For every apathetic member who is voting based on ignorance, there is a zealous member voting based on dogma. The more votes we collect, the more accurate is the representation of the whole.
This isn't true. If voters are voting randomly (or effectively randomly) then that's just noise in the system. Worse, if voting is based on candidate exposure (i.e. voting on who had more TV ads rather than policy) then the votes are explicitly not representative of voter preference (unless the candidate that advertises the most also happens to be the true preference of voters, but we should not assume this to be true). Your statement is only true given a large amount of assumptions which typically do not hold true in practice. It holds true if voters are both informed, vote purely honestly (no strategy or no manipulation which includes through ads), and candidates are fairly representative of public opinions. I don't think anyone would argue that these three assumptions hold true in most elections. Real world doesn't have idealistic conditions.
So no, more voters does not result in better representation.
Many voter beliefs are implicit and how we express our political preferences can sometimes be reducible to a simple matter of group allegiance.
People don't need to be highly informed to effectively participate if the voter's top priority is to support a certain group interest (i.e., a union member supporting labour) rather than individual legislators or laws.
Yes, this is because voting is often non-intuitive. There's a reason we haven't found an amazing system in thousands of years. The problem is that people are trying to apply "common sense" rules and not testing them to check if their assumptions hold true. It follows the typical rule of "if people think the solution to a long standing problem can be solved with common sense it probably cant." Which should be obvious since the problem is long standing... But here's the thing, we've done a lot of testing and aren't going in blind. Unfortunately when solutions are "common sense" we end up not looking at data because why would we? We already know the answer ;)
Accurate representation is not a goal. The goal is freedom, wealth, stability, happiness, etc.
Also, people who vote for a random names just because they are forced to, are not exactly represented by those who they are technically voted for.