Accelerating Loot Council

No loot system is perfect, as I'm sure you're aware, and the biggest problem with loot councils is how long it takes to hand out loot. When you get to items that have equal use to multiple classes, such as the axe you listed in your example, you need to factor in other things besides who gets the biggest upgrade out of it. Actually, you listed a perfect example with that axe. Shaman can use: Axes, Maces, and Fist Weapons while Rogues can use: Axes, Maces, Fist Weapons, Swords, and Daggers. Shaman can use daggers as well, but there is not a single dagger in the game that is slow enough for an enhancement shaman to even consider using so weapon availability for the classes in question needs to play into your decision as well. I would have given that weapon to the shaman because they can use it for both a main and off-hand weapon, where a combat rogue would only use it in his main-hand, as they prefer very fast weapons in the off-hand for Combat Potency procs.

Loot council puts more pressure on the officers on the council so they have to rely on the players to roll main/off on items they know are an upgrade for them.

I would say the council MUST put some sort of time limit on their decision. If they can't determine who it is the bigger upgrade for, just /random it. If it becomes too hard to determine who gets the most benefit from an item because the upgrade is pretty equal, there is nothing wrong with reverting to the good ole "/roll for it you two"

Personally, if I were on a loot council I would also keep track of each upgrade a person is assigned, and in the event of two people being close I would look at when they last received an item as a factor in the loot assignment too.

One thing that my own guild does to keep our Loot Council quick and efficient: Most of the decisions are made before the raid even starts.

Every member is required to post and maintain a 'loot list' to our guild forums - it should contain every item in the current tier of content of interest to that player, as well as a projected BIS setup.

The loot council convenes weekly, and uses those player generated lists, to generate a master list - every item that drops in the instance has a priority order - Axe of Awesome: Player 1 {Has it}, Player 2, Player 3, Player 4.

If Axe of Awesome drops, and Player 2 is in the raid, it's theirs. If they aren't, it goes to Player 3, and so on and so forth. Every item has a list like this, and the master list is updated weekly to keep one player from being at the top of every list or anything like that, and to make sure that gear is being evenly distributed.

This has the advantage of making the actual looting process when items drop extremely quick and efficient, while also giving the council plenty of time to make decisions, and players to argue their case when they happen to disagree. It also allows players to plan ahead a bit more - if I know I'm 5th in line for a Bloodvenom Blade, I might put some extra effort into chasing down Quel'delar. If I'm first, I might spend my time working on other upgrades instead.

The downside of course, is that this is significantly more time-intensive overall. It requires players to have a really good sense of their own class mechanics and future gear plan. It requires the officers/loot council (our council is all non-officers), to spend a great deal of time managing and updating the master list. And it requires everyone involved to make a commitment to the system working. But it does make the raids go much faster, and makes the actual process of handling loot very smooth.