Iraq is an artificial country. Like so many post-colonial states, Iraq was composed of borders drawn for the convenience of the colonial powers and not because of any shared qualities of the folks who live within them. Also, during the Mandatory period, the British used the tactic of installing a minority group (Sunni Arabs) as a ruling class over the majority (Shia Arabs). This followed from Ottoman practice, who also favored Sunni over Shia, as the Sunni followed their chosen branch of Islam and also respected the Ottoman sultans as caliphs (God’s leader on earth — kind of pope/emperors).
Latif al Ani. Yarmouk Housing Project Offices, 1962. © Artist and the Arab Image Foundation.
As importantly, Iraq is the heartland of Shia Islam. The main Shia shrine (Karbala) is in southern Iraq, where the last Shia caliph Hussein was killed in the year 680 CE. Most of the inhabited area of Iraq (the Tigris and Euphrates valleys) was also part of the Persian (Shia) Safavid empire from ~1300 to 1736.
Of course, you also have a substantial Kurdish population in the north and east of the country. The economic power of Iraq’s oilfields also exercises an influence.
If you view Iraq as a chain of city-states (which is probably the best way to get to a Swiss-esque result), you see that the population runs mostly along the Tigris, starting at Mosul (mixed Sunni and Kurdish) in the north, past Kirkuk(mixed Sunni/Kurdish), Bayji (lots of oil), Tikrit (the only big city that is really Sunni), Samarra (host to a major pilgrimage site), Baqubah (Iraq in miniature — Sunni, Shia, and Kurds), Baghdad, Karbala (major Shia pilgrimage site), Hillah (Shia religious center, Sadrist stronghold), Najaf (the Vatican and Oxford of Shia Islam), Nasiriyah (Shia), Basrah (Shia, the other big oil field), the Shatt-al-Arab marshes (Shia but genocide-d by Saddam in the 1990's), and the country’s tiny coastline and only port at Umm Qasr. West of the river valley is very…