  Recent efforts have aimed to improve AI machines in legal case matching by
integrating legal domain knowledge. However, successful legal case matching
requires the tacit knowledge of legal practitioners, which is difficult to
verbalize and encode into machines. This emphasizes the crucial role of
involving legal practitioners in high-stakes legal case matching. To address
this, we propose a collaborative matching framework called Co-Matching, which
encourages both the machine and the legal practitioner to participate in the
matching process, integrating tacit knowledge. Unlike existing methods that
rely solely on the machine, Co-Matching allows both the legal practitioner and
the machine to determine key sentences and then combine them probabilistically.
Co-Matching introduces a method called ProtoEM to estimate human decision
uncertainty, facilitating the probabilistic combination. Experimental results
demonstrate that Co-Matching consistently outperforms existing legal case
matching methods, delivering significant performance improvements over human-
and machine-based matching in isolation (on average, +5.51% and +8.71%,
respectively). Further analysis shows that Co-Matching also ensures better
human-machine collaboration effectiveness. Our study represents a pioneering
effort in human-machine collaboration for the matching task, marking a
milestone for future collaborative matching studies.
