic losss such as wages and medical bills and the noneconomic damages such as pain and suffering, loss of enjoyment of life and any other element of damage allowed under the law of the jurisdiction.
Assuming that a defendant admits liability in a personal injury matter, he/she/it may nevertheless dispute the appropriate amount to compensate the victim. The usual elements of damages include, but are not limites to medical bills, lost wages/earning capacity, pain and suffering, etc. If you lost a pre-paid vacation, or had other "damages" then these too could be sought. The defendant is required to compensate you for all damages proximately caused by the injury. There is no formula. I am sure if you hire a good lawyer on a contingency fee he/she will zealously try and get you as much compensation as possible. In that regard, here is a link to an article from my website that may help you help the lawyer you eventually hire: http://wertheimlaw.com/component/content/article/25-what-to-do-if-you-have-been-injured-in-an-accident
Your question speaks to the general nature of the civil justice system. That is in comparison to the criminal justice system. As we all know, the criminal justice system punishes individuals who commit crimes against both person and property. On the other hand, the civil justice system is not designed to punish an individual, but rather award money damages for harm caused by a variety of circumstances. If it is an injury caused by someones negligence then it is called a tort claim and most auto wrecks fit that definition. If harm is caused by failing to perform under a contract, that is called a claim for breach of contract and so on. However, there is ONLY ONE GUARANTEE in the civil justice system and that is the right to tell a judge and jury your story and ask them to award you money damages. Only the judge and jury can award you money. There is no guarantee that you will get money regardless of your degree of harm or injury. The judge and jury must weigh the credible evidence and reach a conclusion as to the appropriate amount based thereon. Only then can there be compensation.
Unfortunately, it all depends. It all depends on the law of the state where the accident occurred and maybe even the law of the state where the vehicles and drivers are registered. It also depends on the type of insurance coverage you have purchased - full tort or limited tort, and the type of coverage if any, the other driver has. There are lots of variables at play. You should talk to a personal injury lawyer to get an answer to your question.
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