This seems a lot like liquid democracy,
Schemes involving proxy power indeed resemble one another to at least that degree, that they involve proxy power. I would like readers to evaluate them separately, and not tar one with the drawbacks they see in another. And in particular, I live in the US, and am concerned about the effect on the world of US politics, and I would like other US residents to weigh in on my suggestions.
I propose that proxy would only be given in voting booths, with the same ballot secrecy as US people are accustomed to for voting on who can serve in office. And the opportunity would only come up every two years. Proxy could not be revoked except on those opportunities. This would limit the overhead costs of communication and certification of the expressed wills of the citizens. It would limit the risk of votes and proxies being coerced out of citizens.
Here is another variant of my proposal, which could reduce overhead. Instead of having to go to the polls once to allocate space in the legislative chamber to representatives and returning to the polls to give proxy to someone from among those seated, with this variation, only one visit to the polls per election season would be necessary. Voters would fill out two sections on the ballot. The top section would list the candidates and invite approval or disapproval of each for seating. In the bottom section, the voter would list candidates in order of that voter's decision about giving proxy. The highest candidate on the voter's list who is seated would receive that proxy.