Here is an electoral system that I came up with. It's derived from First-past-the-post, and still only elects one candidate per riding, but the process is modified for proportional representation. This idea has probably been proposed before, but I want to know what it's called.
Here is the procedure:
Each voter votes for one of the available candidates to represent their riding, but also for their favourite party.
After the votes are counted, it is determined what percentage of votes each party received. Each party will have this percentage of the seats in the legislature. For example, if the Liberal Party received 40% of votes, and there are 95 seats in the legislature, then the Liberal Party would be given 38 of them. After this is determined, the 38 Liberal candidates who received the highest percentage of votes in their riding are elected. This process is repeated for all other parties until a candidate has been elected from each riding.
The percentage of the popular vote for each party can be determined for the entire country/state/province/etc. Alternately, neighboring ridings can be grouped into "superridings", which each follow this process separately using their own subridings.
This system may not be perfect. I haven't figured out how it should deal with independent candidates.
However, if this system has been proposed before, than what is it called?
EDIT: I consider this system to be distinct from Mixed-member Proportional Representation (MMP). In MMP, candidates are elected through two different methods, with an preassigned number of seats to be given through a FPTP process and the remainder through List Proportional Representation. In the system I'm describing, all MP's are elected the same way (unless if implemented with "remainder ridings").