[math-fun] What to conclude from physics experiment / voting

(True story, but abstracted.) There were three candidate scientific hypotheses named B, F, and H. It was possible to perform a pairwise comparison experiment to decide which hypothesis worked better to explain that experiment, BUT the situation was (somewhat strangely, but this was the situation) that you only got information about TWO among the candidates, and it decided which two, not you. Anyhow, after laboriously performing 19+26+9+8+22+10=94 experiments, the results were BH=19, HB=26, BF=9, FB=8, FH=22, HF=10 meaning B won 19 of the 45 H-versus-B comparisons, etc. So... which hypothesis is the right one, do you think, and what odds would you take in a bet?