What Makes Markets Allocationally Efficient?

What determines the allocative efficiency of markets? Why are double auctions, even with untrained human traders, allocationally efficient? We provide a simple explanation for these complex phenomena by showing how externally observable rules that define a market cause high allocative efficiency when individuals remain within the confines of these rules. We also show how the oft-ignored shape of extramarginal demand and supply affects efficiency by influencing the inverse relationship between the magnitude of efficiency loss and its probability.