A common complaint or source of disenfranchisement in democracies is that many constituents don't feel that their vote "counts" because the margin in most electorates is far greater than a single vote.
What if, in a single-transferable-vote system, the representative elected was subsequently given a number of votes in parliament/congress equal to their margin in the election.
e.g. if the Blue candidate receives 100 votes but the nearest rival, Red candidate, receives (after transfers) 90 votes, the Blue candidate becomes the representative and their vote on bills etc counts as 10 votes for that term. On the other hand, in a 'safe' seat where Blue receives 190 votes and the only other candidate receives 10 votes, Blue becomes the representative with 180 votes on each issue for that term.
Firstly this would mean voters no longer feel that their vote never counted, given it either strengthened or weakened the candidate ultimately elected in parliament.
Secondly, you could never have a party win power without the majority of the popular vote. In a parliamentary system the party in power is the one with the most votes in parliament and that would always correspond to the party that won the most actual votes in the election, even if they didn't get the most seats. There'd be no advantage to playing the percentages to maximise seats while losing on total number of votes.
But thirdly this would force parties and candidates to always contest all seats equally (and allocate spending without favouring marginal or battleground electorates). Because losing 100 votes in a closely contested seat is just as bad for a party's total vote count in parliament as losing 100 votes in a heartland seat.
Has such a system been suggested before and if so what is it called? Are there obvious problems with such a system?
One problem that occurs to me is what happens when the final two candidates are both from the same side of the political spectrum. e.g. a center-left and far-left candidate in a heavily left electorate. If the election was close the winning candidate would only have a few votes even though almost all of their constituents would support them when they voted against a bill put forward by a right-wing party.
Maybe in that case the candidate who comes second would have the choice of deducting their final tally from the winning candidates votes in parliament or distributing their final tally to strengthen other representatives, e.g. of their own party from other seats.
EDIT: Just to sharpen my second point, I think this system would nullify attempts at gerrymandering. Gerrymandering is all about drawing electoral boundaries such that the artifact of most electoral systems (that one citizen's vote doesn't translate directly into voting weight in parliament) can override the natural outcome of a vote. You divide seats so there's a small number of seats that are almost purely, e.g., Blue and the create a larger number of seats that are 51% red, and even though the popular vote might favour Blue, the artifact of seat boundaries elects Red. If a citizen's vote translates directly to votes in parliament it doesn't matter which way you carve the seats, the party in power will be the one with the most citizens supporting it.