The waitress asked if they would ALL like dessert. If the first logician did NOT want dessert, then they could safely answer "no", because then it would not be the case that ALL of the logicians want dessert. Since they do not answer no, we can assume they do want dessert. The same follows for the second logician. The third (who also wants dessert) has heard their colleagues answer, and knows that if either of them did not want dessert they would have answered no, and can therefore now answer "yes, we would all like dessert".

First of all, the joke makes no sense if you put a logistician instead of logician. Second, if you ask one person a question related to the opinions of all others, logically they can't answer yes or no, the only possible answer is "I don't know." Only when you reach the last person you have a chance of giving a definite answer.

Note the first logicians have to answer "I don't know" even if they don't wan't it, otherwise their statement becomes untrue.