The qualitative characteristic that says accounting information can influence users' decisions by allowing them to assess past performance is:

Confirmatory Value

Explanation:

Accounting information has both the primary and secondary qualitative values or characteristics. These actually determine the usefulness of accounting information per time.

The primary characteristics of accounting information are: relevance and representational faithfulness

The secondary characteristics are: timeliness, comparability, understand ability and verifiability.

Specifically, Relevance describes the usefulness of accounting information in making financial decisions and for accounting information to be relevant it must possess the following:

1. A confirmatory value - any quality of accounting information that allows decision makers or users to assess or make use of information from past events or financial performance has a confirmatory value.

2. A predictive value- this quality means accounting information gives users information to predict the possible future and make informed decisions.