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Let's say Mohammed Morsi loses the Presidential Elections in Egypt in 2012. Although the Muslim Brotherhood and other Islamists won the 2011/2012 Parliamentary elections in Egypt overwhelmingly the Presidential elections were much closer. In the first round of elections Morsi came in first but only got 24.78% of the vote. Ahmed Shafik (who represented the old but secular NDP regime) came extremely close with 23.66% and Hamdeen Sabahi (a secular Nasserist candidate) came third with 20.72%, the rest of the vote was split between 10 candidates.
In the second round of elections only Morsi and Shafik ran against each other with Morsi winning 52% to 48%. Morsi was later overthrown by Abdul Fattah el-Sisi in a coup/revolution a year later in 2013.
How might Egypt have turned out if Shafik or Sabahi had won the Presidential election? A secular President and a parliament comprised overwhelmingly of Islamists would be interesting to watch. In OTL the Parliament was suspended by the Supreme Court in 2012 and so I would expect that would happen regardless, this time leaving the Brotherhood excluded from the government. A new constitution would be created that would be far more secular.