In general, conviction means a strong persuasion or belief. It also means the state of being convinced. In law, a conviction is the verdict that results when a court of law finds a defendant guilty of a crime. The opposite of a conviction is an acquittal (i.e. "not guilty"). In Scotland and in the Netherlands, there can also be a verdict of "not proven", which counts as an acquittal. There are also cases where the court orders that a defendant not be convicted, despite being found guilty.
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But letting citizens do police work — encouraging them even, by offering rewards — is not without risks.