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AlexMennen comments on Summary of the first SoCal FAI Workshop - Less Wrong Discussion
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Comments (8)
The basis vectors do not in general correspond to a set of propositions exactly one of which is true, but merely a set of propositions with some set of logical constraints (e.g. if x, y, and z are all logically equivalent, then the assignment is coherent iff x=y=z. The situation where the assignment is coherent iff x+y+z=1 was just an example).
This is correct. My response was thinking he was saying project onto the polytope, (which is not always a simplex), which is a good suggestion, but doesn't work in terms of local moves.
This modified simplex, where some coordinates are constrained to be equal, shouldn't be impossible to project on, but it does seem like you have larger problems. Ah well.
But I figure there should be some approach that works spiritually with whatever you're trying to do (which is not 100% clear to me) just because there are so many ways to project vectors, or sampled versions of those vectors.
What specifically do you hope to gain from your probability distribution over 1/2 probability on all sentences?