It's not a simple question, as Edward Wolfers explains for Al Jazeera:
The impasse between the two would-be prime ministers began when the speaker of parliament accepted the opposition's claims that the prime ministership was vacant. At the time, Sir Michael Somare - who had been elected prime minister in 2007 - had been out of the country for several months while undergoing medical treatment in Singapore. Accordingly, parliament elected a new prime minister, Peter O'Neill.
O'Neill's initial parliamentary majority - of 70 to 24 - included many former members of the coalition previously put together and led by Somare. Other members have subsequently changed sides.
In December, the Supreme Court found, by a majority of three to two, that Somare was still legally prime minister. Parliament responded by retroactively withdrawing the leave on which Somare had relied while he was out of the country and re-elected O'Neill. It also passed a new law preventing a person aged 72 or older from becoming prime minister. As Somare was already 75, the new law - if it is constitutional - makes him ineligible to return as prime minister.
Although both rivals have some claim to legitimacy - O'Neill has parliament's backing, and Somare is supported by the Supreme Court - the country's chief secretary and other heads of government departments have tended to side with O'Neill.
The fight culminated in an failed coup by pro-Somare military officers in late January. For now, the issue is still being deliberated by the courts, though Somare has continued to fight for his old office, and criticize the current government from the outside, including demanding an investigation into allegations that the current deputy prime minister sexually harassed a casino blackjack dealer.
It's been an eventful couple of months in New Guinea politics. O'Neill's predecessor as acting prime minister, Sam Abal, was ousted from office shortly after a woman's body was discovered at his home and his son charged with murder.
The political uncertainty since the leadership switch and the attempted coup is understandably having a negative affect on the country's economic outlook as well. The Australian government, PNG's largest trading partner and former colonial power, seems to be working with O'Neill as the de facto leader, though Australian leaders have said little in public about the dispute.
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