If a MapReduce job aggregates the data by reduce key, then each reduce task aggregates the values for each key within that task. However, when chopping is enabled in Perfect Balance, the rows associated with a reduce key might be in different reduce tasks, leading to partial aggregation. Thus, values for a reduce key are aggregated within a reduce task, but not across reduce tasks. (The values for a reduce key across reduce tasks can be sorted, as discussed in "Selecting a Chopping Method".)
When complete aggregation is required, you can disable chopping. Alternatively, you can examine the application that consumes the output of your MapReduce job. The application might work well with partial aggregation.
For example, a search engine might read in parallel the output from a MapReduce job that creates an inverted index. The output of a reduce task is a list of words, and for each word, a list of documents in which the word occurs. The word is the key, and the list of documents is the value. With partial aggregation, some words have multiple document lists instead of one aggregated list. Multiple lists are convenient for the search engine to consume in parallel. A parallel search engine might even require document lists to be split instead of aggregated into one list. See "About the Perfect Balance Examples" for a Hadoop job that creates an inverted index from a document collection.
As another example, Oracle Loader for Hadoop loads data from multiple files to the correct partition of a target table. The load step is faster when there are multiple files for a reduce key, because they enable a higher degree of parallelism than loading from one file for a reduce key.