Paper Scissors Stone Politics

In order to do away with the 'unfairness' of Western Democracy ie. majority rules, why don't we institute a system of Paper Scissors Stone Politics. It is possible to play this with more than two people...eg. 4 people playing it is constantly tied if all three possibilities come up...However, if 3 people display Stone and the other person Paper....Paper beats all Stones and that person wins. This could encompass the whole of the Franchise, with every decision needing made being played out by the whole voting population in a huge game of P/S/S. This would mean that the eventual winner would have the choice of which particular line the policy would take, thus meaning that even minority groups could see their policies come to fruition, and allow all voices to be heard. Obviously in a country with a population of around 50 million, 49,999,999 people could all support the death penalty (for example), yet the person who opposes it could, feasibly...although it is unlikely, win the P/S/S match and their policy would be implemented. Simple and Fair. People who have no interest in a particular policy need not take part in the match, so only those with strong feelings for or against would compete for the chance to shape their country's policies.