[UHStudent1138]

The attached test question at first seemed very easy to me: the carbocation was the most stable because carbon was the most electropositive molecule.  The nitrogen was the secondmost electronegative and so the second most stable, and the oxygen came in last.  Given that these are all different resonance forms, I fail to see any other relevant factors that would lead to the carbocation being the least stable and the oxygen the second most stable. 

Is there some other stability criterion of which I am ignorant?

[orgopete]

A larger number of completed octets is also used to estimate stability or resonance contributions.

[PhDoc]

Electronegativity values: C, 2.5; N, 3.0; O, 3.5

What effect, if any, on your carbocation does the presence of two electronegative groups have?

[orgopete]

Electronegativity values: C, 2.5; N, 3.0; O, 3.5

What effect, if any, on your carbocation does the presence of two electronegative groups have?

As this hint seems contrary to the question, I am going to offer an answer. If you have a carbocation, adding one or two atoms that are more electron withdrawing logically would destabilize the carbocation. An example is the reduced stability of a carbocation alpha to a carbonyl group. I don't see this should apply here.

If you have a carbocation and electron withdrawing atoms with non-bonding electrons, do these electrons participate? If so, how should this participation be represented? I suggested the rule of most completed octets be applied. Now, granted there are two atoms that can donate. Which atom should be the greater donor? Electron withdrawing properties could be applied here, but so could acid-base properties. Suggesting electron donation I think also biases the original question.