A note on the problem statement: You should probably make it more explicit that mixed strategies are a bad idea here (due to the 0-if-disagreement clause). I spent a bit wondering why you restricted to pure strategies and didn’t notice it until I actually attempted to calculate an optimal strategy under both assumptions. (FWIW, graphing things, it seems that indeed, if you assume both scenarios are equally likely, pure “nay” is best, and if you assume 9 deciders is 90% likely, pure “yea” is best.)
A note on the problem statement: You should probably make it more explicit that mixed strategies are a bad idea here (due to the 0-if-disagreement clause). I spent a bit wondering why you restricted to pure strategies and didn’t notice it until I actually attempted to calculate an optimal strategy under both assumptions. (FWIW, graphing things, it seems that indeed, if you assume both scenarios are equally likely, pure “nay” is best, and if you assume 9 deciders is 90% likely, pure “yea” is best.)