MAMcalc tallies voters' orders of preference using the Maximize Affirmed Majorities voting method (MAM). For more information about democratic principles and MAM, click the link.
ENTER EACH VOTE ON A SEPARATE ROW OF THE INPUT BOX. (Use the "enter" key at the end of each line to begin the next row.) Each vote must be a list of some or all of the candidates, with left-to-right corresponding to "most-preferred to least-preferred." Separate the candidates with spaces or commas or tabs or greater-than signs (>). (Separate equally-preferred candidates with equal signs (=) or enclose them within parentheses.) As a shortcut to save voters' time, any candidates not listed in a vote will be treated as if the vote ranked them least-preferred. Optionally, to facilitate entry of demo scenarios, if the vote begins with a number followed by a colon (:) then that many copies of the vote will be tallied. Example: [3: B C = D A ] means three voters ranked candidate B on top, followed by C & D tied for second in these three votes, and A on the bottom.
NOTES: MAM is a refinement of the voting method tersely described in 1785 by the Marquis de Condorcet, who wrote "... take successively all the propositions that have a majority, beginning with those possessing the largest. As soon as these first propositions produce a result, it should be taken as the decision, without regard for the less probable decisions that follow." (Translated by Keith Michael Baker in "Condorcet: From Natural Philosophy to Social Mathematics" [1975], p.240, Chicago Univ. Press) Condorcet was ahead of his time, but now that computers can tally machine-readable ballots, "industrial strength" voting methods have become practical.
MAM is also similar to Nicolaus Tideman's Ranked Pairs method; the most important difference is that Tideman's Ranked Pairs measures the size of each majority by subtracting the size of the opposing minority. Because of this difference, Ranked Pairs does not satisfy some criteria that MAM satisfies.
Proofs at Steve Eppley's MAM website show that MAM satisfies the following desirable criteria of a good voting method: feasibility, anonymity, neutrality, strong Pareto, monotonicity, resolvability, reasonable determinism, homogeneity, Condorcet-consistency, top cycle, independence of clone alternatives (ICA), local independence of irrelevant alternatives (LIIA), minimal defense, non-drastic defense, truncation resistance, and immunity from majority complaints (IMC). (MAM is the only method that satisfies IMC.)
MAM also satisfies all but one of the criteria that Nobel prizewinner Kenneth Arrow proved cannot all be satisfied. Steve Eppley's presentation of Arrow's theorem calls the criteria prime directive, universal domain, unanimity, non-dictatorship, weak independence of irrelevant alternatives, ordinality, and choice consistency. MAM satisfies all of these except choice consistency (which is failed by most voting methods) but MAM may come closer than other methods since it satisfies ICA and LIIA.
The most important property of MAM is that candidates who want to win will have a strong incentive to be accountable on many more issues. To see this, suppose candidate X is considering what position to take on some issue. If s/he takes a position away from the voters' median position (or to be general, if s/he takes any position such that there exists another position that a majority think is better) the risk is that another candidate can take the median (majority-preferred) position and match his/her positions on the other issues, in which case a majority of the voters will tend to prefer the other candidate. The further from the median, the larger that majority will be. Because MAM pays attention to all majorities and their sizes, the further his/her position is from the median on any issue, the greater the risk of losing. Why would candidates who want to win take that risk? Contrast this with most other voting methods, where elections are determined by a small number of issues (abortion, taxes, etc.), those issues never get settled, candidates are unaccountable on most issues, and two large polarized parties develop.
EXAMPLES FOR TESTING. (Copy and paste into the input box.)
// Example #1: Given only 2 candidates, MAM is identical to majority rule:
53: Obama
47: McCain
// Example #2: The 1992 U.S. presidential election
35: Clinton Perot Bush
8: Clinton Bush Perot
13: Bush Clinton Perot
25: Bush Perot Clinton
14: Perot Bush Clinton
5: Perot Clinton Bush
If you look only at each voter's top choice (in other words, plurality rule) then there are 43 for Clinton, 38 for Bush and 19 for Perot, which match the actual percentages in 1992. Some people claim Perot was a spoiler, meaning Bush would have won if Perot had dropped out just before election day. Probably true, but a professor at UCSD found evidence of a "rock/paper/scissors" majority cycle and that the majority for Bush over Clinton was the smallest of the three majorities, as in the example above. Hence it was proper to elect Clinton, given the majority rule heuristic: The greater the number of people who think X is better than Y, the more likely it is that X is better than Y.