You press someone to accept a claim by making clear what they stand to gain by accepting it. The argument works because the benefit on offer gives the hearer a motive to agree — a carrot instead of the stick of the argumentum ad baculum. It can be attacked in the same way as its mirror image: a reward gives a reason to say yes, but no reason to believe.

Example
We have the best offer on this car; agree to it today and I will throw in a free set of winter tyres
Standardised form
“We have the best offer on this car” (q) is acceptable (A) because “we have the best offer on this car” (q) will be rewarded with a free set of winter tyres if you agree to it today (Z).
Transformations applied: the semicolon replaced by “because”; anaphora resolved — “it” replaced by “we have the best offer on this car”; the imperative “agree to it today” turned into the condition on the premise; the claim’s acceptability made explicit as the conclusion-predicate.

Classification
The conclusion is referred to as a whole in the premise, so the argument form is delta (q is A because q is Z).
The premise attributes the conclusion to the addressee, so the argument substance is II.
The keyword OFFERED REWARD describes the relationship between predicates Z and A. The argument lever can thus be formulated as “Being rewarded with a free set of winter tyres if you agree to it today (Z) is an OFFERED REWARD for being acceptable (A)”.
Not to be confused with
- Argumentum ad baculum — The mirror image: a threatened harm instead of a promised benefit.
NEGATIVE MOTIVATION - Argumentum ad hominem — Also addressed to the second person, but it attacks the claim through the character of its source.
CHARACTERALLY AUTHORITATIVE,U - Teleologic argument — Form, not lever: there the good consequences follow from doing the thing, here from accepting the claim.
alpha - Argument from expert opinion — The premise names a third party’s knowledge, not a benefit for the hearer.
III
Source
Invented example.
Notes
The argumentum ad carotam is the mirror image of the argumentum ad baculum: the two types share form, substance and shape, and differ only in whether the consequence held out to the hearer is a benefit or a harm. “Carota” is Latin for carrot, and the pair is the familiar carrot and stick.
