DC Exclusive: Table of Election Method Properties and Criteria

Table of Election Method Properties and Criteria by Michael Ossipoff

Names of voting systems head the columns and names (or their abbreviations) of criteria head the rows. Compliances are shown by green. Failures are shown by red.

Explanation: Table of Election Method Properties and Criteria


by Michael Ossipoff

December 24, 2012

The table compares voting systems by some precisely-defined criteria, but also by some loosely-defined criteria. The precisely-defined ones have already been defined in previous articles in this Properties article series. I’ll briefly summarize their definitions here.  I’ll also explain what I mean by the loosely-defined criteria. The definitions below are brief summaries, not precise definitions.

Some method-name abbreviations

ICT: Improved-Condorcet-Top

SICT: Symmetrical ICT

MJ: Majority-Judgment

IRV: Instant-Runoff

Criteria defined in previous articles:

FBC:  Favorite-Betrayal Criterion. There should never be any strategic need, incentive or reason to vote someone over your favorite.

CD:  Chicken-Dilemma Criterion.  The method avoids the chicken dilemma.

LNHe:  Later No Help. You needn’t vote for additional candidates to help candidates you’re already voting for.

ZLNHe:  0-info LNHe. In a 0-info election, voting for one or more of a set of candidates shouldn’t decrease the probability that one of them will win.

S. ZLNHe:  Strong ZLNHe. As above, but, in a 0-info election, voting for one or more of a set of candidates should increase the probability that one of them will win. The justification of this criterion was explained in a previous article. It’s ZLNHe, but more so.

MMC:  Mutual Majority Criterion. A sincere voting majority who prefer a set of candidates to the others should elect one of that set.

Usu. MMC:  Usually passes MMC. For pairwise-count methods, that means that it passes MMC unless there is a cycle among the majority-preferred candidates.

CC:  Condorcet Criterion. If there are one or more unbeaten candidates, then one of them should win. In a previous article, I included a general CC definition.

LNHa:  Later No Harm. Voting for additional candidates, not over already-voted-for candidates, and below the already voted-for candidates if the balloting allows it, should never prevent an already-voted-for candidate from winning.

Participation:  Adding a new ballot that votes X over Y shouldn’t change the winner from X to Y.

Consistency:  If voting region is divided into parts 1 and 2, and if counting the ballots in part 1 would elect Smith, and counting the ballots in part 2 would elect Smith, then counting all the ballots together shouldn’t elect Jones instead of Smith.

M.A.U.T.:  Mono-Add-Unique-Top. Adding a new ballot that votes X over everyone else shouldn’t make X lose.

M.A.T.:  Mono-Add-Top. Adding a new ballot that votes X at top shouldn’t make X lose.  (M.A.U.T and M.A.T. are more-easily-passed versions of Participation. Because they’re easier to pass, they’re worse to fail.)

Mono R.: Mono Raise. Raising a candidate in your ballot shouldn’t make him/her lose.

IIAC:  Independence from Irrelevant Alternatives Criterion. Removing a losing candidate from the ballots and from the election, and then recounting the ballots, shouldn’t change the winner.

Smith:  Smith Criterion. If there’s a set of candidate each of whom pairwise-beat everyone outside that set, then the winner should come from that set.

CL:  Condorcet Loser. Never elect a candidate who is pairwise-beaten by all of the other candidates.  Note: Failing CL sounds bad, but, for a non-complying method to fail CL, the winner would have to be a peculiarly popular Condorcet loser. Additionally, of course would happen only very rarely, if ever.

Clone-Ind.: Clone Independence. Adding a candidate identical to existing ones shouldn’t change the matter of whether the winner is one of those identical candidates.  This criterion is more fully-defined in a previous article.

Definitions of loosely-defined criteria

Easy:  Loosely-defined, the count should be as easy, having as little count-labor, as that of Approval, or at least Score.  Plurality, Approval, Score, and Majority-Judgment all pass.

Enactable:  Possessing an unarbitrary, natural, obvious, and simple definition.  Doesn’t fail any criteria that Plurality doesn’t fail, and thus is in no way worse than Plurality, and is only a clear improvement over Plurality. As intrinsically easy to enact as Approval or Score would be. Plurality, Approval, and Score pass.

Non-Cplx:  The count isn’t as complex as a Condorcet count. The count doesn’t entail a kind of counting significantly different from, or more difficult or complicated than, that of Plurality—even if there is more counting to do, as in the case of IRV. Plurality, Approval, Score, Majority-Judgment, and IRV pass.

