I just finished reading several papers by Malin Björnsdotter describing her randomly averaged searchlight method and am very excited to try it.
In brief, instead of doing an exhaustive searchlight analysis (a searchlight centered on every voxel), searchlights are positioned randomly, such that each voxel is in just one searchlight. The parcellation is repeated, so that each voxel is included in several different searchlights (it might be in the center of one, touching the center of another, in the edge of a third, etc.). You then create the final information map by assigning each voxel the average of all the searchlights it's a part of - not just the single searchlight it was the center of as in normal searchlight analysis.
Malin introduces the technique as a way to speed searchlight analysis: far fewer searchlights need to be calculated to achieve good results. That's certainly a benefit, as searchlight analyses can take a ridiculous amount of time, even distributed across a cluster.
But I am particularly keen on the idea of assigning each voxel the average accuracy of all the searchlights it's a part of, rather than the single centered searchlight accuracy. In this and other papers Malin shows that the Monte Carlo version of searchlight analysis produces more accurate maps than standard searchlighting, speculating that the averaging reduces some of the spurious results. I find this quite plausible: a single searchlight may be quite accurate at random; the chance high accuracy will be "diluted" by averaging with the overlapping searchlights. Averaging won't eliminate all distortions in the results of course, but might help mitigate some of the extremes.
Malin points out that averaged information maps can be constructed after doing an exhaustive searchlight mapping, not just a Monte Carlo one. I will certainly be calculating some of these with my datasets in the near future.
Björnsdotter M, Rylander K, & Wessberg J (2011). A Monte Carlo method for locally multivariate brain mapping. NeuroImage, 56 (2), 508-16 PMID: 20674749