Cash for vasectomy....

[Existentialist]

Because getting something for making a decision that will be economically advantageous in the near term is bribery.

While we're at it, can we call giving someone money for undertaking an action of their own free will?

Where I come from, that's work. You always have a right not to work (and they always have the right to not pay them).

Bribery is something used to coerce someone into doing a disadvantageous, immoral or illegal action.

This has nothing even close to that.

I think a bribe is simply a financial inducement (or an inducement of some value to the recipient) designed to get them to agree to a course of action that breaks an ethical standard. The ethical standard here is a medical one: that if people undergo operations on their bodies, those operations should be carried out with genuine consent. A financial inducement is a deliberate interference with the principle of genuine consent. It's a bribe.

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Definitions of bribe on the Web:
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and...?