Condorcet voting methods avoid the paradoxes of voting theory

Democratically choosing a single preference from more than two candidate options is not a straightforward matter. In fact, voting theory has established a number of paradoxes which assert seemingly innocuous attributes to be incompatible. One of the most desirable attributes - independence of irrelevant alternatives - is proven by Arrow to be incompatible (in a worst-case sense) with nominal fairness constraint. Another theorem states that all voting systems will have opportunities for a voter to improve their outcome by voting contrary to their true preferences. What we show in this work is that Condorcet methods, which uniquely satisfy the independent of irrelevant alternatives property whenever possible, actually avoids these paradoxes both in practice (based on real data) and in theory (in a probabilistic sense).