Exhaustive ballot
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The exhaustive ballot is a voting system used to elect a single winner. Under the exhaustive ballot the elector casts a single vote for his or her chosen candidate. However, if no candidate is supported by an overall majority of votes, the candidate with the fewest votes is eliminated and voters engage in a new round of voting to determine the winner. This process is repeated for as many rounds as necessary until one candidate has a majority.
The exhaustive ballot is similar to the two-round system but with key differences. Under the two round system, if no candidate receives a majority of the votes on the first round, only the two most-popular candidates advance to the second (and final) round of voting, and the plurality winner is declared elected in the second round. (This winner may or may not hold a majority of votes as cast originally.)
By contrast, in the exhaustive ballot system, if no candidate receives a majority of the votes on the first round, only one candidate is eliminated per round. Several rounds of voting may be required until a candidate reaches a majority of the vote still in play. (In some circumstances, two or more of the least popular candidates can be eliminated simultaneously if together they have fewer votes than the candidate next above them. In other words, this "bulk exclusion" cannot change the order of elimination, unlike a two-round system.)
Because voters may have to cast votes several times, the exhaustive ballot is not used in large-scale public elections. Instead its use is in elections involving, at most, a few hundred voters, such as the election of a prime minister or other leader of a party, or the presiding officer of an assembly.
The exhaustive ballot is currently used, in different forms, to elect the members of the Swiss Federal Council, the First Minister of Scotland, the President of the European Parliament, and speakers of the House of Commons of Canada, the British House of Commons and the Scottish Parliament. It is also used to choose the host city of the Olympic Games and the host of the FIFA World Cup. Formerly, the Knesset used the exhaustive ballot system to elect the President and the State Comptroller of Israel. Holders of those positions are still indirectly elected but now the Knesset elects them using a two-round system.