Proxy voting is a standard practice in for-profit corporations where each share gets one vote, and shareholders may appoint others to vote their shares as their agents, called proxies. It enables fair representation of each share, but also accommodates those who don't want to travel to shareholder meetings to vote their shares in person. However, this successful method could be applied to representation of voters in legislative bodies, and thereby avoid many of the shortcomings of existing methods of electing members, such as single-member districts.
Proxy Voting for Members of U.S. House of Representatives
Each state is allocated some number, say 32, of members in the House of Representatives. Now, instead of trying to divide the state into 32 single-members districts, with arguments on how to draw them, we hold a statewide election at large for all 32 positions. The decision rule is that the top 32 vote getters are declared the winners, and those take their place in the next session of the House. All this could be done by acts of state legislatures. No constitutional amendment, state or federal, would be needed to do that.
But clearly it would not work for each member thus elected to cast only one vote in the proceedings of the House. That would be unfair. Some members might have gotten many times as many votes as others.
The solution is for each such elected member to cast as many votes in proceedings of the House as he received on election day. In effect, each member would be the proxy for his voters. That means for every House vote, from organizing it, to votes on bills, to votes on committees and on other matters. That would only require amending the Rules of the House. Again, it would require no constitutional amendment, if every state adopted the same legislation for electing members.
Now we can see the advantage of this method. Any constituency in that state with 32 members assigned that could cast at least 1/32 of the votes would be represented. We would no longer have the situation of a minority that is more or less uniformly distributed over the state, so that it didn't win any of the seats. This method would insure that minority views would be heard in deliberations of the House, even if they don't have enough votes to carry any legislation by themselves.
What happens, however, if a member dies, resigns, or otherwise becomes unable to serve? Appointment of a replacement by the governor or a special election wouldn't work. The obvious solution would be for each member to designate a chain of successors who would replace him in turn if he leaves office before his term has expired. That means that when one is campaigning, a candidate is doing so with disclosure of who is next in line to replace him, and that would be important information voters might use to help decide whom to vote for.
How might we get every state to pass the same legislation, coordinated with the rules change in the House? We would probably need a constitutional amendment to ensure such coordination. Here is how one might be worded:
Members of the United States House of Representatives, and houses of state legislatures whose members represent political subdivisions that elect a number of representatives in proportion to their population, shall elect representatives at large, and the number of allocated representatives receiving the most votes shall be declared elected. Each such elected representative shall cast the number of votes he or she received in the last election in all proceedings of the house to which elected. Each candidate shall, prior to election, declare a list of successors if he or she becomes unable to serve, or is removed from office, who shall be appointed to replace him or her.
Note that this applies to the U.S. House of Representatives, but also applies to state legislative houses based on population. At present that is all of them, based on a Supreme Court decision, Burns v. Richardson, 384 U.S. 73 (1966), but we need to allow states to have one house of their legislature that is not based on population, such as one member per county.
Proxy Voting for Members of One House of a State Legislature
The purpose of representation is not to enable the will of the majority to always prevail, but to insure that minority views are deliberated, and that minorities have some ability to block the will of the majority. Representation properly operates to require more than mere majority support to take action. Having one house of a two-house legislature can enable that principle.