I taught a young man when I first came to my current school who was very passionate about politics. Eventually he would find his way to the Corbyn-era Labour Party, but before this he stood for election in 2015 in a local constituency, for a party whose main political idea was that we should have a none of the above option on ballot papers. When speaking to the candidate, my former student said that he felt there should be far greater levels of direct democracy in the UK, perhaps using apps or internet voting. In short, he wanted a referendum, or citizen input on everything.
Firstly, one interesting impact of such a policy would be to shift the nature of our political system completely. We currently have, as in most countries, a representative democracy, where your representative makes decisions based on their best judgement, rather than specifically adhering to what you, or their other constituents, want. Your representative would become a delegate, going back to their constituents to determine what they want.
There are certainly some points in favour of this - proponents of referendums would point out the high turnout in the Scottish independence referendum or of the vote to leave the EU. This increase in engagement could be very good for politics in general. Others may feel that politicians are out of touch, and on a range of issues the true views of the electorate aren't really shown. A good examples of this, other than Euroscepticism, may be the death penalty, where there are limited calls for it in general from politicians, but large numbers of the British population are in favour. This blog from the London School of Economics suggests that we would be well served by following the Swiss model, where voters are able to have referendums on any topic where they get sufficient signatures. Trevitt argues that this leads to an increase in citizen engagement and will make politicians more responsive to the public.
However, there is also evidence that referendums can have very low turnout, and lead to problematic results. Even in the 'golden era' of referendums in the late 1990s, some of the New Labour changes gained approval but on very low turnout. In London the turnout to approval the new mayoralty and assembly was only 34% and Wales approved its own assembly on a very low turnout of just over 50%, with just over 50% of that number voting yes, meaning barely a quarter of the Welsh population had approved the assembly. I remember, but have never been able to source, a cartoon from the time where a Welsh dragon mumbled a yes, while Tony Blair leaped for joy and shouted YES in the background. And this shows a further problem of referendums - that they are often open to manipulation, in terms of timing by those in power. Often, rather than being a symptom of a strong government, they are, in fact, a signal of a weak government without the authority to act.
Hugely varying turnout in elections.
There are far more referendums now, around the world, than ever before. They are a tool for pushes for independence, and according this Guardian article by Henley, Carroll, and Rice-Oxley, suggests that this is evidence of a pick and mix approach to modern politics, where people expect to be able to have their views heard on all issues. Whilst turnout in Switzerland has often been around 40-45%, Ireland has often had far higher turnout and has been successful in totally transforming the nature of the country. They are normally used on binary issues, with the theory being that you should use them to finalise binary issues. For example, when Ireland voted to legalise same-sex marriage, that was fairly cut and dried. However, issues can drag on, as seen by Brexit, which took (at least) 4 years after the vote to be at a point remotely close to being finalised.
Ultimately, despite their flaws many people may still support referendums due to them being a more 'democratic' form of electoral activity. I would disagree. The vagueness of Brexit meant that the actual nature of it took a long time to decide, and can hardly be in any realistic way be described as the will of the people. Finally, the best argument I've heard comes in the form of a question - the most Googled question in the UK the day after the EU, and one that shows that sometimes it may be better to leave decision making up to those with expertise. And what was the question? "What is the EU?"
I also used the following page in this blog: https://www.instituteforgovernment.org.uk/blog/never-mind-ballots-referendums-uk