Plato and Aristotle set the classifications of government into a six box matrix. The quantitative measures were: one, few, many. The qualitative measures were: good or bad. You can substitute other value judgments for good or bad; but the matrix box is what we still have. BTW, "democracy" was in their "many, bad" box.

There is no magic set of quantitative metrics that determines what democracy is or is not. It is an intangible. If you want to have some fun, attempt to classify the British parliamentary system from the time of Simon de Montfort to the present. And, if you want to talk about more modern concepts, are you talking about actual democracy, representative democracy, constitutional democracy, economic democracy, social democracy or popular democracy - or a combination of one or more of those (plus some others, I've probably forgotten).

As to your link, see p.8 pdf, as to democracies:

How important is democracy to post-conflict rebuilding and sustainable peace? About half of all post-conflict countries today have some form of democratic governance. But many are semi-democratic regimes in which, typically, electoral processes and legislatures are at the whim of autocratic executives. In 2008, a total of 86 countries had consistently democratic regimes, 28 were autocracies, and the remaining 45 were anocracies, a term we use for hybrid regimes (Pate, Chapter 4). The empirical evidence is compelling that factional, semi-democratic regimes are fragile and subject to failure, whether through armed challenges or institutional failure or both. In fact competitive elections in such regimes often precipitate armed violence and massacres, as happened in Kenya in 2008.

Consistently democratic regimes are unlikely to be challenged by civil wars in the first place. If fully democratic institutions can be established after wars, economic redevelopment is more rapid, the risks of conflict recurrence are less, and transitional justice is more effective (Hegre and Felde, Chapter 8; Meernik et al., Chapter 10). Democracies also have a relatively good track record of reducing political discrimination against minorities, thereby reducing the salience of one major source of grievance around which anti-regime movements coalesce (Pate, Chapter 4). And democratic regimes have a better record of incorporating women into the political process (Caprioli et al., Chapter 9). Yet women seldom are recognized participants in peacemaking or societal reconstruction. So opportunities are lost that might give women more leverage to minimize the risks of war recurrence.
All this we know as a qualitative rule: the more a country looks like a nice, tidy "Western" democracy (whatever its "kind"), the less likely is a substantial segment of its population to revolt. On the other hand, a substantial segment of the population of a very effective (read that as an effective state security service) authoritarian regime is also less likely to revolt.

Yes, there are quantitative measures (I do read this stuff) for classifying "failed states". That is what your link (and a lot of other ones) is all about. The moral and ethical question that the individual making the decison has to face is whether intervention in a "failed state" has a decent probability of preventing more deaths than the intervention will cost. The question a nation has to face is where does the intervention fit into its priorities and into its capabilities. And, whether regional military groups (or non-kinetic groups, for that matter) could handle the matter - perhaps, not as well as we "exalted" Westerners; but handle it.

When I get home, I'll add the monograph to my folder on Peace Enforcement; and read the articles - and also check out the webpage. Thanks for the link.

PS: I don't buy the "lowly CPT" line - if you want to address GEN's topics, then you have to be able to present a GEN's arguments, even if you aren't one.