Dave, Doug, and Cindy want to divide a cake fairly using the lone chooser method. After drawing straws, Cindy gets to be the chooser and Dave has to make the first division of the cake. Assuming that each of them plays the game correctly, which of the following statements is true?
◦ Dave, Doug, and Cindy may each believe that their share is worth more than 1/3 of the cake.
◦ Dave will believe that the share he ends up with is worth 1/3 of the cake although he may also believe that the shares that Doug and Cindy end up with are worth more than his share.
◦ Doug may believe that the share he ends up with is worth more than 1/3 of the cake although he may also believe that the shares that Dave and Cindy end up with are worth more than his share.
◦ Cindy may believe that the share she ends up with is worth more than 1/3 of the cake and may also believe that the share that Dave ends up with is worth more than her share.
◦ none of these
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