"instant run-off" voting that we use in San Francisco, which failed; and then the recent vote for Brexit, the vote to leave the EU. Brits don't do this very often.
Compared with what we have in California -- for better or worse -- Brits have a much more attenuated democracy. Without a written constitution, all power resides in Parliament; the party that controls the House rules. Brits have elections for Parliament, but the politicians don't seem to very closely mirror the sentiments of their electors. In the Brexit vote, only 24 percent of the members of Parliament came out for leaving the EU. This suggests that probably more than half of them were out of tune with their constituents. Pointing this out is not to fault them as individuals for failing at some ideal representative function; it is merely to point this is far from unusual in British democracy.
In general elections for Parliament, the regular mode in which British voters express their democratic druthers, it is possible to get quite distorted outcomes that don't look very democratic (small "d") from over here. I've grabbed some charts from the Wikipedia on the 2015 election. Note how little correspondence there is between the percentage of the vote each of the parties won and the number of seats that vote translated into. In particular, the over 12 percent of all voters who picked UKIP (the anti-immigrant party) and got one lousy seat for their pains likely were thoroughly pissed. This can happen in a multi-party system where the victory goes to whoever claws out a plurality within a geographical constituency.
E J Dionne in the Washington Post does his pundit thing:
That is, in Dionne's view, the kind of not very democratic democracy Britain employs only works if smart leadership is in place to rescue a volatile electorate from itself.
Yet it does seem obvious that if large segments of the electorate felt, accurately, that they were more fairly represented, they might be less volatile, less inclined to throw the system into tipsy gyrations as they just have.
And yes, our electorate here also needs to feel represented, at least in substantial majorities, or our institutions won't work either.