Your opponent would offer the bet only if (2p-1)10>0, so if p>5>p, it seems like you should have a horse race But this can't actually happen To see this let's put some structure on learning Remeber bayes Rule P(B|4)=P(B∩AP(A) This is always the key to understanding belief formations So more information structure The unconditional probability of a lemon squirting is p If the lemon is squirting, then every person receives a positive signal with probability Z If the lemon is not squirting then every person recieves a positive signal withYour opponent would offer the bet only if (2p’-1)100, so if p’.5p, it seems like you should have a horse race. But this can’t actually happen. To see this, let’s put some structure on learning. Remeber Bayes’ Rule PB|A  PB  A/PA This is always the key to understanding belief formations. So more information structure. The unconditional probability of a lemon squirting is p. If the lemon is squirting, then every person receives a positive signal with probability z. If the lemon is not squirting then every person recieves a positive signal with