OLLP by itself is not guaranteed to make progress, but it is easy to prevent starvation via exerting more control at the preprocessing layer. The three papers to read related to this subject are:
(1) http://www.cs.umd.edu/~abadi/papers/determinism-vldb10.pdf
(2) http://www.cs.umd.edu/~abadi/papers/calvin-tods14.pdf
(3) http://www.cs.umd.edu/~abadi/papers/determinism-eval.pdf
Aborts due to OLLP are state-based aborts, so other shards fail via the conditional logic described in the blog post.