The thought occurs to me that Washington DC, being an evil cesspool, will work out a way to ascertain the manner in which Representatives are voting, regardless of what we do. We might be the only people who end up not knowing how they voted.
That is a good point. Although, I would think there would be full-proof ways to administer the vote to prevent such a thing. It is more a logistical question rather than a moral, ethical or philosophical one.
There are smarter people than me who devise these types of systems but I am thinking one option would be like a raffle ticket system. In this system representatives would randomly pick from a box filled with 435 “raffle tickets”. Each ticket has two parts: a “YES” with a long random number and a “NO” with the same random number. When it is time to vote you rip either the “YES” or the “NO” off your ticket and stick your choice in a box. When everyone present has voted, the votes are read in this manner, “387344923847941987619874 votes AYE, 45167898723465138917098377 votes NAY, etc...” Each Rep would know if their vote was counted wrong. Nobody would know how anybody else voted.
They key to this would be to anonymously collect the leftover tickets at the end of the voteand make it a felony for a Rep to take it off the floor, take a picture of it, make a copy of it, etc.... If they were permitted to do so, they would in effect have a receipt of their vote to show party bosses or campaign donors.