Advantages and Disadvantages
Advantages
It is the purest form of democracy. If democracy is the only means of achieving legitimate rule- direct democracy is seen as its purest form.
Direct democracy includes citizens' juries ( a panel of non-specialists, often randomly chosen to express a view about public policy) which are widely used in the USA and countries like Germany, Denmark and the Netherlands- unlike referendums they allow for consultation and thoughtful deliberation rather a then a simple choice- for or against. They can help to develop a mature and thoughtful idea of public (see sortition) opinion- they help to counter the view that the electorate is too ill-informed to engage with complex issues.
It disperses power widely among the population and so prevents a concentration of power in too few hands. The EU referendum could be seen as a victory for popular sovereignty over the elites such as Banks and Business- which generally supported remain.
Referendums cut through the influence of elite groups such as corporations, who use money and the media to influence elections and dominate parties. They are also the voice of 'ordinary people' who reject the idea that they need politicians to decide what is best for them. When voters rejected the proposal for a devolved assembly in the North East region of England they rejected something they saw as an unnecessary imposition by politicians.
It means that decisions may be more acceptable to the population this can help to settle an issue which has been causing social divisions and conflict e.g the referendum in N Ireland over the Good Friday Agreement.
It increases popular participation and therefore enhances democracy- this is particularly useful if there is a participation crisis. The Scottish referendum on independence had a very high turnout and high levels of popular engagement in the debates. 16 Year olds were also given the vote.
Referendums and consultations are a form of political education for the general population. The Scots referendum saw high levels of engagement in complex economic and constitutional issues.
Referendums can 'entrench' or safeguard important constitutional changes. In the absence of an entrenched constitution, some of the most important changes to the UK have become effectively entrenched by referendums- e.g it would be unthinkable for any government to ignore the EU referendum without at least having another referendum.
Disadvantages
Direct democracy means majoritarianism— government by a simple majority. This may represent the 'tyranny of the majority', which oppresses minorities. The winning majority can ignore the losing minority-.eg 2016 48% voted to remain in the EU- but will be taken out. A majority of voters in Scotland voted to remain but will be forced to leave. In the USA referendum (initiatives) have been used to ban same sex marriage and exclude children of immigrants from schools.
Many decisions may be too complex for the people to understand e.g AV referendum 2011- high levels of ignorance about the working of AV and FPTP. In 2016 there was considerable confusion over what Brexit meant and misinformation about its consequences.
Direct democracy often creates an emotional, rather than a rational, response from the people and the media. The EU referendum seemed to focus on fears of immigration and terrorism.
Direct democracy can be subverted or distorted by wealthy groups who influence. The 1975 EU referendum saw the Anti-EU campaign outspent by a far richer pro-EU campaign- back by most of the press and big business.
Referendums undermine the sovereignty of Parliament and make it more difficult for governments to make difficult decisions. The North East referendum killed off Labour's plan for regions devolution and left and unbalanced distribution of power in the UK (see West Lothian Question) A precedent has been created which means governments and Parliament can no longer make big constitutional changes.
Referendums do not 'settle' an issue- ever since the Scots independence Referendum there have been calls for another referendum by the SNP.
Referendums force complex issues to be decided by simple 'yes' or 'no' alternatives. It was clear that many people wanted voting reform but not AV and many people wanted to remain but not on the terms which existed.
Governments tend to use referendum to resolve a political problem and generally agree to them when they think they will get the result they want- e.g 1975 Labour used a referendum because the party was split over EU membership. In 1978 the devolution referendum required a super majority- which meant although a majority voted for devolution in Scotland - they did not get it. This was seen a a 'fix' by the government to get the result they wanted.
If required to participate too much, the population may become politically 'fatigued' and apathy will grow