Preponderance of the evidence is the level of burden of persuasion typically employed in the civil procedure and administrative law. In plain English, the phrase roughly means "more likely than not."
By contrast, in criminal procedure, the required burden of proof is beyond a reasonable doubt.
The difference between the two can perhaps be seen in the criminal and civil trials of O.J. Simpson for murder. Jurors acquitted Simpson in the criminal trial, which required "proof beyond a reasonable doubt", whereas in the civil trial, a different jury looked for a "preponderance of the evidence" and found it, ruling against Simpson and finding him "liable" for the two deaths.
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