Governance reforms in the International Monetary Fund have been years in the making. A historic deal sealed in 2010 - and supposed to come into force this week in Tokyo where the IMF and World Bank are holding annual meetings - would make China the third-largest voting member and revamp the Fund's board to reduce Western Europe's dominance.

But that has been stalled by the U.S. presidential election. Washington has effective veto power over the 2010 package. Approving it would mean putting more money into the IMF, something the Obama administration is reluctant to do before the election.

The 2010 deal was part of a broader plan by the IMF to recognize within the organization the growing economic clout of emerging economies.

The next phase, which the IMF had hoped would be completed by January 2013, involves establishing a formula that would determine voting shares based on economic size, capital flows, foreign exchange reserves and other variables. Depending on the weighting, different countries benefit, which helps explain the wrangling over the math.

"The message being sent by the institution is that it is having enormous difficulty adapting its structure and functioning to the 21st Century," Paulo Nogueira Batista, the IMF executive director for Brazil and a constituency of other Latin American and Caribbean countries, told Reuters.

China, Brazil and other large emerging market economies have long contended that the IMF's current voting set-up unfairly benefits Europe and the United States, which dominated the IMF since its founding after World War Two.

They argue that if the IMF expects them to contribute more both to IMF resources and to the global economy, they deserve more power within the Fund.

That was the reasoning behind two sets of IMF reforms in 2008 and 2010.

PRIORITIES

Ted Truman, a senior fellow at Washington's Peterson Institute and a former assistant Secretary of the U.S. Treasury for international affairs from 1998-2001, said IMF reforms may not be Washington's highest priority even after the election.

"One question is whether the U.S. will be able to do this as part of the lame duck exercise, which would be positive. But my sense is maybe it won't be the highest priority of the administration and not the lowest either.

"I don't think you have to be too partisan to say if (Mitt) Romney wins... this is not going to be the highest national priority for the new administration. If Obama wins, then you are likely to have a continuity of policy with regard to the Fund," said Truman.

Ironically, it was the United States that pressed hard for IMF quota and board reform in 2009. U.S. Treasury Secretary Timothy Geithner, himself a former IMF official, conducted shuttle diplomacy between European and emerging economies to try to reach a reform deal.

David Lipton, the No. 2 official at the IMF and the highest ranking American, said the Obama administration had been clear that it would not be able to seek congressional approval for more IMF funding before the November election.

He said there was still time to reach a compromise on IMF governance reform and described an "emerging consensus" behind increasing the weight given to GDP to determine voting shares.

"It is a complicated matter and different countries have different interests right now, but I think it would be wrong to surmise the membership doesn't stand strongly behind modernizing the governance structure of the IMF to keep up with the evolution of the global economy," Lipton told Reuters in an interview in Tokyo.

"There will be some elbow-throwing in the course of these discussions."

MATHS BECOMES POLITICAL

Any change to the quota formula that gives more weight to purchasing power GDP - which measures the buying power of an economy instead of just the dollar value - would benefit China and other developing economies.

European countries want to put more emphasis on openness, the most hotly debated of all the measurements, because it captures among many things the vast trade flows among euro zone countries. Removing the openness measure, or scaling it back, would sharply reduce Europe's influence in the IMF and shift power to China, India and Brazil, according to an IMF report.

"There is no room to compromise with nonsense. Openness makes no economic sense, it has no meaning, it is just a device to sustain over-representation of Europe and other small developed economies," Nogueira Batista said.

"I have been in this institution long enough to know that the call for compromise is often coded language for status quo," he added.

European representatives to the IMF declined to comment. In Brussels, European officials said the U.S. delays had given them more time to hammer out a reform agreement.

The January 2013 target for a reconfigured formula could be delayed until 2014, in time for the deadline of the next review of membership quotas, according to officials with knowledge of the talks.

The wrangling with Europe over the formula has added to frustrations among developing countries over what they say is Europe's resistance to giving up some of its power in the Fund.

Added to that now is growing anger among many developing countries over Europe's handling of its debt crisis, which they say risks pushing the rest of the world into another recession.

Earlier this year, emerging and developing countries ponied up billions of dollars to help countries cope with the euro zone crisis and some want that reflected in the voting power shift.

"The Europeans are losing ground relative to the rest of the world all the time, both in the economic and political sense," Peterson's Truman said. "So the very fact that many of the non-European members of the Fund are annoyed with Europe for pushing the world economy to the edge of another recession doesn't help their economic posture."

(Additional reporting by Vincent Lee in Seoul; Editing by Emily Kaiser and Neil Fullick)

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