With security improving, the toughest part of Saturday's Iraqi provincial elections might be educating voters about how to mark their ballots. An attempt to explain a truly complex process: 

The elections are for the provincial councils in 14 of the country's 18 provinces. The councils are powerful entities that will choose the governors, who control the police forces among other things. The Baghdad province council has 57 members. Others have as few as 26 members. In all, voters will choose between a total of 14,431 candidates to fill 440 seats. Candidates are grouped on lists, or slates, put together by political parties and coalitions of parties; there are more than 400 parties fielding candidates.

The current council was elected in 2005, using a different process than the one now being implemented.Then, people could only vote for the entire list and the individual candidates were barely known to the public, in part because of the security risks then. This time, an "open" list format will let voters choose a slate and an individual they support on that slate.

Having that many candidates makes printing ballots difficult. In Baghdad, with more than 2,400 candidates, a ballot with all their names could run to 60 pages. The solution: Only the slate names, not the candidate names, are spelled out on the large ballots. Voting for the slate is easy. You just tick the box next to the slate you want (which is shown with its electoral number, name and logo).

If you want to vote for a particular candidate on that slate, it's trickier. To the left of the slate names are columns of boxes, each with a number. There's a box for every seat on the council. In Baghdad, for example, there's a box next to a number 1, another for two, and up to 57.

You have to know your candidate's number on their slate's list so you can check the box by that number. To find that number, you have to scan a dazzling array of posters throughout the polling center that show the names of the candidates on each slate and what number they correspond to. For example, in Baghdad a list for for each slate would be on the wall showing the candidates numbered from one to 57. The voter has to find the number that corresponds to their preferred candidate. The voter then ticks the box with that number. Got it? To make this easier, some candidates are handing out palm cards that show exactly the numbers for the two boxes to tick for specific parties and people.

You can vote for a slate and leave all the candidate boxes blank. But if you vote for a candidate and don't mark the slate, your ballot won't count. This makes sense. Say you just chose box number 10 on the ballot, that means you're voting for the 10th person on some party list. Unless you marked the party list you're choosing from, it's impossible to tell which person you are referring to.

Tabulating the votes is also complicated. First, elections officials have to figure out how many council seats each slate wins. To do that, they look at how many votes were cast and divide that by the number of seats on the council. Say it turns out to equal 40,000 votes per seat, then a slate will get a seat for every 40,000 votes it wins. Or, roughly, if one slate wins a third of the votes, it will get a third of the seats on the council. The slate's seats are then divvied up based on who its biggest individual vote-getters were. If a slate wins just one seat, only its top vote getter will get to be on the council. If it wins two, the top two get seated. Complicating this a quota to help women win representation. Slates are supposed to make one third of their seats go to women (this originated with a clause that U.S. diplomats insisted be included in the Iraqi constitution).

In most cases, the first seat would go to the top vote getter, who would probably be a man. The second seat would also likely go to a man. The third seat would go to the slate's highest vote-winning woman, even if she won fewer votes than some of the remaining men. (It does not mean women will comprise one third of each council, since many slates will just get one or two seats and give them both to men). Some provinces also have seats set aside for minorities, such as Christians. Those will go to the highest vote-getters within those minority groups.

United Nations officials insist that such procedures have been used in other countries, including Germany, Macedonia, Spain and Bosnia, with success. But the system leaves open many scenarios that people here are just starting to figure out. For one, it tends to favor the established parties. People dazed by all the choices between parties with similar sounding names might just revert to the ones they're most familiar with. And many might just vote for a party without doing the extra math to choose their specific candidate.

On the other hand, a very popular candidate could win so many votes that he or she wins extra seats that the party can use to hand out to others. And, yes, as in other elections, voters will have their fingers dipped in ink--about 88,000 bottles have been imported from India--to limit them to one trip to the polls.