"I'm not sure what this is supposed to do are you saying some representatives could have a vote worth, say 1.1435 that of another representative?"
No, this is a population based system. In other words the number of people who vote for a representative in an election determines the votes a representative has to cast in the House.
If for example 300,000 people vote for a candidate in an election, the candidate will be able to cast 300,000 votes in the House. It is literally a "representative democracy".
"What problem are you trying to solve?"
A large number of inequities in our current system have been on my mind in recent months, this is the product of hours of thinking throughout that time, however, because it is the first time I have shared this idea with other people I may have to think about a particular inquiry for a while before answering it.
In particular:
1. gerrymandering
2. winner-takes-all-system
3. lack of diversity in political discourse
4. lack of response to popular will
5. the odd arrangements that must be made in order to have an election to fill a Representatives seat
"And other nits:
One doesn't "stand for election" in the US. It's a british expression."
I am an American, and I also use the phrase, and you can get over it! :P
"I can petition 10,000 people by running an ad in a newspaper, asking for their support. Do you mean they must have 10k signatures?"
The various States may regulate the method of registering support, it may include signatures on a written petition, or other methods of registering support.
"Are you saying representatives who live in districts with a higher voter turnout get a bigger vote in the House?"
Yes, and not only that, but in general a Representatives' vote in Congress is determined by how many votes are cast in approval of the Representative.
People who don't vote won't get Representation, which is quite frankly what happens in reality.
"Overall, the whole idea seems way too complicated and pointless. Each rep should have one vote. If you want to address gerrymandering, offer an amendment that all districts must be compact and contiguous to the greatest extent possible."
I agree, it is complicated to some degree, but I think if you sit and think about it for a little while it will show itself to be a fairer system than the current one. I very much disagree with the "every rep should have one vote" part, because what it says it that some people are more important than others simply because of their location or their political preference. And when you say an amendment should be offered that states a district must be "compact and contiguous to the greatest extent possible" I think you will find that people can change the definitions of those words to suit the moment and what they feel to acceptable. Those are qualitative descriptions, not quantitative ones. The law should always be specific so that people can easily understand it. My wording might be off because I'm not the greatest writer, but in general the provisions are very specific and outline processes that are hard to circumvent.