I was wondering if there is any literature on voting systems where voters elect representatives, and in the representatives' assembly the vote of each representative is weighted by the number of votes she was elected with.
E.g.: A special but easy example would be the US supreme court. The 'voters' here are the US senators, their 'representatives' are the supreme court judges. Instead of each judge having an equal vote their vote could have a weight equal to the number of votes they were confirmed with. This would make a difference, as consensus candidates seem to be confirmed by more votes - at least in the current system. Changing the supreme court's voting mechanism could of course affect confirmations, but this may be a way to incentivize consensus.
In case of general elections and parliamentary representatives such a weighted voting system would incentivize representatives to try to represent all the voters in their district, not just the majority. (Assuming representatives care about their voting power, but one could always tie their salary to the number of votes they were elected by.)
The idea is simple, so it has probably been raised before. Please refer me to some literature.