He offers two definitions of the democratic method, which is that institutional arrangement for arriving at political decisions... in the "classical" case
...which realizes the common good by making the people itself decide issues through the election of individuals who are to assemble in order to carry out its will
and his alternate is:
...in which individuals acquire the power to decide by means of a competitive struggle for the people’s vote.
The classical definition is of course the one that people feel allegiance to, will go to the barricades for, and so on. The alternate, we immeadiately see, is more realistic. If I now go and look at the wiki article I get Democracy... is a form of government in which the people ... to choose governing officials to [deliberate and decide legislation]... Cornerstones of democracy include freedom of assembly, association and speech, inclusiveness and equality, citizenship, consent of the governed, voting rights, freedom from unwarranted governmental deprivation of the right to life and liberty, and minority rights. Later, in the "theory" section, there is a somewhat confused discussion. Although wiki lists some "cornerstones" we should note that although these are largely preconditions for democracy, they have no unique connection to it: it is easy to imagine an autocracy that offered most of them.
That's mostly it for this post; I could analyse further but you take the point, I'm sure; and if you want further analysis, I've pointed you to the text. This is a good point to note that I don't believe in the Will of the People; per for example this. I will confess that you an re-write the "classical" defn above to get rid of some but not all of the WOTP bits2.
Update: and Brexit
I don't want to derail this with Brexit ranting, but I think it is interesting to consider Brexit in this context. The point being that "compete for votes" very often turns into the major political parties taking opposite stances upon issues-de-jour. Which, in turn, generally means that you-the-voter have a way of choosing between those issues. Admittedly, it is crude: you get one choice to represent all the choices; but when one issue is overwhelmingly important, it works. Which is why Brexit is anomalous: both Labour and The Tories are currently in favour of make-Brexit-work; the Lib Dems offer (arch) We’re consulting on our next steps laying out our approach to the UK’s relationship with the EU.
* "Don't Look Up" and the cinema of existential risk by Matthew Yglesias; or more generally ACX.
1. We are all aware that definitions, per Popper, need to be considered in practical rather than Platonic terms to have any use.
2. I can manage by making the people itself decide issues through the election of individuals who are to assemble in order to carry out (their) will(s), which erases "the common good" at the expense of losing any purpose; but can't quite erase the ghost of the WOTP. I ought to confess that when young and foolish I have used the phrase myself; if you care enough to press me I will bring the two into conformance.