4/28/04: Tom Ruen here. I edited the IRV page today, added a second for special cases including rules to break ties. I'm not sure if it is appropriate for the level of article, but it definitely was a vital point missing from the existing article. That is, tie-breaking consideration is vital, but I also included optional rules for quickly eliminating many weak candidates on the first round. Some may object to this approach, although in reality it is very difficult for different elimination rules to affect the winner.  You can always imagine examples where a weak first round candidate wins, but usually it takes core support AND Compromise appeal to win and few candidates survive merely on compromise appeal.  Examples include:  Round 1) A=38%, BD=29%, CD=16%, D=9%, ED=8% Round 2) A=38%, BD=29%, D=17%, CD=16% Round 3) A=38%, D=33%, BD=29% Round 4) D=62%, A=38%   Here a 4th place, 9% supported candidate wins IRV on a cascade of transfer votes, always avoiding last place.  Imagined elections like this are actually the biggest fear from people happy with plurality, that some voters can offer 2,3,4,5 votes to affect the winner while others only get 1 vote.  The reality is that IRV retains the power of the two-party system to thrive because when there are 3 strong parties, voters can't safely vote for a favorite if that favorite isn't also likely to be ranked highly on votes supporting the candidate they hope to eliminate.  First round rules that immediately eliminate a bunch of weak candidates at once help reduce fears that IRV helps weak parties.  -  