Can someone help me with this problem? I think that it is something with the Dirichlet.
Suppose that a group of voters is to elect a mayor. There are $a$ voters that intend to vote for candidate A, $b$ voters for candidate B and $c$ voters for candidate C, where $0 <a <b <c$.
During the pre-election silence it is not allowed to meet with more than 2 voters to discuss candidates for mayor. In a meeting of 2 voters from different "camps" both will change their beliefs and vote for the only non-present camp. (So for example if voters for candidates $A$ and $B$ meet, they will leave the meeting wanting to vote for $C$)
If subsequently one of them would meet with another voter who voted for $A$ these two after the conversation would vote for candidate C.
The question is whether it can happen that all of $a + b + c$ voters will become convinced to vote for the same candidate?