LessWrong's Dutch book arguments challenge halfing positions in Sleeping Beauty

The Sleeping Beauty problem remains a litmus test for anthropic reasoning and decision theory. In a new LessWrong post, jessicata constructs Dutch books against both single-halfing and double-halfing positions under causal decision theory (CDT). For single-halfers, a Sunday bet on the coin flip combined with a Monday bet after learning it's Monday yields a sure loss if the agent's conditional probabilities are as the theory requires. For double-halfers, a more elaborate two-bet structure — involving a conditional bet on Tuesday — also forces a guaranteed loss. In contrast, thirders (who assign P(Heads)=1/3 upon waking) avoid such Dutch books because their betting odds remain consistent across all potential awakenings. The argument generalizes to the related anthropic principles: SSA (self-sampling assumption) maps to single-halfing, SIA (self-indication assumption) to thirding, and FNC (fully non-indexical conditioning) to double-halfing under controlled scenarios. The author assumes a controlled setup where Beauty's information is identical across awakenings, a charitable interpretation for double-halfing. The analysis focuses on CDT, noting that EDT agents may fare differently. This work provides clear decision-theoretic grounding for the 1/3 answer, challenging proponents of halfing positions to reconcile their probabilities with Dutch book vulnerability.