A Dutch book for group decision-making?

Distribute white and black hats in a dark room to a group of three rational players with each player having a fifty-fifty chance of receiving a hat of one colour or the other. Clearly, the chance that, as a result of this distribution, (A) "Not all hats are of the same colour" is 3/4. The light is switched on and all players can see the hats of the other persons, but not the colour of their own hats. Then no matter what combination of hats was assigned, at least one player will see two hats of the same colour. For her the chance that not all hats are of the same colour strictly depends on the... Mehr ...