In contrast, those with a common birthday or name have no distinguishable political desires in aggregate, so the likely result would be 538 generic congress members.
Furthermore, if we assume people exhibit a bias toward candidates from their home state (they do, on average), grouping by birthday or last name is actually a net negative choice since it would likely result in overrepresenation of Californians in congress (assuming first-past-the-post).
But ultimately, what political needs would a community of last-name-starts-with-C need?
None, which is why that grouping would only make sense in a society of extremely generic robots.