Democracy may be a great thing, but incredibly honest it is not. Democracy is flawed but it is the least worst system we have yet come up with.
I think we're talking about different facets when we say democracy is honest/dishonest. My view is that in a non-coerced democratic system then whoever wins can claim a mandate of majority of the electorate. They might have lied to get that mandate and that's a different matter altogether but the point is that democratic results are generally incontestable.
The referendum was incredibly flawed and dishonest, because it allowed both sides plenty of poetic licence and due to incompetence it provided a result that actually proved nothing, it gave no majority because not everybody voted. That is an inherent flaw of democracy because the power of not voting is negative power not positive power. A true democratic mandate should be 50% + 1 and then no argument can be made to the contrary because that mythical "will of the people" will have been truly expressed.
Really though that's more a flaw of how we manage our elections rather than inherently built into a democratic system. A "None of the Above" type vote could cure this issue.
More to the point though, the fact that everybody didn't vote isn't in itself a problem or a message. Maybe they didn't care? Maybe they didn't want to? Maybe maybe maybe? Like with anything you can only gauge the opinions of those who are willing to share them and it's perfectly legitimate on principle that some people do not wish to vote.
I agree that there needs to be a positive option in any democratic choice and this is a problem at the present time.
There is also the issue of using direct democracy in a system that uses representative democracy, they are incompatible and due to our lack of written constitution open to interpretation as we have witnessed since the result was announced. There was no clear winner. As much as leavers and remainers argue about the point, it is a fact that neither has a truly democratic mandate. I didn't vote because I believed the referendum to be flawed from the beginning, that is my right to exercise my negative power as there is no recourse for me doing so.
I don't personally believe direct and representative democracy are incompatible with each other. I'm sure you know Switzerland manage it pretty well. I'd argue that the problem inherent in our system is that there's not ENOUGH democracy. Democracy are like goals in football - if something is going wrong then it can always be cured by more democracy. In the days of speed of light worldwide communication, streaming media, and Google, representative democracy such as what we have is badly formed and somewhat out of date.
I think I'd like to see a mixed system one day where we have almost complete direct democracy but instead vote for local representatives to inform us of the ins and outs of issues. If we don't trust them or we've found they're lying or giving us out of context information as we'd find during debates then we'd kick them out and elect a new person. Representation in democracy should be used to save people time, it should not be used as some mythical ideal of "voting on behalf of me". I don't need anyone to vote on my behalf, I need people to carefully summate legislation in a short form (expanding into greater detail on request) so that I can vote on it myself. Representative democracy in the 21st century should be advisors to a direct democracy that we elect.
I can have a news application on my phone that tells me in real time when American singer Miley Cyrus has broken up with her boyfriend in Tunisia but I can't have this?
We now face a situation where a minority of the electorate are using our flawed system to dictate to the majority. That is not incredibly honest democracy that is a sham and it makes a mockery of the term "will of the people"
It is the incompetence and arrogance of Cameron and Osborne that have put us into this situation, they assumed they would win the day and instead of using some sort of qualitive measure to ensure democracy did reflect the mythical "will of the people" it has caused division that may take generations to heal.
The issue here though is that whilst you claim it's the minority of the electorate, we don't actually know that. We can't presume that all non-voters wanted to Remain or Leave. What we CAN presume though is that using statistics, the people who voted represented a fair and unbiased representation of the electorate. No different than how we can tell large scale opinions based on small polls.
Saying all that and with all its flaws the result now must be respected, the problem is because there was not 50% + 1 of the whole electorate in favour we are now in the situation of interpretation of the result. This process is because of our inherently dishonest flawed democracy and frankly the good people of the UK deserve better than the farce we have ended up with. A clear mandate would have rendered all arguments against the result null and void, but because of the flaws and dishonest democracy we used those arguments will continue for decades.
To me I don't think that's the issue. I think that even if it ended 60/40 we'd still see the same furore as is going on now. Ultimately, many Leave voters feel that there is a metropolitan liberal elite class that dictates to them what they can do or not do, what is good for them or not; using their channels of the mainstream media, social media, educational facilities, etc, etc. Whether that is true or not is irrelevant, it only matters whether a significant amount of people think that it is. And I think they do. I think that politicians and journalists and commentators have generally gotten away from the opinions of the "man in the pub" and he doesn't feel that they are on "his side". They are Other to him. This is also why Tommy Robinson has done so well - he looks and sounds like an actual human being, you could imagine having a conversation with him in a pub or on the train or whatever.
People are tribal, it is built into us for better or worse. White people
generally vote for white people, asians
generally vote for asians, black people
generally vote for black people within the caveats of reasonable political disagreement and choice. We might not like that that is true, we might try to justify it for hundreds of different reasons but we cannot argue against the very documented fact that it is true. Race is tribal. Obviously not just race; working class people want to vote for working class people, upper class people want to vote for upper class people, City fans want to vote for City fans; the more tribes we share with a person directly correlates to our desire to vote for them almost no matter what their politics. Which is mental when you think about it. I've spent a long time wrestling with whether this is down to arrogance or anxiety and I still can't answer it.
The point in this being, what we're seeing with Brexit is a phase in an ongoing culture war in the UK. The days of the miner unionist working classes are now gone. The "dignity" of the working classes is gone. The working classes now consist of what many people term as chavs or doleys or immigrants or scumbags. People sometimes euphemistically call these an underclass because they don't want to lump them in with the working class monikor which they've taken silent pride in for so long. But ultimately we have to ask if these people are politically represented in any arena at all outside extremists such as Robinson? I don't feel they are. Certainly not in the Labour Party, everybody there looks like they are more at home at a dinner party than a pill popping knees up down at Wigan Pier or a day spent reading the paper in the bookies watching the horses come in.
I'd argue that a significant amount of historical strife culturally has come down to a simplistic and single idea of representation. When people don't feel represented in the decision making process then they will rebel, sometimes politically but sometimes violently. Remain-Leave is just a battleground in this war when really most of the people who are married to their designated box could better communicate by the Leave guy saying "I feel like you think you're better than me" and the Remain guy saying to the Leave voter "I feel like you aren't seriously considering the impact on people in your decisions".
Until the so called underclass is represented, we will have this cultural war going on and people will vote for the opposite of what the "comfy class" want them to out of sheer bloody mindedness.