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 above.


Enter the votes in this box, then click the button below the box. (See the instructions below the button.)


INSTRUCTIONS: 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 (:) or period (.) then that many copies of the vote will be tallied. Example: 3: B C = D A means three votes rank candidate B on top, followed by C & D tied for second, 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." (As 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 like MAM have become practical.

MAM is also similar to Nicolaus Tideman's Ranked Pairs method. The two most important differences are that Ranked Pairs measures the size of each majority by subtracting the size of the opposing minority, and Ranked Pairs does not allow voters to rank candidates as equals (to express indifference or to employ a benevolent defensive strategy. Because of these differences, Ranked Pairs does not satisfy some criteria that MAM satisfies. (Note: Because of the two methods' similarity, some people use the name Ranked Pairs to mean MAM or to mean either method.)

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 voting 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 a candidate 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 to her 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 (or slates) 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 2008 U.S. presidential election if the Democrats nominated two candidates. (Hypothetical.)
22: Clinton Obama McCain
26: Obama Clinton McCain
5: Obama McCain Clinton
27: McCain Obama Clinton
20: McCain Clinton Obama
// If you look only at the top choice of each voter (in other words, plurality rule) there are 47 for John McCain, 31 for Barack Obama, 22 for Hillary Clinton, and McCain would win (seemingly by a landslide). MAM would allow parties to nominate more than one candidate (avoiding the expense of primary elections, and avoiding the risk of "putting all their eggs in one basket" by nominating only a loser when a different nominee would win). MAM elects Obama in this example since 53% rank Obama over McCain and 58% rank Obama over Clinton.

// Example #3: The 2000 U.S. presidential election if the Republicans nominated two candidates. (Hypothetical.)
47: Gore McCain Bush
4: McCain Gore Bush
16: McCain Bush Gore
33: Bush McCain Gore
// If you look only at the top choice of each voter (in other words, plurality rule) there are 47 for Al Gore, 33 for George W. Bush and 20 for John McCain, and Gore would win (seemingly by a landslide). MAM elects McCain in this example since 53% rank McCain over Gore and 67% rank McCain over Bush.

// Example #4: 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 the top choice of each voter (in other words, plurality rule) there are 43 for Bill Clinton, 38 for George H. W. Bush and 19 for Ross 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. Possibly true. But a professor at UCSD found evidence of a "rock/paper/scissors" cycle of majorities and that the majority for Bush over Clinton was the smallest of the three majorities, as in this example. 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.


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