It is said that in Islam, collective affairs are to be decided through the principle of consultation and the majority opinion is to be imposed and accepted. My question is: What guarantee do we have that the majority has taken the correct decision?

When it is said that all differences of opinion in an Islamic state shall be settled by a majority vote, it does not mean at all that the opinion which is ultimately accepted shall necessarily be correct. It only means that just to run the affairs an opinion has been enforced until the time a stronger opinion emerges to take its place. This is only a way of settling differences of opinions and is no criterion for the correctness of a viewpoint. Only reasons and arguments decide what is right or wrong, and a majority or a minority opinion has no say in this regard.