I think 2, 3, and 5 are your better arguments.
The notion of a median doesn't require a strict left-right scale, but we'd get the same kind of conception, even if political distribution 2 dimensional or 3 dimensional, as really the issue is just capturing as much of the cluster of votes as possible, and the cluster centers on the middle.
The issue of the freedom of information only works as a supporting argument for 5. However, it, in and of itself, doesn't really change how a politician is viewed. Often policy alignment is a matter of fitting into an ideology, and identifying an ideology isn't usually the most difficult thing to do. Politicians sell themselves more on ideology(which people can understand) than policy(which people get more perplexed about sometimes).