vicariously

Vicariously means indirectly or as a substitute for someone else. (adjective)

When an employer is liable for the negligence of his employee simply because of the employment relationship, this is an example of a situation where the employer is vicariously liable.
When a parent makes her child take ballet lessons because the parent always wanted to take those lessons as a child, this is an example of the parent living vicariously through the child.

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