While I still try to figure out just what kind of list was used for the elections to Iraq’s recent provincial elections, I finally went looking for a sample ballot. It was not hard to find. (See p. 9 of the “Polling and Counting Procedures Annex” linked at the bottom of one of the electoral commission pages.)
Here is an image of the sample ballot (and you might want to see the larger image in a new window.)
With the obvious caveat that I don’t read Arabic, this ballot design certainly appears typical of preferential list ballots elsewhere. The section on the left would appear to be for marking a candidate’s number, for voters who choose to cast a preference vote. However, because each list would repeat the same set of numbers for its candidates, the ballot is validly marked only if the voter also checks a party (or “political entity,” in the terminology of the electoral law) in one of the other three columns.
(On the non-validity of ballots with an otherwise valid candidate vote but no list vote, see page 30 of the English language PDF on “Polling and Counting Procedures,” at the same web page.)
Of course, this still does not resolve how preference votes are counted at the intraparty level: whether the lists are unranked other than by preference votes (an open list) or whether they are ranked and candidates move up the ranking only if they obtain a certain threshold of preference votes (a so-called felxible list). Some things I have read give me the impression it was the latter. I am still trying to find out.
Annex 12 of the first-noted PDF might contain some clues. It appears to show how one calculates a formula for determining a candidate’s final ranking, which would imply flexible list. Someone who reads Arabic would be of great help here!