Most — but by no means all — scholars say an amendment is unnecessary. The Constitution says that the House shall be composed of members chosen by 'the people of the several states.' But it also gives Congress the power 'to exercise exclusive legislation' over the seat of the federal government, interpreted by some to mean that Congress can, if it wants, give D.C. voting rights.I doubt "most ... scholars" is correct, but this argument has been mooted by former judges Kenneth Starr and Patricia Wald in an op-ed piece in The Washington Post:
Finally, and equally important, the most analogous legal precedent addressing Congress's authority over the District confirms that Congress can act now to give the vote to D.C. residents. That precedent concerned the fact that Article III of the Constitution confers on federal courts jurisdiction to hear suits brought by citizens of different states against each other. But the Constitution did not give any such express jurisdiction over suits brought by or against citizens of the District of Columbia. As a result, Congress, relying on its broad Article I power over the District of Columbia, remedied that unfairness through legislation that extended the right to District residents. In a 1949 case called National Mutual Insurance Co. v. Tidewater, the Supreme Court upheld that extension and also said that Congress was entitled to great deference in its determination that it had power to address this inequity. The logic of this case applies here, and supports Congress's determination to give the right to vote for a representative to citizens of the District of Columbia, even though the Constitution itself gives that right only to citizens of states.