Two facts in support of proportional representation

When it comes to democracy there are primarily two competing systems of election, one is the first-past-the-post method and the second is so-called proportional representation. It is possible to have a legislative democracy without representation and this is direct democracy where laws are approved by the people using referendums and not votes in a legislative body. If we consider the first-past-the-post (fptp) system against proportional representation we can see that with the former (fptp) voters who vote for a party which is not expected to do well risk wasting their vote and so tactical voting emerges and is rewarded. This tends to lead to a two-party system with less real choice for voters. We might think it strange that people who accept the use of first-past-the-post (itself a kind of democracy) refuse to accept the use of proportional representation given that fptp inherently recognises the right to democracy. But many people do defend fptp over proportional representation...

To reject proportional representation in favour of first-past-the-post is to be in denial of (at least) one of two facts. Those facts are as follows:

i) That democracy is a good thing and the people should have the right to hold their government to account, via the ballot box.
ii) That proportional representation is more 'democratic' than the first-past-the-post system. And by democratic we mean that it gives voters more control over their representatives, which is the intention of democracy in the first place...

If someone accepts either of these facts then they must deny the other to support their position of opposition to proportional representation (in defence of fptp). If someone recognises that pr is more 'democratic' than first-past-the-post then (to reject pr) they must be of the view that democracy itself is not a good thing. Conversely, if someone likes and accepts the principle of democracy then if they support fptp and reject pr it can only be for the reason that they deny pr is more democratic than fptp.

Proportional representation is logically preferable to first-past-the-post unless one of the two claims above is false, that is to say that if democracy is good and pr is more democratic than fptp then it follows that pr is better than fptp.