On Election Day, Democrats had 31 winners and Republicans 30. Two races were too close to call though Democrats appear to be in a position to gain at least one of them.

So Democrats will have a clear majority in the 63-seat chamber to advocate their issues, right?

Wrong.

Four members of a breakaway group called the Independent Democratic Conference fled a then-chaotic Democratic conference in 2010 and have often allied with the Republican majority. They don’t intend to rejoin the Democrats now.

So Republicans have a working majority?

No.

Last week, the Independent Democratic Conference said it wants to create a third group in the Senate, with its own leaders and a seat at the table for every policy and spending decision. It’s an unprecedented attempt at a coalition government in a Capitol deeply rooted in an unusual and notorious system where the majority party has near absolute control of everything from budget negotiations to how many pens a legislator gets.

So a three-way power structure is likely?

Hardly.

“There’s no legitimate rationale for a group of four people to have equal authority as groups of 31 or 28,” said Sen. Michael Gianaris, a Queens Democrat who may find himself in the nearly powerless minority Jan. 1. “That would mean a voter represented in those four districts had greater representation than voters in other districts.”

The four-member coalition, however, says bipartisanship and shared power are exactly the changes people want.

“This is what needs to be done for anyone who is serious about a bipartisan agenda,” said Sen. Jeffrey Klein, a Bronx-Westchester Democrat and a leader of the conference.

Plus, Democratic Sen.-elect Simcha Felder of Borough Park has already decided to sit with Republicans, meaning they’ll have a majority if George Amedore wins the ongoing count in a district that stretches from Montgomery to Ulster counties.

Richard Brodsky, a senior fellow at the Wagner School at New York University who spent 20 years in the Legislature as a Democrat, sees similar tension in “Lincoln.” But the 16th president found a way to work with factions within his Republican Party, win the Civil War and end slavery.

“Any time you have a one-vote majority, every member of that majority is in charge,” said Brodsky, a Democrat. “What you saw happen four years ago was that there were individuals who were prepared to play that card. That’s dangerous, whatever party.

“I have partisan and ideological preferences, no doubt,” Brodsky said, “but the fact of the matter is that politics, even when there is ugliness in it, is the way we avoid shooting each other.”

In 2009, a Senate coup came about from Republicans and three dissident Democrats, two of whom were later convicted of corruption. The third was expelled from the chamber after an assault on his girlfriend.

The tarnished image of New York’s senior house isn’t being helped by the newest power struggle.

But some find all of this predictable for Albany.

“It’s about the motivation,” said Bill Samuels, founder the New Roosevelt good-government group and EffectiveNY.org think tank. “Being in the majority not only affects the size of your office, but the size of your staff and, depending on where you are in history, member items,” also known as pork-barrel grants, which are currently suspended under Gov. Andrew Cuomo.

The greatest of majority powers is redistricting, the once-a-decade process majorities to redraw election districts, traditionally used to protect the jobs of the majority’s lawmakers and to shore up their power. Every senator and Cuomo promised to end that process this year, but Republicans continued it with Cuomo’s OK.

“It hasn’t been a good year, no matter how this turns out,” Samuels said.