In order to have Proportional Representation, you have to elect more than one member from each district, because one person can't "look like" a district if the district looks like a lot of different things. If we want the members of the legislature to "look like" the state, then we have to advocate that the House of Representatives elect more than one representative from each district.
See wikipedia for a complete description of this system.
In Ireland, they have 42 districts that elect from 3 to 5 officers to the 166-member Dail (lower House), using this method. In Ireland, they have seven political parties represented in the Dail, plus thirteen Independents. This is one of the effects of electing more than one member from each district. It is also the method used by Cambridge to elect its city council and school committee.
Advantages of this method include very accurate proportional representation and very little need (or use) for strategic voting. Disadvantages are that it is very difficult to count the votes, and very difficult to understand why one person was elected and not another.
See wikipedia for a complete description of this system.
This method used to be used in Illinois. You get three votes that you can give to the same or different people, to elect three officers from your district. It also achieves proportional representation while requiring little strategy.
Advantages of this system include making it easier to achieve proportional representation, ease of counting, and compatibility with current voting machines. Disadvantages include making it easier to use strategic voting to achieve disproportionate results.
See wikipedia for a complete description of this system.
This method used to be used in Japan. You get one vote to elect, say, three representatives. The top three vote-getters win. It also achieves proportional representation while requiring little strategy.
Advantages of this system include making it easier to achieve proportional representation, ease of counting, and compatibility with current voting machines. Disadvantages include making it easier to use strategic voting to achieve disproportionate results.
This is part of Dan Keshet's Voting Systems website.