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When loot drops in a fixed price system, raid members are asked in order of their DKP whether they want the item. The person with the highest DKP score who wants the item gets it, and pays a fixed DKP price.
Item Price Edit
One central problem of this type of loot system are the item prices. Some guilds maintain large item lists with prices on their web site, others use special UI mods which calculate an item value for each object. Both methods can easily become the subject of heated debates. These debates and the disenchanting issue below both have the same reason: The central dictum of a fixed price system is that each item has a well-defined and unchangeable value. The subjective item values though can differ greatly from player to player and over time. There is no possible solution for this conflict inside the system.
Since a fixed item price is nearly always wrong anyways, the easiest solution is to use just one single price for all items.
If all raid members feel that the fixed price is too high for the item, it must be disenchanted. If it's not, but instead offered at a discount or free roll, all the problems (primarily collusion) are introduced back into the system (usually along with heated debate on what's an upgrade or not).
Unfortunately, disenchanting is no good solution, because the guild as a whole profits if the item is taken by somebody as a minor upgrade. It's also generally bad for player morale to see a "I might use it for farming/my off-spec/for PvP" item getting disenchanted under their noses. It's equally unsatisfying to pay full price, particularly for hybrid classes who may have to collect gear for more than one role, or for tanks who have to acquire several sets of resist gear. Enchanting mats are nice to have, but usually are available in large enough quantities from class items which really nobody had any use for.