Implementing an algorithm on part of our causally-interconnected physical environment requires three choices that are typically considered arbitrary, i.e. no single option is innately privileged without invoking an external observer perspective. First, how to delineate one set of local causal relationships from the environment. Second, within this delineation, which inputs and outputs to designate for attention. Third, what meaning to assign to particular states of the designated inputs and outputs. Having explained these types of arbitrariness, we assess their relevance for (...) algorithms from various computational theories of mind (CTM) seeking to account for phenomenal consciousness. Some CTM accounts can survive some of these arbitrariness challenges, but eventually each one examined faces a trilemma. Each is under pressure to dilute at least one of three important CTM desiderata: its causal relevance, its substrate neutrality, or its assignment discrimination (e.g. ability to avoid near-panpsychism). However, unlike previous research, we suggest the debate cannot be fully settled at the level of principle. Certain complex CTM algorithms may be salvageable, albeit not the algorithms specified to date. The paper specifies three areas of investigative work, as well as further theoretical avenues of research, which computationalists may wish to explore to escape the trilemma. (shrink)