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If the constitution is approved by a simple majority of voters, the Islamists empowered after the overthrow of Mubarak would gain more clout. The upper house of parliament, dominated by Islamists, would be given the authority to legislate until a new lower house is elected.

If the draft proposal is rejected, elections would be held within three months for a new panel to write a new constitution. In the meantime, legislative powers would remain with Mr. Morsi, who won the presidency in June.

The official website of Egypt‘s state television reported that 68 percent and 72 percent of voters cast “no” ballots in Cairo and Alexandria, respectively, Egypt‘s two largest cities. The only other two provinces where the “no” vote won the majority were Gharbiyah and Daqahliya in the Nile Delta, north of Cairo.

The Brotherhood and other Islamists enjoy wide support in most of the 17 provinces voting on Dec. 22, something that could work in favor of the “yes” vote.

But the Islamists led by the Brotherhood are widely thought to have lost some of their popularity because of the perception that Mr. Morsi and the Islamist-backed government of Prime Minister Hesham Kandil have failed to resolve any of the country’s major problems such as high unemployment, rising prices and security.

Egyptians are bracing for a wide range of steep price increases as part of the government’s program to boost revenues and restructure the economy to secure a $4.8 billion loan from the International Monetary Fund. Last week, Egypt delayed the request for the loan after Mr. Morsi rescinded tax increases a day after he imposed them, fearing this would only add to political turmoil.

There were no serious incidents of violence during Saturday’s vote. Although there was no evidence of mass fraud, monitors from the opposition and rights groups said the boycott of the referendum by most judges was reflected in the chaos prevailing in some polling centers.