I think this paper does a reasonably good job of promoting its new objective function. This sort of objective function has been used in HMM's before, hasn't it? I thought the Viterbi algorithm was an improvement on using this sort of greedy algorithm for HMM evaluation. The motivations for C1, particularly for CRF's, seemed somewhat obscure. I think C1 is a good alternatice objective function, depending on what the actual task to be accomplished is.