The election of the mayor of the city of Giulio takes place in two rounds: if no one obtains an absolute majority in the first round, there is a ballot between the two most voted candidates. In the first round, the candidate voted by Giulio obtained 45% of the votes and 68% of those entitled to vote. In the ballot, Giulio's candidate won with 52% of the votes, but only 56% of those entitled voted. In absolute terms, did Giulio's candidate get a higher number of votes in the first round or in the second round? What is the difference in votes if the beneficiaries are 150,000?

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The central feature of the Two-Round System is as the name suggests: it is not one election but takes place in two rounds, often a short time apart. The first round is conducted in the same way as a single-round plurality/majority election. In the most common form of TRS, this is conducted using FPTP. It is, however, also possible to conduct TRS in multi-member districts using Block Vote (as in Kiribati) or Party Block Vote (as in Mali). A candidate or party that receives a specified proportion of the vote is elected outright, with no need for a second ballot. This proportion is normally an absolute majority of valid votes cast, although several countries use a different figure when using TRS to elect a president. If no candidate or party receives an absolute majority, then a second round of voting is held and the winner of this round is declared elected.

The details of how the second round is conducted vary in practice from case to case. The most common method is for it to be a straight run-off contest between the two highest vote winners from the first round; this is called majority run-off TRS. It produces a result that is truly majoritarian in that one of the two participants will necessarily achieve an absolute majority of votes and be declared the winner. A second method, majority-plurality TRS, is used for legislative elections in France, the country most often associated with the Two-Round System. In these elections, any candidate who has received the votes of over 12.5 per cent of the registered electorate in the first round can stand in the second round. Whoever wins the highest number of votes in the second round is then declared elected, regardless of whether they have won an absolute majority or not. Unlike majority run-off, this system is not truly majoritarian, as there may be up to five or six candidates contesting the second round of elections.

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