Kn u/a:  Known u/a strategy. The traditional unimproved Condorcet methods, represented here by Beatpath, are distinguished by generally unknown u/a strategy.

Soc Opt:  Social Optimization.  Approval and Score uniquely possess social optimizations.

Comments on the Table

FBC-compliance is essential with our current electorate. Most voters have been convinced by the media to believe 1) That the corrupt Democrat is acceptable; and 2) That the winner will always be a Democrat or a Republican; and 3) That the election of the Republican would be an unprecedented and terrible disaster (though it’s been happening periodically).

People who prefer the Democrat to the Republican typically regard the Republican as unacceptable.  To anyone who believes the above-specified beliefs, when the method in use is Plurality, IRV, Beatpath, or other FBC-failing method, the optimal strategy requires voting the Democrat over everyone else—which often amounts to burying one’s favorite.

Favorite-burial makes nonsense of the election-result, with obvious adverse societal consequences. Though Beatpath meets CC, CL, Smith, and MMC, its failure of FBC and CD would tend to strategically distort voters’ preferences so much as to eliminate the benefit of meeting CC, CL, Smith and MMC. Because of the need for FBC, and the importance of Easy and Enactable, the only voting system proposals that can be recommended for our current electorate are Approval and Score.

I emphasize that Approval and Score are the only alternative methods proposed that don’t fail criteria met by Plurality. They’re the only methods that can’t be claimed to, in some way, be worse than Plurality. IRV, due to its FBC-failure, is entirely unacceptable and unsuitable for our current electorate. IRV can’t be recommended for our current electorate. But the Greens (GPUS) propose IRV as the single-winner voting system, for the government proposed in their platform.

Of course, for the Greens’ platform to take effect, the Greens would have to be elected to the presidency and most of Congress. Any electorate who could accomplish that, using Plurality, would be an electorate that is competent enough to make good use of IRV. It would be an electorate that wouldn’t believe the media-promotion regarding what is acceptable and what is winnable. It would be an electorate that wouldn’t be as vulnerable to FBC-failure.

So, as I said, such an electorate could make good use of IRV, and IRV’s FBC-failure wouldn’t be the problem that it would be with our current electorate. So, if the Greens enacted IRV, after being elected to the presidency and most of Congress, IRV would be okay. Of course there’d be opportunity to get a better method, such as Approval or Score, via improved powers of initiative or referendum.

I emphasize that, even though, with that electorate, FBC isn’t as necessary it would still remain very desirable. Approval or Score would still be considerably better than IRV, even with that better electorate.

Why bring this up? I don’t want to discourage people working for good voting-system reform. But few if any people seem to be doing that work. I guess that even local voting system initiatives are difficult and expensive. And state initiatives are probably prohibitively expensive and difficult.  And genuine improvement depends on widespread improvement at least at the state level.

I encourage and support anyone who is, or intends to be, working to enact Approval or Score, but it’s likely that the only way that voting-system reform will happen will be by electing to office a party that wants to do voting-system reform. And it’s much easier to vote for such a party in the elections that we already have, than to somehow organize and finance a state ballot initiative for voting-system reform.  Of course, with the election of such a party, voting-system reform would be one part of a larger package of reforms and improvements.

Thank you for your continued interest in voting systems.  Please take a look at some of my other articles on Democracy Chronicles.  

  • Adrian Tawfik

    A highly original product here for all election method reform supporters. Congratulations to Mr. Ossipoff on a fine finished product.

  • http://VoteFair.org Richard Fobes

    I like that the article writer has presented a comparison of some methods according to different criteria.

    However, be careful not to fall into the trap set by this comparison. It implies that the NUMBER of criteria that a method passes (rather than fails) is important. What is even more important to consider is HOW OFTEN a method passes or fails each criterion.

    Also, some of the criteria are highly subjective, such as “enactable.” This “criterion” is just the article-writer’s personal opinion, and it does not match the opinions of other election-method experts.

    Finally, the chart does not include my favorite single-winner method, which is the Condorcet-Kemeny method.

    In spite of the article’s weaknesses, this is a good introduction to the idea that there is no obviously “best” voting method. Every method has both advantages and disadvantages.

    • Anonymous

      Thanks the comments.

