The Moscow Times reports:

When a French journalist asked President Vladimir Putin recently how United Russia captured almost 100 percent of the vote in Chechnya and Ingushetia during the State Duma elections, an Ingush reporter jumped in and said 10 of his relatives voted for the pro-Putin party.

It was, perhaps, fitting that the reporter cited a round number.

Two bloggers have crunched the election results and found that a disproportionate number of polling stations reported round numbers -- that is, numbers ending in zero and five -- both for voter turnout and for United Russia's percentage of the vote in the Dec. 2 election. The analyses by chemist Maxim Pshenichnikov and a LiveJournal blogger nicknamed Podmoskovnik offer mathematical proof of either election fraud or extremely anomalous voter behavior, economists said. "It is a study that explicitly demonstrates that the results were manipulated," said Konstantin Sonin, an economist at the New Economic School who writes a column that appears in The Moscow Times.

Without the statistical anomalies, United Russia would not have secured a constitutional majority in the Duma, concluded Podmoskovnik, who declined to give his real name when contacted by e-mail and also declined to be interviewed by telephone. In most elections, one would expect the turnout to follow a normal, or Gaussian, distribution -- meaning that a chart of the number of polling stations reporting a certain turnout would be shaped like a bell curve, with the top of the bell representing the average, median, and most popular value.

But according to Pshenichnikov's analysis [see chart at left], the distribution looks normal only until it hits 51 percent. After that, it begins spiking on round numbers, indicating a much greater number of polling stations reporting a specific turnout than a normal distribution would predict.

The same trend is seen in the analysis of United Russia's results conducted by Podmoskovnik [see chart below right]. United Russia, for example, received 89 percent of the vote at 633 polling stations, according to Podmoskovnik's analysis of the results. But 927 stations reported 90 percent for the party, while 770 stations reported 91 percent. A suspicious voter might say polling officials stuffed ballot boxes to achieve a nice, clean 90 percent figure.

Podmoskovnik found that the spiking on round numbers begins after United Russia's returns hit 55 percent. Taken together with Pshenichnikov's calculations, it appears that the higher the turnout, the higher United Russia's percent of the returns -- a correlation not seen in returns of the other 10 parties on the ballot. Furthermore, the spikes in both analyses coincide on several round numbers, including 75 percent, 80 percent, 85 percent and 90 percent.

The anomalies are not necessarily evidence of fraud, Podmoskovnik dryly wrote on his blog, Podmoskovnik.livejournal.com: "One could well imagine that United Russia voters radically differ in their social behavior from other parties' voters and are distinctly predisposed to collective voting for their favorite party when turnout is at its peak."

If the anomalies were smoothed out, turnout would have been 50.2 percent, rather than the official figure of 63 percent, Podmoskovnik said. Furthermore, United Russia would have secured only 277 seats in the Duma, he concluded. This would deny the party the 300 seats needed for a constitutional majority.

Official election results gave United Russia 315 seats. The other parties represented in the Duma -- the Communist Party, the Liberal Democratic Party and A Just Russia -- took 57, 40 and 38 seats, respectively. According to Podmoskovnik's analyses, the three parties should have received 73, 51 and 49 seats, respectively.

The Central Elections Commission declined to comment when asked to explain the anomalies revealed in the two analyses. But several economists agreed with Podmoskovnik's findings. Mikhail Delyagin, head of the Institute of Globalization Problems, said local election officials clearly decided in advance what the figures would be for turnout and United Russia's percentage of the vote. "As many human beings do, they were thinking in round numbers," Delyagin said. The disproportionate amount of round numbers indicates that low-level officials were manipulating returns as they saw fit rather than as part of a centralized effort to fix the vote, said Sergei Shulgin, an analyst with the Institute of Open Economics who studies elections. "Men on the ground decide which digits will please their bosses," he said.

Low-level officials do not grasp that hundreds of polling stations reporting figures in round numbers distort normal distribution, thus clearly revealing manipulations, Delyagin said. More round numbers could emerge in Sunday's presidential election, which Putin's preferred successor, First Deputy Prime Minister Dmitry Medvedev, is expected to win in a landslide. Officials in the far eastern Primorye region have been ordered to ensure 65 percent of the vote for Medvedev, Kommersant reported last week, citing a copy of a document distributed to local officials. Administration and election officials in the region denied the report.

Meanwhile, the Kirov region weekly Vyatsky Nablyudatel last month cited local officials as saying they were preparing to guarantee 80 percent of the vote for Medvedev. But given the resonance of Podmoskovnik's study in the Russian blogosphere, election officials will likely try to avoid such spikes in turnout and results in Sunday's election, Delyagin said. Shulgin disagreed, saying anomalies indicating manipulation of returns have increased with each presidential election since 1996. Furthermore, the spikes on round numbers in Putin's re-election in 2004 were even more evident than those in United Russia's victory in the December 2003 Duma elections, he said. "So my forecast is that ... the anomalies in the upcoming presidential election will be even more explicit than in the latest Duma election," he said.

n Central Elections Commission chief Vladimir Churov on Wednesday called on election officials in regions where turnout was exceptionally high in the Duma elections to encourage independent observers to conduct "alternative counts of all voters," Itar-Tass reported. This, Churov said, would help to verify that near 100 percent turnout in some regions is in fact genuine. Meanwhile, Churov on Thursday shrugged off Western criticism about the fairness of the presidential vote, calling it part of a campaign against Russia.