People often need to make collective decisions, whether at a state level for electing their leaders or adopting new laws, or at the level of an organization or informal group of people for deciding what to do collectively. There are different methods for making such decisions, and each method has its advantages and disadvantages. There is a branch of science, social choice theory, which systematically studies such voting systems and group decision methods. To do this, it studies the properties of these systems that are generally considered desirable, for example, that a system should be fair, i.e. should not favour any voter or any of the eligible alternatives. One of the surprising basic results of this theory is that there is a set of basic properties generally considered desirable such that no voting system has all of the desirable properties in the set. In other words, every system has some serious flaw. The overview of the basic results of social choice theory presented here mainly aims to address the question of what practical conclusions we can draw from the theory in order to improve our collective decisions.