A day after an election that scrambled Greek — and potentially, European — politics, party leaders are surveying the new reality of Greek parliamentary politics in search of a workable governing coalition.

The center-right New Democracy (Νέα Δημοκρατία), which finished in first place, and which accordingly won the greatest number of seats in the Hellenic Parliament.  Under Greece’s new election law, 250 seats are distributed by proportional representation, while an additional 50 seats are awarded to the party with the highest support — even if, as in this election, the “winner” gets less than 19% of the total votes cast.

Nonetheless, even with its skewed number of seats, New Democracy is projected to hold just 108 seats, far below what it would need to form a government.   Accordingly, ND leader Antonis Samaras will have the first shot of forming a coalition — and will attempt today to build one among pro-euro and pro-bailout parties.

The most natural coalition for ND would be with PASOK (Panhellenic Socialist Movement – Πανελλήνιο Σοσιαλιστικό Κίνημα).  The two parties, traditional Greece’s largest center-right and center-left parties, have long dominated Greek politics in the modern era — in 2009, their combined total of the vote was 79%.  Yesterday’s election, however, scrambled Greek politics to such a degree that the two parties won just around 32% of the vote, demonstrating the unpopularity of Greece’s most recent bailout.  PASOK and ND joined in November to support prime minister Lucas Papademos for a further round of budget cuts as required under the latest terms of the bailout.

The far-left SYRIZA (the Coalition of the Radical Left — Συνασπισμός Ριζοσπαστικής Αριστεράς) exceed expectations and finished a strong second place on Sunday, just around 2% behind New Democracy.

Accordingly, because PASOK is projected to have won just 41 seats, Samaras will not be able to form a ‘grand coalition’ with just PASOK — the coalition would fall just short of a majority (149 of 300 seats) in Greece’s parliament.  Although Samaras has announced that he will look to form a coalition of all parties that want Greece to remain in the eurozone, he might have a hard time finding additional coalition partners among the remaining parties.

Earlier today, for example, Fotis Kouvelis, the leader of the Democratic Left, ruled out any coalition with New Democracy — his party is a pro-Europe, but anti-austerity, group that is perhaps the most moderate of the three far-left groups and was the likeliest of the three to join a grand coalition.  Likewise, Samaras will also have a difficult time forming a coalition with Panos Kammenos, the leader of the Independent Greeks, a splinter group of anti-austerity center-right rebels that split with New Democracy just last November over its support of the bailout and the Papademos government.

Accordingly, perhaps the best chance for Samaras is to form a minority government (with or without a formal coalition with PASOK) with working support from a handful of the most moderate members of the Independent Greeks and the Democratic Left.

If Samaras fails to form a coalition, SYRIZA’s leader, Alexis Tsipras, will have an opportunity to form a government.  But if Samaras’s path to a governing coalition is tricky, Tsipras’s is nearly impossible.

Together, SYRIZA, the Democratic Left and the KKE, Greece’s communist party, would command just 97 seats.  Even the support of the anti-austerity Independent Greeks would not command a majority of seats, however, and neither the pro-bailout nor anti-bailout parties want to enter into a coalition with the neo-fascist Golden Dawn party, which won 21 seats in Sunday’s election.

Furthermore, the KKE has ruled out any coalition with SYRIZA (which split from the KKE in 1991 over differences in the direction of Greece’s radical left in the post-Soviet era).  Despite Tsipras’s best efforts, Kouvelis has also resisted any coalition of the far left — indeed, the Democratic Left is itself a splinter group of moderates that left SYRIZA in 2010.

If Samaras and Tsipras both fail, Evangelos Venizelos, former finance minister and leader of PASOK, will have an opportunity to form a coalition — at that point, however, it is unlikely that he will have found any winning combination that has not already eluded Samaras and Tsipras.

Samaras will thereupon have one final opportunity to bring together a ‘national unity’ government if Venizelos fails — if that fourth and final opportunity does not succeed, Greek voters will go back to the polls, likely in a new election to be held in June.

As stocks fell over 7% in Athens this morning, it is becoming clear that markets are betting on new elections, which may further boost the anti-austerity parties, to the continued detriment of PASOK and New Democracy.  When a government emerges, its first task will be to turn to further budget cuts of around €11.5 billion, the amount of expected budget shortfalls in 2013 and 2014, under the terms of Greece’s bailout with the ‘troika’ of the European Central Bank, the European Commission and the International Monetary Fund.

Even amid the electoral turmoil, European and German leaders implored Greece not to turn its back on the harsh terms of the bailout, although it remains uncertain that an anti-austerity government would maintain the reforms agreed to by earlier governments.  At best, it would be expected that an anti-austerity government would seek to renegotiate the terms of the bailout with more favorable terms for Greece.  At worst, such a government could rip up past agreements, trigger a Greek default on its loans or even pull Greece out of the euro, Europe’s single currency.