The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point to the class of its closest neighbour in the feature space, that is C_n^{1nn}(x) = Y_{(1)}.
As the size of training data set approaches infinity, the one nearest neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data).