For the old bisect, the perf dashboard has code that assigns the bugs, and marks them duplicates if the culprit is the same as another bug:
https://github.com/catapult-project/catapult/blob/master/dashboard/dashboard/update_bug_with_results.py#L207

For pinpoint, the dashboard side code doesn't run, and instead pinpoint assigns the bug itself, with no logic for duplicates:
https://github.com/catapult-project/catapult/blob/master/dashboard/dashboard/pinpoint/models/job.py#L231

This takes up a lot of time for users duping bugs (enne had to dupe 16 bugs manually into issue 865617, for example), and it's also quite error prone because when you dupe a bug on the monorail side the dashboard doesn't show the alerts on the bug it was merged into.