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A quick discussion on Direct Democracy and Referendum Voting. Direct Democracy can be used in tandem with Representative democracy with little issue. The two best countries to see this are Switzerland, which has referendum voting at the Federal Level and The United States, which has some system of referendum voting at the state level (The most common being referral voting, where the legislature can opt to pass a law by citizen vote, which is available in all 50 states. Delaware is the only state that doesn't offer this option for the state constitution. 24 states have some form of citizen initiated veto on laws, and 19 have citizen initiated law proposals, 21 have citizen initiated constitution amendment processes).
Swiss Direct Democracy exists on the Federal Level (with some slight changes in the nature of the executive branch, is pretty much the same as the United States federal system.). Here, citizen Democracy is a futher check and balance on government and is itself checked by other branches of government. Swiss citizens can create or repeal a law by getting 50,000 signatures from any Swiss citizen across any of the cantons (similar to States in the US; At the Canton and local level of government, these numbers will be smaller.). For constitutional amendments, this number is doubled. If a petition achieves this threshold, it will be placed on the next election's ballot. To pass, it must achieve simple majority for all canton and lower levels. At the Federal level, double majority is needed. This requires a simple majority of both the general population of Swiss citizens AND a majority of Cantons to favor the proposal. (For a U.S. perspective, this would be similar to a rule that the President must get both the electoral college vote and the popular vote, rather than just the electoral college). The Swiss hold elections four times a year because of this, which does create some voter appethy at times. Compared to the United States, which votes once every two years not counting special elections.
Historically, Athens is the most famous direct democracy, though they had no sufferage. The 1871 Paris Commune was decentralized direct democracy and everything was up for a vote. Again, women sufferage was not established, though women were highly involved in campaigning. It fell apart in less than year due to lack of infrastructure needed to facilitate voting.
New to the scene is Rojava (officially known as the Democratic Federation of Norther Syria) which is an unrecognized state, which declared autonomous status in late 2012 and federated in March of 2016. They seem to follow a model similar to the Swiss, but include neighborhood level governments. Uniquely, they have co-executives at every level, one male, one female. At this time, it is quite early in their history to make remarks, and its still disputed if they will be a new nation, or a successor state to Syria writ large.