Robustness as a Ground for the Failure of No-Choice Indifference

An option can be available to an agent and available only just: it survives in the circumstance she occupies and fails under small departures from it. This paper represents that difference by assigning each option the set of circumstances across which it remains available, and defines erosion as the contraction of that set with loss of interiority at the agent's actual circumstance while the option survives there. Domination is the central instance, and adaptive preference a second on one reading. The negative result is that erosion is invisible to every transitive freedom ranking satisfying indifference between no-choice situations and semi-independence, on any individuation that gives each available option one token, so refining options by their modal profile does not help. The proof is direct and needs neither monotonicity nor finiteness. The positive result characterizes the tag-anonymous rankings that keep monotonicity and semi-independence and register erosion: they are exactly those that strictly prefer a robustly held option to a precarious one in every context a situation can produce. The same dominance condition imposed on every subset is strictly stronger than registration requires. Under domination, two single options may be alike in value and distinctiveness and still differ in freedom, so this ground for rejecting no-choice indifference is independent of the preference-based and diversity-based grounds already in the literature.