Here’s an example to illustrate. Suppose there are 3 alternatives, call them Left, Center and Right. (L, C and R.) Suppose the voters have the following preferences:

40% think L is best, C is second best, and R is worst.

8% think C is best, L is second best, and R is worst.

17% think C is best, R is second best, and L is worst.

35% think R is best, C is second best, and L is worst.

The winner will depend on the voting method. (1) If everyone is asked to express just their favorite and the winner is the alternative selected by the most voters, then L wins with 40% of the votes. (2) If the voters are asked to rank the alternatives and the rankings are tallied by the Single Transferable Vote method (a.k.a. Alternative Vote or Instant Runoff) then R wins with 52% (35% + 17%) of the vote. (3) If the Robert’s Rules agenda voting method is used–in which two of the alternatives are voted on, one gets eliminated by majority rule, and then the other is paired against the third alternative in another majority rule vote–then C wins, since 60% prefer C over L and 65% prefer C over R. (3) If the voters are asked to rank the alternatives and the votes are tallied using any “Condorcet” method–the best being the Maximize Affirmed Majorities method (MAM) in my opinion–then C wins, again because 60% prefer C over L and 65% prefer C over R.

MAM is a generalization of the majoritarian heuristic–the more people who think x is better than y, the more likely it is that x is better than y–to handle typical case where there are more then 2 alternatives. MAM works by first identifying all the majorities. (When there are 3 alternatives, there are 3 majorities. If there are 4 alternatives, there are 6 majorities, etc.) Since the number of votes that rank C over L (60%) exceeds the number that rank L over C (40%), there is a majority for C over L. Since the number of votes that rank C over R (65%) exceeds the number that rank R over C (35%), there is a majority for C over R. Since the number of votes that rank R over L (52%) exceeds the number that rank L over R (48%), there is a majority for R over L.

Then MAM constructs the order of finish by considering the majorities one at a time, from largest to smallest (again: the more people who think x is better than y, the more likely it is that x is better than y), adopting into the order of finish each majority preference that doesn’t conflict (like rock-paper-scissors) with the (larger) majorities’ preferences already adopted. Since the majority for C over R is largest (65%), MAM finds that C finishes ahead of R. Since the majority for C over L is second largest (60%), MAM then finds that C finishes ahead of L. The majority for R over L is third largest (52%) so MAM then finds that R finishes ahead of L. The order of finish is 1:C, 2:R, 3:L. The winner is C.

If MAM were used in public elections, candidates who want to win would have a strong incentive to take median positions on many issues. That’s because a candidate who doesn’t take the median position on some issue is risking that another candidate will take the same positions on other issues and the median position on that issue, so that a majority would tend to prefer that other candidate.

MAM has many attractive properties. Spoiling would be minimized; MAM probably comes as close as is possible to satisfying Kenneth Arrow’s “independence of irrelevant alternatives” criterion without violating any of Arrow’s other criteria. Because candidates who want to win would take similar (median) positions on many issues, voters would be free to rank the less corrupt candidates over the more corrupt, reducing corruption. Issues would tend to get settled (until the median changes significantly), enhancing stability and incrementalism. Because more issues would get settled, politicians would become accountable to the electorate on additional issues, reducing corruption further.

There’s another voting method that has properties similar to MAM’s but would be much easier for the voters. It asks each voter simply to pick one candidate. It’s called Voting for a Published Ranking (VPR). Prior to election day, each candidate would publish a preference order ranking of all the candidates. When a voter picks a candidate on election day, her vote would be treated as if it were the ranking published by her selected candidate. Then those (indirectly voted) rankings can be tallied by MAM. (This is similar to a shortcut available in Australian elections: A voter who wants to avoid the tedium of ranking all the candidates can instead select a party, in which case her vote will be treated as if it were the ranking published previously by the party.) Candidate L would have an incentive to rank C over R, since ranking R over C would be loudly criticized by L’s significant supporters. Similarly, R would have an incentive to rank C over L. Assuming neither L nor R is the favorite of a majority, C would win. As with MAM, candidates who want to win would tend to take median positions: candidates C1, C2, C3, etc. With VPR, good candidates wouldn’t need as much campaign money, since the way to win is to persuade other candidates to rank them over worse candidates, and it wouldn’t cost much to communicate with the other candidates. ]]>

Actually, the favourite from an arbitrary list drawn up by someone else…

]]>