The people in charge are largely hated by the electorate. They won by default effectively due to a quirk of how UK elections work (which was less of a problem when the monarch/aristocracy was still involved to counter balance things like this, but now that that's gone the state is effectively out of control.)
Unless by "democracy" you mean "sleepwalking administration everyone hates" the current UK government is unusually undemocratic.
The electorate hated the politicians, then they still vote for the same guys. The general public doesn't care about politics, those who cared treats it like tribalism and don't want to learn what are actually happening, they don't want to think they only want to be told whatever feeding their brain chemistry.
Essentially:
1. Generate uniformly random values u,v between 0 and 1.
2. Then find their spherical coordinates as:
theta = 2 pi u; phi = acos(2 v -1)
Honestly I’m unsure why you’d choose a method any more complicated.