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A person ( or group ) may be considered an " authority " on a subject matter if their expertise is well established.
This means that any statements the person makes, with regard to their field of expertise, will have the burden of proof in their favor.
That is, if a professor of mathematics makes a statement about numbers, it will be assumed to be true in the absence of evidence to the contrary.
This will also overrule any unsupported objections by an individual without such expertise.
Professional scholars are common examples of this, but they are not the only examples.
A carpenter might be considered an authority on wood, for example.

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