[sampo]

> the theorem states that if there are more than 2 candidates, then there is no voting system that has all 4 properties above.

There is no rank order voting system that has all those properties. (Rank order means, that the voter puts the candidates in the the order of preference: 1., 2., 3. etc.)

But there are other voting systems, e.g. a system where you give each candidate points between 1-100 or whatever, and you can give the same amount of points to several candidates if you want.