The prime minister was proposed by the party leaders but can only be appointed by the president of democracy in this case Carolos Papoulias then the parliament has to provide a confidence vote to the new PM and to the new government If you want you can read the part on the Greek constitution there s an on line edition if you google it in English too I think where it is explained in details how a PM is appointed But the general idea is that after elections the party that comes first in votes proposes a P M the president appoints him and the parliament has to give the confidence vote to the new PM and the government In this case were we have a coalition government consisting of three parties they all came to the conclusion of proposing mr Papademos and then the same procedure takes place