The Jigsaw Man
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For the 1983 film see The Jigsaw Man (film)
"The Jigsaw Man" is a short story in the Known Space universe by Larry Niven. It shows a way in which good intentions can lead to disastrous consequences for society. In the story, criminals convicted of capital offenses are forced to donate all of their organs to medicine, so that their body parts can be used to save lives and thus repay society for their crimes. However, high demand for organs has inspired lawmakers to lower the bar for execution. The protagonist of the story, certain that he will be convicted of a capital crime (in his case, repeated speeding offenses), but feeling that the punishment is unfair, escapes from prison and decides to do something really worth dying for.
The story appears in the collections All the Myriad Ways and Tales of Known Space