Rank Ballot Election Calculator
by Kevin Venzke [Home]

A calculator to compare a lot of methods at once, without resolution details.

Method list
  • RMPA and RMPFPP, meaning River Majority Pass Approval or FPP: Ideas of mine. We choose a metric (approval or FPP respectively), and apply Heitzig's River algorithm using only the full pairwise majorities, using the chosen metric as the defeat strength. In practice this means going down the list of candidates in metric order and not worrying about defeat strength as such. We just act on each of the candidate's pairwise majorities. Start out each candidate in their own "bin." For each pairwise majority you encounter, take every candidate from the pairwise loser's original bin (which may be no one, or may even include the pairwise winner) and move them (if anyone) to the bin that the pairwise winner is currently in. Once we've gone through all pairwise majorities, elect the candidate in whose bin the metric leader ultimately ended up (possibly their own bin, of course). RMPA and RMPFPP both satisfy Plurality and minimal defense and so could be included in the /misc calculator. RMPA is very similar to MDDA, but fixes its Plurality problem while losing Favorite Betrayal compliance.
    These methods were formerly called on this page "Majority Rule Approval" and "Majority Rule FPP."
  • Top-Two Runoff: Hold a one-on-one election between the two candidates who received the most first preferences in a first round. When conducted as a single round of voting (an instant runoff) this is better called the "contingent vote."
  • Schulze: Markus Schulze's method in which one elects the candidate whose strongest beatpath to each other candidate is at least as strong as each respective path back. It's provided with WV as the measure of defeat strength.
  • SV: Eivind Stensholt's "Smallest Volume" method pursues the same goal as BPW, and has similar monotonicity concerns. And again it's a three-candidate method that I attempt to extend. In the absence of a Condorcet winner, we elect a candidate with a certain lowest score. If for some candidate A, B is the candidate with the most first preferences who beats or ties A, and C is the candidate with the most first preferences whom A beats or ties pairwise, then A's score is (50% - C's first preference vote share) divided by (50% - B's first preference vote share). Any Condorcet Loser (who would have no candidate C) is precluded from winning. Experimentally I don't find SV (or my generalization) to be better than BPW with respect to strategy incentives. In some ways it seems worse. SV is just more monotone. But I should note that SV is motivated by a geometric argument that I have not considered when evaluating it.
  • TACC: "Total Approval Chain Climbing," a 2005 method by Jobst Heitzig. "Chain climbing" is a mechanism popularized by him and also Forest Simmons. Start with an empty set. Starting (in this case) with the least approved candidate, evaluate whether the candidate pairwise beats all candidates currently in the set. If so, add them to the set. Elect the last candidate who can be added. In this way the TACC winner should never be "covered" by another candidate.

  • Use your own method(s)
    See here for examples of what to enter below. Note ⚠️ you could hang or crash your browser here!

    Enter your ballots like this, one per line:
    456: Alice>Bob>Carl=Debra
    or equivalently to the above:
    456: Alice>Bob
    The number represents the size of the voting bloc. Decimals are OK. The size can also be left off and it will then be randomized.
    Note that this calculator does allow equal ranking above the bottom, but not every method is supported in this case. With some methods, equal ranking is allowed only below the top rank.
    Candidate names can contain spaces. Each candidate in the list should be separated by > or =. Pipes (i.e. |) and any series of > will be interpreted as single >s. Not every candidate needs to be listed; candidates present on the ballots but missing from one faction's ranking will be interpreted as ranked tied for last, below any explicitly ranked candidates.

    Click submit to generate an analysis.

    Enter the ballots for an election:

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