A referendum (plural: referendums or less commonly referenda) is a direct vote in which an entire electorate is invited to vote on a particular proposal. This may result in the adoption of a new law. In some countries, it is synonymous with a plebiscite or a vote on a ballot question.
Some definitions of 'plebiscite' suggest it is a type of vote to change the constitution or government of a country. The word, 'referendum' is often a catchall, used for both legislative referrals and initiatives. Australia defines 'referendum' as a vote to change the constitution and 'plebiscite' as a vote which does not affect the constitution. whereas in Ireland, 'plebiscite' referred to the vote to adopt its constitution, but a subsequent vote to amend the constitution is called a 'referendum', as is a poll of the electorate on a non-constitutional bill.
Etymology and plural form
'Referendum' is the gerundive form of the Latin verb refero, literally "to carry back" (from the verb fero, "to bear, bring, carry" plus the inseparable prefix re-, here meaning "back"). As a gerundive is an adjective, not a noun, it cannot be used alone in Latin, and must be contained within a context attached to a noun such as Propositum quod referendum est populo, "A proposal which must be carried back to the people". The addition of the verb sum (3rd person singular, est) to a gerundive, denotes the idea of necessity or compulsion, that which "must" be done, rather than that which is "fit for" doing. Its use as a noun in English is not considered a strictly grammatical usage of a foreign word, but is rather a freshly coined English noun, which follows English grammatical usage, not Latin grammatical usage. This determines the form of the plural in English, which according to English grammar should be "referendums". The use of "referenda" as a plural form in English (treating it as a Latin word and attempting to apply to it the rules of Latin grammar) is unsupportable according to the rules of both Latin and English grammar. The use of "referenda" as a plural form is posited hypothetically as either a gerund or a gerundive by the Oxford English Dictionary, which rules out such usage in both cases as follows:
It is closely related to agenda, "those matters which must be driven forward", from ago, to drive (cattle); and memorandum, "that matter which must be remembered", from memoro, to call to mind, corrigenda, from rego, to rule, make straight, those things which must be made straight (corrected), etc.
The term 'plebiscite' has a generally similar meaning in modern usage, and comes from the Latin plebiscita, which originally meant a decree of the Concilium Plebis (Plebeian Council), the popular assembly of the Roman Republic. Today, a referendum can also often be referred to as a plebiscite, but in some countries the two terms are used differently to refer to votes with differing types of legal consequences. For example, Australia defines 'referendum' as a vote to change the constitution, and 'plebiscite' as a vote that does not affect the constitution. In contrast, Ireland has only ever held one plebiscite, which was the vote to adopt its constitution, and every other vote has been called a referendum. Plebiscite has also been used to denote a non-binding vote count such as the one held by Nazi Germany to 'approve' in retrospect the so-called Anschluss with Austria, the question being not 'Do you permit?' but rather 'Do you approve?' of that which has most definitely already occurred.
The term referendum covers a variety of different meanings. A referendum can be binding or advisory. In some countries, different names are used for these two types of referendum.
Referendums can be further classified by who initiates them: mandatory referendums prescribed by law, voluntary referendums initiated by the legislature or government, and referendums initiated by citizens.
A deliberative referendum is a referendum specifically designed to improve the deliberative qualities of the campaign preceding the referendum vote, and/or of the act of voting itself.
From a political-philosophical perspective, referendums are an expression of direct democracy, but today, most referendums need to be understood within the context of representative democracy. They tend to be used quite selectively, covering issues such as changes in voting systems, where currently elected officials may not have the legitimacy or inclination to implement such changes.
Referendums by country
Since the end of the 18th century, hundreds of national referendums have been organised in the world; almost 600 national votes were held in Switzerland since its inauguration as a modern state in 1848. Italy ranked second with 72 national referendums: 67 popular referendums, 3 constitutional referendums, one institutional referendum and one advisory referendum.
A referendum usually offers the electorate a choice of accepting or rejecting a proposal, but not always. Some referendums give voters the choice among multiple choices and some use Transferable voting even.
In Switzerland, for example, multiple choice referendums are common. Two multiple choice referendums were held in Sweden, in 1957 and in 1980, in which voters were offered three options. In 1977, a referendum held in Australia to determine a new national anthem was held in which voters had four choices. In 1992, New Zealand held a five-option referendum on their electoral system. In 1982, Guam had referendum that used six options, with an additional blank option for anyone(s) wishing to (campaign and) vote for their own seventh option.
A multiple choice referendum poses the question of how the result is to be determined. They may be set up so that if no single option receives the support of an absolute majority (more than half) of the votes, resort can be made to the two-round system or instant-runoff voting, which is also called IRV and PV.
