You should probably spend the time to really dig through the web or your local library to find out all the complex stuff she favored. She was(is) a very bright lady with some interesting ideas.
The “proportional representation” issue was not, however, about quotas. (Some of her other ideas arguably were–or were not.)
Under out current form of republicanism, we generally follow a “winner takes all” method of election. The candidate with the largest number of votes, even if by a slim plurality, is the simple winner. (There are cities who have other rules, but I am not aware of any other rules at the national level.)
When choosing representatives to Congress or to state legislatures, this provides a lot of opportunities for state legislatures to stack the decks so that the party in power remains in power. Looking at any state, you can find geographic regions where either cultural or ethnic groups, who could reasonably expect to think similarly on certain issues, can have their voting power reduced by gerrymandering. This can happen in two ways: dilution or overconcentration.
In dilution, we set the voting boundaries so that the recognizable group is split up so that it will never have a large enough block of voters to get one of their own elected. (E.g., set the boundaries of each district near a city to divide the city into parcels, linking each inner city parcel to a much larger group of suburban voters who could be expected to vote differently so that each city is never able to put forth a winning candidate.)
In overconcentration, we recognize that there are so many people of one specific class that we cannot possibly divide the districts so that they never have a majority. What do we do? Map the districts so that all of those people are contained in a single district so that they can only have one possible vote in Congress or the legislature.
In the last census, there were two attempts to address this issue by creating really distorted districts that would guarantee that, at least, some representatives would be elected by black voters in one of the Carolinas and another state. Despite the good apparent intentions, the districts were so clearly gerrymandered that the Supreme Court threw both of them out.
Proportional representation attempts to do away with those issues by, first, eliminating the district boundaries. All of the representatives are selected “at large.”
Now, the “at large” election has its own problems. A number of cities went to an “at large” system in the 1950s and 1960s as a form of dilution. 15 candidates run for 10 offices with no candidate representing any specific district. However, when the votes are counted, using winner-take-all and plurality logic, the eight candidates who culturally represent the majority (even though we are all playing by the fiction that all candidates represent all voters) have totally overwhelmed the seven candidates who culturally represent the minority and the city council simply runs as an 8 - 2 rubber stamp for the majority–even if the population is divided 55 - 45.
So the next step in “proportional representation” is to establish different methods of actually tallying the votes. I don’t remember all the rules that were suggested. One that I vaguely remember was that each voter was given a ballot with a certain number of “points.” They could divide their points up among the various candidates, or they could throw all their points to a specific candidate that they chose. The idea was that they traded off their voting powers of breadth vs depth.
I have not been convinced of the benefits of this system (although it has worked in some smaller settings), but it would clearly require a Constitutional Amendment to be enacted at the national level.
It is also not simply a Lani Guanier/kook idea, having support from a number of political science theorists.