      Richard said:

      However, be careful not to fall into the trap set by this comparison. It implies that the NUMBER of criteria that a method passes (rather than fails) is important.


      What I wanted to emphasize was that certain criteria are particularly important. In my previous articles of the Properties series, I defined criteria, and told why I claim that some are important.

      Richard continued:

      What is even more important to consider is HOW OFTEN a method passes or fails each criterion.


      I tried to include that consideration, with “Usu MMC”, standing for “Usually Mutual Majority Criterion”. Mutual Majority is a desirable criterion, and it would be good to always comply with it, but, it’s worth something merely to comply with it only when there isn’t a collective-preference cycle among the majority-referrred candidates.

      But I don’t think that “sometimes” or “usually” helps much, when a method fails FBC. As I’ve said, most voters in our country have been convinced by the media 1)That either the Democrat or the Republican is acceptable, in spite of corruption; 2) That the winner will always be the Democrat or the Republican; and 3) that (if you prefer Dem to
      Repub) the election of a Republican would be an unprecedented, unacceptable, and terrible disasster.

      Given those media-propagated beliefs, and an FBC-failing method, your best strategy, if you prefer Dem to Repub, is to vote Dem over everyone else. That’s true in Beatpath, Plurality, IRV. And it’s true in Condorcet-Kemeny.

      And it’s true even if the FBC-failure won’t happen often. If you know that the winner will be Dem or Repub, and it is all-important that it not be Repub, then all that matters is making Dem win instead of Repub, whatever that takes. And it takes voting Dem over everyone else (even over your favorite).

      Some-of-the-time criterion-failure. All-of-the-time strategy-need.

      Nothing distorts public preferences as much as strategic need to bury your favorite. The societal results are miserable, as can be observed all around us.

      Richard continued:

      Also, some of the criteria are highly subjective, such as “enactable.” This “criterion” is just the article-writer’s personal opinion, and it does not match the opinions of other election-method experts.


      I stated what makes a method qualify for “Enactable”: Great simplicity of definition and count, and not failing criteria that Plurallity passes. By “great simplicity”, I mean simplicity equal to that of Plurality, and the two similiarly simple methods, Approval and Score.

      Do other voting-system reform advocates say that complicated methods that fail criteria met by Plurality are equally enactable?

      Fine, let’s discuss that.

      Richard continued:

      Finally, the chart does not include my favorite single-winner method, which is the Condorcet-Kemeny method.


      My earlier version of the chart included Kemeny, but, for simplicity, I left it out, because it doesn’t have many advocates. Beatpath is by far the most popular traditional unimproved Condorcet (TUC) method, and so I decided to let the popular Beatpath method represent TUC in my criteria-compliance chart.

      Kemeny passes a number of the criteria that Beatpath passes, including the Condorcet Criterion. I don’t know if Kemeny meets Mutual Majority. It fails Clone-Independence, the main criterion whose failure ICT and Symmetrical ICT are criticized for.

      I felt that it was desirable to include Condorcet methods that pass FBC and CD, (methods that don’t give strategic need for favorite-burial, and automatically avoid the chicken-dilemma), and so I included ICT and Symmetrical ICT.

      Yes, there’s no one best voting-system. Different voting-system reform advocates want different criteria, and prefer different methods.

      I’ve told why I consider FBC and CD to be particularly important, and I’ve defined Enactable, Easy, and Non-Complex, and have told why those are important.

      But, though we voting-system reform advocates don’t agree exactly on what we want, we should still be able to compromise, to agree on what proposal is the most do-able one.

      Speaking for myself, my favorites are Symmetrical ICT, and ordinary ICT, though Approval and Score have strong advantages too.

      So, when I advocate Approval and Score, as the most do-able voting-system reforms, and as the natural compromise, I’m not just promoting my favorite.

      We voting-system reform advocates have got to set aside our differences, and work together for the attainable, enactable improved voting systems. I claim that those are Approval and Score.

      It’s a question of getting improvement, or not getting improvement because we won’t work together.

      Michael Ossipoff

      Democracy Chronicles

  • Michael Ossipoff

    I should complete my reply a bit, and update it. I looked it up, and Kemeny does evidently meet Mutual Majority, according to the website I checked.

    But Kemeny (just like Beatpath) fails the Favorite-Betrayal Criterion (FBC) and the Chicken-Dilemma Criterion (CD).

    In other words, Kemeny, like Beatpath, gives strategic need for favorite-burial, and fully has the chicken-dilemma.

