On point 2, there's quite a complex answer. Firstly, the vote was basically "Leave or Remain". Remain meant stay in the EU on the current known terms. Leave meant... well: You could leave the EU but remain a part of the single market for trade (this was promised during the referendum), you could leave but have a custom arrangement with the EU like Switzerland which means you retain EU law but have no vote (this was also promised during the referendum), or you could leave all the EU institutions and then re-enter a random assortment of them like Euratom (this was also promised during the referendum) or you could leave the EU entirely and just start negotiating some free trade agreements like the EU's relationship with Canada (this was also promised in the referendum).

The key is that because the 'Leave' campaign weren't in government and weren't one single organised group and didn't actually hold power they could promise literally anything safe in the knowledge that they'd never have to actually deliver it. In fact after 'Leave' won the referendum the Prime Minister resigned and none of the key Leave campaigners actually mounted a serious campaign to replace him- someone who campaigned for remain was put in charge almost unchallenged.

So through all this murkiness you end up with one key fact: 48% of the country wanted to remain, 52% wanted some form of leaving but each of those options I listed above probably garner no more than 20% of the vote by themselves. So we're 52:48 in favour of leaving, and 80:20 against any specific way of leaving.

If only god had created runoff voting.

According to the Alternative Vote referendum "No to AV" campaign, God cannot simultaneously handle runoff voting and care for newborn babies.

Mathemarically, a slim victory with a large percent of the population abstaining does not indicate “majority desire”.

Democrasy doesn’t measure majority desire, it measures electioneering. Majority desire is definitely an aspect of elections, but it’s not the thing that gets measured.

There are better ways to accurately measure majority desire, and they are not one person/one vote systems.

What the system purports to give us is not accuracy, but fairness. It’s acknowledged that no matter what system you put in place, its ideals will be perverted. The best we hope for is that multiple parties all have access to those same perversions. So the difference between the U.S. and Russia is that both Bush and Gore had a right to sue the state of Florida. Of course the outcome doesn’t represent the will of the people in any meaningful way, but we take comfort in knowing that both candidates had the same games open to them.

In Russia, Putin is playing a wholly different legal game than everyone else. That’s anti-liberal, and anti-democratic.

Much hand wringing is happening in the U.S. today because the American President is mostly above the legal system, as its executor, with only the Senate holding him in check. And it’s not clear our current Senate is committed to the rule of law. We will see when Mueller’s report comes out. And perhaps some governors can also hold him to account.

Again, none of this bears any direct relation to the “will of the people” except that there is a method to the madness and any citizen can volunteer for any aspect of the game.

>Also an American, but from the outside I don't see how a majority desire can be so objectively determined beyond a vote.

My personal opinion is "majority" wins isn't necessarily a proper majority. Given how our Congress votes party line on most things, and the ratio is more or less 50:50 Dm to Rep, a 66% majority seems minimal for passing any law unblemished with party bias.

With 72% of registered UK voter turnout, Brexit won with only 52%. That's not a mandate for anything except perhaps another vote after clarifying what it would actually mean and how it would actually happen.

In the United States we require super majorities to amend the Constitution. 2/3 of Congress and 3/4 of the state legislatures.

Something as important as Brexit should require more than 50.1% to pass. But it was actually non-binding anyway so the government could just ignore it.

The referendum was enacted as part of an elected party's manifesto that promised to implement the result.

After the election, parties voted to enact Article 50.

After enacting Article 50, the parties that campaigned in the following general election on a promise to implement the decision to leave were overwhelmingly successful.

Ignoring the referendum would have been a poor decision.

If that applied, then major changes to the structure of the European Union such as Maastricht or the Lisbon treaty should also have required the >50% vote.