Condorcet method
Many proponents of instant-runoff voting (IRV) are attracted by the belief that if their first choice does not win, their vote will be given to their second choice; if their second choice does not win, their vote will be given to their third choice, etc. This sounds perfect, but it is not true for every voter with IRV. If someone voted for a strong candidate, and their 2nd and 3rd choices are eliminated before their first choice is eliminated, IRV gives their vote to their 4th choice candidate, not their 2nd choice. Condorcet voting takes all rankings into account simultaneously, but this makes it fail the later-no-harm criterion and the later-no-help criterion. With IRV, indicating a second choice will never hurt your first choice. With Condorcet voting, it is possible that indicating a second choice will cause your first choice to lose.