When Lebanon was released from French mandate after World War II and given its independence, the Lebanese wanted their constitution to remain the same. This required inter alia that the President always be a Maronite (Catholic), the Prime Minister, a Muslim, and the Speaker of the House, an Orthodox, so effectively distributing secular power between the three major religious groups of the country.
A proposal in the case of Northern Ireland is that Catholics and Protestants would be registered on separate rolls. An elector who is neither has half a vote on the Catholic roll and half on the Protestant role. The electors of each roll elect their own MPs by proportional representation. Alternatively electors could remain as now on one common electoral roll and the MPs could be classified after the election as Catholic or Protestant or Catholic/Protestant, on the basis of opinion surveys of a sample of the electors who voted for them. In addition to the above normal MPs, there is a small number of "Arbitrator MPs" (AMPs). Each AMP is appointed by one out of a set of governments of foreign countries which have been accepted as impartial both by a majority of Catholic MPs and by a majority of Protestant MPs. AMPs occupy seats in the parliament, speak in dates, attend committees, and so on, but do not have a vote except in a defined situation of deadlock.