A commonly proposed voting method is Instant Runoff Voting (IRV), where each voter ranks the candidates. The counting process eliminates candidates one at a time. Each round eliminates the candidate whom the fewest voters most prefer (among the remaining candidates). The process ends when only one candidate remains (or equivalently, when one candidate is most preferred by a majority of voters). One problem with this method is that it can eliminate a broadly acceptable candidate (everyone's second choice) and instead elect a very polarizing candidate (hated by almost half the voters).
I propose Inverted Instant-Runoff Voting, which is similar but inverts the elimination criterion: Each voter ranks the candidates. Each round eliminates the candidate whom the most voters least prefer. The process ends when only one candidate remains.
My intuition is that this method would tend to elect candidates with broader appeal who are less polarizing, which I think would better represent the electorate, but I haven't done any analysis. I'm curious how this method would compare to Approval Voting, which is persuasively advocated by The Center for Election Science.
This proposal is similar to, but simpler than, Coombs' method, which likewise eliminates the candidate whom the most voters least prefer, but also immediately elects the candidate whom the majority of voters most prefer, if that ever happens in any round. That extra criterion brings in some of the behavior I dislike about IRV.
One issue with having voters rank candidates is that an optical scan ballot needs O(n2) bubbles to express all possible permutations. This can be reduced to O(n) if we don't mind approximating the ranks into buckets. For example, the voter could put each candidate into one of four or five buckets, no matter how many candidates there are. Voters probably don't want to think about finer granularity than that anyway. When we count voters who rank a candidate as least preferred, we include voters who put the candidate in a tie for least preferred.
Another issue with ranking candidates is making the order of the bubbles intuitive. Using numbers is not intuitive: Does 1 mean most preferred (1st choice) or least preferred (lowest score)? It would be a shame for some voters to accidentally vote the exact opposite of their intention. Another idea is to use different sized bubbles. A larger bubble looks like a larger vote, which intuitively means more preferred. Filling no bubble for a candidate is the least preference (less than the smallest bubble).