In 2018 the Irish Citizens' Assembly considered the conduct of future referendums in Ireland, with 76 of the members in favour of allowing more than two options, and 52% favouring preferential voting in such cases. Other people regard a non-majoritarian methodology like the Modified Borda Count (MBC) as more inclusive and more accurate.
Swiss referendums offer a separate vote on each of the multiple options as well as an additional decision about which of the multiple options should be preferred. In the Swedish case, in both referendums the 'winning' option was chosen by the Single Member Plurality ("first past the post") system. In other words, the winning option was deemed to be that supported by a plurality, rather than an absolute majority, of voters. In the 1977, Australian referendum, the winner was chosen by the system of preferential instant-runoff voting (IRV). Polls in Newfoundland (1949) and Guam (1982), for example, were counted under a form of the two-round system, and an unusual form of TRS was used in the 1992 New Zealand poll.
Although California has not held multiple-choice referendums in the Swiss or Swedish sense (in which only one of several counter-propositions can be victorious, and the losing proposals are wholly null and void), it does have so many yes-or-no referendums at each Election Day that conflicts arise. The State's Constitution provides a method for resolving conflicts when two or more inconsistent propositions are passed on the same day. This is a de facto form of approval voting—i.e. the proposition with the most "yes" votes prevails over the others to the extent of any conflict.
Another voting system that could be used in multiple-choice referendum is the Condorcet rule.
Criticism of populist aspect
Critics of the referendum argue that voters in a referendum are more likely to be driven by transient whims than by careful deliberation, or that they are not sufficiently informed to make decisions on complicated or technical issues. Also, voters might be swayed by propaganda, strong personalities, intimidation, and expensive advertising campaigns. James Madison argued that direct democracy is the "tyranny of the majority".
Some opposition to the referendum has arisen from its use by dictators such as Adolf Hitler and Benito Mussolini who, it is argued, used the plebiscite to disguise oppressive policies as populism. Dictators may also make use of referendums as well as show elections to further legitimize their authority such as Benito Mussolini in 1934, Adolf Hitler in 1936, Ferdinand Marcos in 1973, Park Chung-hee in 1972, and Francisco Franco in 1947. Hitler's use of plebiscites is argued as the reason why, since World War II, there has been no provision in Germany for the holding of referendums at the federal level.
British politician Chris Patten summarized many of the arguments used by those who oppose the referendum in an interview in 2003, when discussing the possibility of a referendum in the United Kingdom on the European Union Constitution:
I think referendums are awful. The late and great Julian Critchley used to say that, not very surprisingly, they were the favourite form of plebiscitary democracy of Mussolini and Hitler. They undermine Westminster. What they ensure, as we saw in the last election, is that if you have a referendum on an issue, politicians during an election campaign say: "Oh, we're not going to talk about that, we don't need to talk about that, that's all for the referendum." So during the last election campaign, the euro was hardly debated. I think referendums are fundamentally anti-democratic in our system, and I wouldn't have anything to do with them. On the whole, governments only concede them when governments are weak.
Closed questions and the separability problem
Some critics of the referendum attack the use of closed questions. A difficulty called the separability problem can plague a referendum on two or more issues. If one issue is in fact, or in perception, related to another on the ballot, the imposed simultaneous voting of first preference on each issue can result in an outcome which is displeasing to most.
Undue limitations on regular government power
Several commentators have noted that the use of citizens' initiatives to amend constitutions has so tied the government to a jumble of popular demands as to render the government unworkable. An 2009 article in The Economist argued that this had restricted the ability of the California state government to tax the people and pass the budget, and called for an entirely new Californian constitution.
A similar problem also arises when elected governments accumulate excessive debts. That can severely reduce the effective margin for later governments.
Both these problems can be moderated by a combination of other measures as
strict rules for correct accounting on budget plans and effective public expenditure;
mandatory assessment by an independent public institution of all budgetary implications of all legislative proposals, before they can be approved;
mandatory prior assessment of the constitutional coherence of any proposal;
interdiction of extra-budget expenditure (tax payers anyway have to fund them, sooner or later).
The Federal Authorities of the Swiss Confederation, statistics (German). https://web.archive.org/web/20081210071708/http://www.bfs.admin.ch/bfs/portal/de/index/themen/17/03/blank/key/stimmbeteiligung.html 
Turcoane, Ovidiu (2015). "A proposed contextual evaluation of referendum quorum using fuzzy logics"  (PDF). Journal of Applied Quantitative Methods. 10 (2): 83–93.
Referendums by country
Right to petition