Jurij wrote: >this system becomes similar to AV if the number of candidates to be >elected is large and the number of all candidates is small. For example 3 >members to be elected and four candidates altogether. Or evenmore: 7 >candidates to be elected and 8 candidates overall. But what if there were >20 candidates in your district and only 3 to be elected? That would be >nothing like approval voting. Therefore a coincidence is needed to end up >with a system similar to AV.
I would argue that, even in the case of N+1 Candidates and N positions, we still do not have an outcome as satisfying as the outcome of single-winner Approval Voting. This is because, in the multi-winner case, a tiny majority can completely silence a large minority and produce a grossly non-proportional result. For example, let's say that in your local election, 55% of the voters prefer a certain set of three candidates, A, B, and C. The other 45% strongly prefers candidate D, and has no real preference between A, B, and C. Who wins the election? A, B, and C do. Clearly, this makes no sense. 55% of the voters get three representatives, while 45% of the voters get zero representatives. In single-winner, electing one of A, B, and C is the right thing to do, but if there are at least two seats on the council, D should get one of them. The way to correct this, while sticking with Approval voting, is to go to proportional Approval voting. In PAV, the strength of a ballot's vote for unelected candidates is diminished each time a candidate that is approved on that ballot is elected. PAV is to Approval Voting as STV is to IRV. Those are slightly inaccurate oversimplifications, but they give the idea. Forest Simmons has posted many times on this subject. -Adam