A simple interpretation of undirected edges in essential graphs is wrong

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Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs, however. In particular, experts and non-experts both have difficulty quantifying the likelihood of uncertain causal arrows being pointed in one direction or another. A simple interpretation of undirected edges treats them as having equal odds of being oriented in either direction, but I show in this paper that any agent interpreting undirected edges in this simple way can be Dutch booked. In other words, I can construct a set of bets that appears rational for the users of the simple interpretation to accept, but for which in all possible outcomes they lose money. I put forward another interpretation, prove this interpretation leads to a bet-taking strategy that is sufficient to avoid all Dutch books of this kind, and conjecture that this strategy is also necessary for avoiding such Dutch books. Finally, I demonstrate that undirected edges that are more likely to be oriented in one direction than the other are common in graphs with 4 nodes and 3 edges.

Original languageEnglish (US)
Article numbere0249415
JournalPloS one
Issue number4 April
StatePublished - Apr 2021

Bibliographical note

Publisher Copyright:
© 2021 Erich Kummerfeld. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


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