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Yuge (sometimes spelled yooge) is the pronunciation of the English adjective "huge" in a dialect called "New York City English", which causes the /h/ to be reduced to a /y/ sound because of the presence of /u/ and /j/. The pronunciation became popular during the 2016 Presidential Election because of its frequent use by both Bernie Sanders and Donald Trump, both of whom are New York City natives that speak New York City English.
New York City English is a dialect of English spoken by natives of New York City and the surrounding areas, and is often featured on television as a stand-in for a blue-collar or middle-class manner of speaking. There are generally two forms of the dialect – one is spoken by those who were born in the area before 1950, and one is spoken by those who were born after.
However, according to Wikipedia, the modifications of consonants as is seen in yuge, is not necessarily as common as the modifications of vowels. This makes it unusual that two presidential candidates in the same year would both present the same consonant modification, but Donald Trump and Bernie Sanders were only born 5 years apart; the former in 1946 and the latter in 1941. This time-based relationship increases the likelihood of their accents being similar. Yooge, the alternative spelling, was first defined by Urban Dictionary by the user Canuckian on March 19th, 2004 as "Overblown, ostentatious;" the example given immediately linked the word to Trump.
The New York Times first noticed that Bernie Sanders used yuge in a 2007 profile, and the first known reference to Donald Trump's use of yuge by the media was by People in 2004, who included the adjective in a short slideshow referencing Trump's scandalous divorce in the 1980s. In November 2009, it was used in the headline of a piece about Trump's bankruptcies in Atlantic City that was published by Gawker.
As both Sanders and Trump announced their campaigns and began to run in their party's respective 2016 election, the word was often used to describe the size of their crowds and the candidate's presences by the media. In July 2015, a YouTube user called Florida for Sanders uploaded a supercut of Bernie Sanders saying yuge in various speeches and appearances (below left); the video gained 11,000 views as of February 2016. On September 11th, 2015, Jimmy Fallon, imitating Trump in a comedy sketch which also featured Donald Trump, used the word to describe the importance of the first Republican debate to Trump's campaign (below right). The YouTube upload of Fallon's sketch earned 8.6 million views.
As both Sanders and Trump emerged as leaders in their respective fields, the adjective's use in the media then shifted to being used to compare and contrast their electoral approaches, which were both seen as outside the general political establishment. On August 19th, 2015, MSNBC ran a segment on the show All In with Chris Hayes detailing both candidates' use of the word. And when both Sanders and Trump won in the 2016 New Hampshire Primary, a variety of media outlets, including Vox.com, the Tampa Bay Times, and the Washington Post ran articles describing the results as yuge.
 The Tampa Bay Times – For some N.H. voters, 'yooge' choice between Donald Trump and Bernie Sanders
 The Washington Post – For some N.H. voters, ‘yuge’ choice between Donald Trump and Bernie Sanders