Up to a third of votes cast for Dmitri Medvedev to be Russia's next President were likely to have been rigged, a comprehensive new study of the election results has found.

Millions of votes for the Kremlin's favoured candidate were the product of mass fraud or the use of “administrative resources” by government officials to pressure state employees into supporting Mr Medvedev, the study states.

The results inflated Mr Medvedev's margin of victory and the overall turnout, making it appear that he enjoyed massive popular support as Vladimir Putin's chosen successor.

The scale of manipulation was exposed by Sergei Shpilkin, a physicist and computer programmer, who concluded that 14.8 million of the 52.5 million votes cast for Mr Medvedev could not be explained in any other way.

He also calculated that only 56 per cent of Russians had voted, instead of the 69.7 per cent officially declared by the Central Election Commission (CEC).

“It is a combination of fraud and administrative resources and it is difficult to distinguish between them,” said Mr Shpilkin. “One vote in three is not explainable and probably the administrative factor is a little more than that.

“I don't think it was really necessary to do all this pressure and rigging because he would easily have won without it.”

Mr Medvedev won 70.3 per cent officially but Mr Shpilkin calculated that it was just under 63 per cent once “abnormal” voting was discounted.

On a reduced turnout, this meant that only a third of Russia's 100 million voters supported Mr Medvedev, far from the overwhelming endorsement claimed by the Kremlin.

Mr Shpilkin analysed the ballot returns from electoral commissions throughout Russia, published on the CEC website. He presented his research at a seminar on Wednesday organised by the Carnegie Centre in Moscow.

He found that unusually high numbers of polling stations had reported turnout and percentage results for Mr Medvedev that ended in a five or zero. Support for the candidate also followed unusual patterns.

Voting in normal elections usually follows a bell curve, rising gradually on one side to a plateau representing the average level of support before sloping down again.

Mr Shpilkin found that Mr Medvedev's support appeared normal until it reached 60 per cent, then continued to hit a series of sharp spikes instead of sloping down.

The spikes matched percentages ending in five or zero, showing that disproportionate numbers of polling stations had reported these results.

Sergei Shulgin, an election analyst at the Institute for Applied Economics, said the anomalies showed that local officials had tried to impress their superiors by “improving the results”.

Andrei Buzin, the head of the Interregional Association of Voters, said that the study revealed “blatant manipulation” of the results.

The analysis adds force to criticism by international observers that the election was neither free nor fair. They infuriated the Kremlin by concluding that Russia's “democratic potential was unfortunately not tapped”, although they acknowledged that the result reflected the popular will.

The CEC has rejected any criticism of the conduct of the election. But it found itself unwittingly confirming claims of manipulation when it presented awards to polling agencies that accurately forecast the presidential results.

The company that won the prize for predicting turnout said that its methods took account of the number of votes that would be added through government pressure.

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