A recent op-ed in the New York Times advocated for a law requiring bystanders to help people in emergencies. It says that such laws are common in Europe, but only a few US states have them. The value of such laws would lie mostly in the social message they send, since the penalties are usually weak and they're probably not strictly enforced. The article notes that people are more likely to judge an action to be immoral if it is illegal. Perhaps these laws (in places that have them) could be used to argue against omission bias in general.
This "sensible statute" sounds as though it could describe most of the population, if it were to be given a utilitarian interpretation.
With the exception of a few jurisdictions, the “no duty” rule remains largely the same as it was famously described by William L. Prosser, the dean of American tort law: “The expert swimmer, with a boat and a rope at hand, who sees another drowning before his eyes, is not required to do anything at all about it, but may sit on the dock, smoke his cigarette, and watch the man drown.”
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A sensible statute might read like this: “Any person who knows that another is in imminent danger, or has sustained serious physical harm, and who fails to render reasonable assistance shall be fined up to $5,000, imprisoned for up to three months, or both.” Civil liability could also be established, as in other countries.
This "sensible statute" sounds as though it could describe most of the population, if it were to be given a utilitarian interpretation.