Organizers of the protest are unhappy with the current electoral system,which at present only allows residents to vote for a pre-approved list of candidates. This makes it impossible for critics of Beijing to get on the ballot. Chinese authorities had promised reform by 2017, but on August 31 decreed that it would continue to vet candidates wishing to run for Hong Kong's leadership.
Much of the anger has been directed toward Leung, a Beijing loyalist who has been in power since mid-2012. Leung was blamed for authorizing the territory's police to use tear gas on the protesters on Sunday—a move which has drawn broad criticism considering Hong Kong has not used such severe methods since 2005.
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Chants for Leung's resignation have been heard throughout the week's demonstrations. Meanwhile banners depicting Leung with vampire fangs have become a common image throughout. Student protesters have even refashioned a stranded city bus into a coffin for him.
Any concessions to the protesters' demands look unlikely at this stage,however, as Leung is widely regarded as a "stooge" for Beijing authorities, and Chinese authorities are nervous that any sign of weakness could trigger unrest in mainland China.
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But while protesters would likely see Leung's resignation as a symbolic victory in their campaign—with many analysts saying that such a move would be the easiest way for Beijing to placate protesters—there are doubts about how helpful it would be.
"I think it's actually better to keep him there because it's better to know who you have rather than to come up with a new person that is representing the Communist Party in Hong Kong... and then they have to start again," Paul Zimmerman, southern district councilor of Hong Kong, told CNBC on Thursday.
"It's better to find a way of talking and working [together] but CY is now the one who has to pick up the phone and come down to start getting a discussion going," he added.