    Another thing that should be mentioned: Kemeny’s count-computation is NP-Hard. That isn’t true of Beatpath, or the other popular Condorcet methods. It isn’t true of ICT or Symmetrical ICT.

    ICT, Symmetrical ICT, Beatpath, Ranked-Pairs, and IRV can all be counted in polynomial time–but not Kemeny.

    As I said, IRV is no good for our current electorate, due to its FBC failure. But opponents of IRV have sometimes gone a bit overboard, in looking for criticisms of it. For instance, IRV is often criticized because it isn’t “precinct-summable”. That criterion is designed to make Condorcet look good, and to make IRV look bad.

    Actually, for a national presidential election, with 20 candidates, IRV would just amount to 20 Plurality elections. If one Plurality election can be handcounted securely, then so could 20. And each of those 20 Plurality elections is a little easier than the last,due to having one fewer candidate.

    More count work, sure, but it’s nothing different from Plurality counting.
    Handcounting IRV would take a little longer than Plurality, but it wouldn’t be a problem.

    (When I speak of a national presidential election, I’m assuming a direct popular vote, without the electoral college)

    With all Condorcet methods, it’s a different matter entirely. The count is a complicated series of pair-comparisons, with each candidate being compared to each of the other candidates, to find which is ranked over the other on more ballots. That much-more-complex count makes for more opportunity for count-fraud or error, in a handcount.

    That’s true of Beatpath, and it’s also true of the Condorcet methods that i like, such as Symmetrical ICT.

    But at least Beatpath and Symmetrical ICT are countable in polynomial time (the counting-time is a polynomial function of the number of candidates).

    Not so with Kemeny, whose count time can increase much more rapidly, with the number of candidates.

    If you could find more counters (people to count the election), dividnig the work among more count-teams, you could do a handcount of Beatpath or Symmetrical ICT.

    Ask a Kemeny-advocate how long it would take to count a Kemeny presidential election, with 20 candidates, 100 million voters, and 1000 count-workers. :-)

    In fact, how long would the count take on a typical home computer?

    Approval has the simplest and easiest count, of any method other than Plurality.

    Score and Majority-Judgment are next easiest. They require only as many tally-marks as does Approval.

    But approval, compared to Score and Majority-Judgment, doesn’t require as many tallies to be kept, making for the simplest and easiest count, next to Plurality.

    Michael Ossipoff

  • Michael Ossipoff

    When I spoke of counting a Kemeny presidential election, I was referring to a handcount.

    Instead of saying “with 100 count-workers”, I should have said “with 100 count-workers at each precinct, and, say, 100 or 1000 at the national central count location.”

  • http://www.geometricvoting.org.uk Peter Mendenhall

    Your table is a good means of highlighting the comparative strengths and weaknesses of rival single-winner voting systems. Perhaps you could extend this table by adding the Borda Count and Consecutively Halved Positional Voting (CHPV) to it?

    • Anonymous

      Peter Mendenhall wrote:

      Your table is a good means of highlighting the comparative strengths and weaknesses of rival single-winner voting systems. Perhaps you could extend this table by adding the Borda Count and Consecutively Halved Positional Voting (CHPV) to it?
      Democracy Chronicles


      Well, I don’t know if it would be feasible for Democracy Chronicles to re-do the table, but I can say a few words about Borda.

      Regarding the criteria that I consider the most important (under current conditions):

      Borda fails FBC. That alone would be enough to disqualify Borda for use in our official public elections.

      Borda fails CD (the Chicken Dilemma Critrion).

      Borda fails MMC

      Borda fails the Condorcet Criterion.

      Borda passes LNHe(if the candidate-list is fixed in advance), but that isn’t nearly enough, given all of Borda’s failures of important criteria.

      Some academic authors studied the ability of a method to keep electing the same two unliked parties forever, at equilibrium, where voting is influenced by media claims that those two parties are all that can win, and when people vote according to that belief, the results seem to confirm that prediction.

      It seems to me that, in regards to that ability to keep electing that unliked pair of parties forever, at equlibrium, Borda was even worse than Plurality.

      I’m referring to Borda as it’s usually defined and proposed.

      Actually, I’ve introduced a version of Borda that I call “Summed-Ranks”. Here is its definition:

      Summed-Ranks (SR):

      Voters may rank any number of candidates in order of preference. Voters may rank any number of candidates at the same rank position.

