Egyptian President Mohamed Morsi speaks to reporters. (Maya Alleruzzo/AP)

A new report on Egyptian electoral trends, released by Rand, finds that Islamist political parties such as the Muslim Brotherhood are likely to see their political majority decline over time. Still, the report predicts, Islamists will probably remain the primary political faction in Egypt, though challenged by increasingly powerful non-Islamist parties.

"Egypt appears headed toward a much more competitive political environment in which Islamists will be increasingly challenged to maintain their electoral edge," the report states. That could be good news if it forces the Muslim Brotherhood to better consider the many Egyptians outside of its political base and could hold its political party, Freedom and Justice, more accountable.

President Mohamed Morsi, whose government has so turned on critics that a prominent TV satirist was recently arrested, could probably stand to feel a bit more constrained by electoral politics and by non-Islamist parties.

"We see public support for Islamists waning over time," Rand analyst Jeffrey Martini says in a video. "We're likely to see the Islamists remain the primary power brokers in Egypt, but again their support is waning over time. So we would suspect that in future years, there's going to be stiff political competition between Islamists and non-Islamists. And the non-Islamists will have a say in Egypt's future."

In democracy, though, you have to play in order to win, and a number of non-Islamist parties have threatened to boycott future elections. This has not proven a winning strategy for them in the past, and Rand's analysis finds that -- no surprise -- future boycotts will make it tougher for them to gain the increased support that Rand otherwise predicts.

"If non-Islamists choose to contest the next election -- right now they are choosing to boycott -- our analysis suggests they would pick up seats," Martini says, arguing that "the trend lines we identify actually offer hope for optimism that Egypt is headed" in the direction of "a competitive, multi-party state" that "will not be dominated by a single party or ideological bloc."

The report also confirms that non-Islamists do best in and around Cairo, which is of where both the Egyptian government and most reporters are based. This may help to explain the sense we can sometimes get from outside Egypt that Morsi and the Brotherhood are enormously unpopular; we mostly see the reaction from Cairo. Outside the capital, in places like Upper Egypt, the Islamists are still popular.