Why does the total credit associated with a data structure must be nonnegative at all times for the accounting method?
The amortized analysis calculates complexity for a sequence of $ n \in \mathbb{N} $ operations, no matter how large $ n $ is and what is the structure of sequence (i.e. which operations are within the sequence). If you would allow $ \sum_{i = 1}^{n}{\hat{c_i}} &lt; \sum_{i = 1}^{n}{c_i} $ for some $ n $ and some sequence of operations, then the same inequality would hold for any multiplication of $ n $. Thus you would not have an upper bound, so no analysis would be possible. This reasoning is for both accounting and potential method.