hi pster, the missing piece of the puzzle is this - the general rule is that first declension nouns have recessive accents - see rule and its exceptions in chandler s62:http://archive.org/stream/accentuationg ... 7/mode/2up
and then see the rules for various combinations of words ending in iota plus alpha starting from chandler s89 - see in particular s95:http://archive.org/stream/accentuationg ... 3/mode/2up
so the answer to your query, at least as i understand your query, is this - you can see from the dictionary entry δημοκρατία that it's not short-alpha ending, otherwise it'd be *δημοκράτια in the dictionary, which it isn't.
highly recommend that you work through probert's new guide to accentuation of ancient greek. there's a chapter or two on base accents which covers this point.
for getting more comfortable with quantity in general, the most useful thing i did was lots of verse comp – you spend a lot of time looking up the quantity of vowels by seeing them in non-anceps positions in iambic tris – to see some e.g.s from my own notes, see pgs 58 and ff. of my notes on tragic iambic verse comp, particularly the lines in red on the left-hand side (where i've looked up each doubtful vowel in anceps position and found its quantity by finding another verse where that doubtful vowel is not in anceps position)http://mhninaeide.webs.com/GrkIambicComp-23-Apr-06.pdf
if all those references to anceps etc. are vocab overload, perhaps have a go at my intro to iambic verse comp article, where i tried to "hide" the main rules for verse comp in a much simpler technique where you just slot words into a table:http://www.aoidoi.org/articles/meter/WritingIambics.pdf
hope this helps.