      The winner is the candidate with the fewest candidates ranked over him, as summed over all of the ballots.

      Additional rule:

      If a ballot doesn’t rank some set (S) of candidates, then each candidate in S is scored as if that ballot ranked _all_ of the other candidates over hir, including all of the other candidates in S.

      [end of Summed-Ranks definition]

      That additional rule is a feature that I call “power truncation”. It confers, on SR, compliance with Later-No-Help.

      SR also meets FBC.

      In other words, SR has some of the most important criterion compliances of Approval and Score.

      In fact, if you rank all of the acceptable candidates in 1st place, and don’t rank anyone else, then you’re effectively voting an Approval ballot.

      SR can be regarded as Approval, with the option to use more than 2 rank positions, if you want to give, to some candidates, ratings between max and min.

      Of course Score also is equivalent to Approval, with the option to give some candidates ratings between max and mi.

      The difference is that SR (just like any Borda version) decides for you what ratings it will give to those inbetween-rated candidates.

      SR doesn’t have ordinary Borda’s problems. Its shortcoming, in comparison to Score, is that it doesn’t let you choose the inbetween ratings. But the reason why someone would choose Borda would because they didn’t _want_ to choose the ratings themsselves, but rather wanted the method to choose the inbetween ratings for them.

      SR is for electorates that want that, or that specifically want Borda.

      I haven’t included SR in an article, because it isn’t a recommendation of mine. It’s only for the above-mentioned purpose.

      SR and IRV are the most briefly-defined rank counts. Here’s a description of IRV’s rank count rule:

      Repeatedly, cross off from the rankings, the candidate who currently tops the fewest rankings.

      [end of brief IRV definition]

      Sure, that definition doesn’t specify all the details, but it clearly implies all that it doesn’t specify.

      The above description doesn’t actually say how to determine the winner. But, as increasingly many candidates get crossed off, eventually there will be only one who isn’t crossed off. Surely that must be the winner–and of course it is.

      Official IRV rules say that when a candidate has a majority, or tops a majority of the ballots, then s/he is immediately elected. But that isn’t necessary, because such a candidate is certain to be the last remaining un-crossed-off candidate.

      The word “currently” clarifies that the matter of who tops what ranking is something that varies over time, due to candidates being crossed off from rankings.

      You mentioned another method, Consecutively-Halved-Positional-Voting (CHPV).

      What is its definition?

      When introducing or advocating a voting system, several things are needed:

      1. First, the rationale: What problem does it solve or avoid? What purpose does it serve. What goal does it accomplish?

      2. A complete and precise, but concise, definition.

      3. What are its properties? What criteria does it meet? What are its advantages, compared to other methods. What are its disadvantages (every method has a disadvantage).

      Those things must all come from the introducer, proponent, or advocate of the method.

      Does CHPV meet FBC? I claim that FBC is absolutely essential, under current conditions.

      Does CHPV meet CD? I claim that any method that doesn’t meet CD doesn’t improve significantly on Approval and Score.

      By “current conditions”, I refer to:

      1: A disinformational media system that promotes the belief that only a Democrat or Republican can ever win, and that therefore corruption is unavoidable, and that therefore corruption is acceptable.

      2.An electorate who believe that.

      Under current conditions, as defined above, any method that doesn’t meet FBC is entirely inadequate.

      Michael Ossipoff

      • http://www.geometricvoting.org.uk Peter Mendenhall

        Mike, I really appreciate your fulsome reply. Many thanks. Consecutively Halved Positional Voting (CHPV) is an intermediate system between first-past-the-post (FPTP) and the Borda count (BC) so it too fails FBC. FPTP suffers from vote splitting but not teaming whereas for BC the reverse is true. Using a geometric voting (GV) algorithm, CHPV is the closest GV variant to BC and the furthest from FPTP that always enables voters – rather than the system itself – to thwart any attempt at teaming. I would therefore argue that CHPV is an improvement on BC when the strategic nomination of clones is an issue.

        As for the requested definition and properties of CHPV, a comprehensive description and evaluation as well as comparisons with other methods is provided at my http://www.geometricvoting.org.uk website. I believe it to be a fair ‘warts-and-all’ coverage of this new system. All substantive claims are backed by mathematical proofs for anyone and everyone to review. Despite its failure to met FBC, I nevertheless hope CHPV may be of some interest to you or your readers.