Critique my Copeland-cardinal hybrid method


Hi CESers,

I thought up this voting method last week. It’s a hybrid between cardinal and ranking methods, but a sort of opposite of STAR. I think it strikes a uniquely good balance between simplicity for voters at the ballot box, expressiveness, resistance to basic strategies, accounting of relative preference strength, and (sort of) electing Condorcet winners. I would love to hear your thoughts!

The Ballot

Voters rate candidates on a 4-level scale, where the levels are labeled “Strong Approve”, “Approve”, “Oppose”, “Strong Oppose”. [1]

Choosing the Winner - Copeland + Approval

  1. (Approval) Eliminate all candidates with approval (strong or mild) from fewer than 25% of voters. [2] [3]

  2. (Copeland) Match every candidate against every other candidate. Candidate “A” defeats candidate “B” if more voters rate A above B than rate B above A. [4] Candidates get one point for every other candidate they defeat. [5]

  3. (Copeland) Rank the candidates by the number of points (i.e. pairwise wins). When one candidate defeats all other candidates (i.e. the Condorcet winner), this candidate will have the highest ranking.

  4. (Approval) Resolve any ties by using overall approval rates. [6]

  5. Elect the highest ranked candidate.


  1. The exact number of levels in the scale is not critical. I chose 4, but I can see strong arguments for 5, 6, or 7 levels, particularly for elections with many competitive candidates. However, it should be clear which levels on the scale constitute “approval”.

  2. The 25% approval threshold was chosen somewhat arbitrarily. (Also, this step may not be valuable.) 10% seems pointlessly low; 50% seems prohibitive. This threshold could alternatively be defined in terms of number of candidates (e.g. top 5 most approved candidates). The goals here are to minimize the impact of dark horses and losers on the final result and to incentivize all candidates to find at least a modicum of approval.

  3. If no candidate meets the threshold, simply elect the candidate with the most approval votes.

  4. In cases where voters omit ratings for candidates, approved candidates can be considered preferred over unrated candidates.

  5. This method could count close pairwise matchups (e.g. margins below 1% of votes) as ties, granting both candidates half a point in the matchup. Explicitly allowing pairwise ties might reduce the probability of majority rule cycles and avoid costly recounts.

  6. Ties in the Copeland score could also be broken by a different scoring metric. I favor approval here, as it keeps the incentive to give extreme ratings low.

Strengths of its cardinal properties

  • The rating scheme is simple enough for any voter to understand, and it would fit easily enough on a ballot. It is certainly more approachable than a full ranking scheme (when there are 5+ candidates) or a scoring scheme with a large number of ratings.
  • The rating scheme (a Likert scale) is pretty expressive and comports with how social scientists often measure human opinions.
  • In a race with 5+ candidates, voters are forced to differentiate between stronger preferences (giving candidates different ratings) and weaker preferences (giving candidates the same rating). Therefore, only stronger preferences influence the results. This is, in a sense, the goal of score methods. Still, most pairwise preference relations are preserved.
  • The ratings can be used to avoid the most pathological issues with ranking methods. For example, true dark horses can be eliminated by an initial approval threshold.
  • Some omitted preferences can be inferred from the ratings (approval > unrated).
  • Ties arising from majority rule cycles can be broken using voter ratings, which are more understandable than heuristics based on pairwise defeat strength. This also addresses the Copeland method’s problem with ties.

Strengths of its ordinal properties

  • While this method is not a true Condorcet method, as it derives voters’ preferences from a cardinal scale with limited slots, it seems extremely likely that it would elect the Condorcet winner, should one exist. In absence of a Condorcet winner, Copeland winners are still in the Smith Set. It is also highly unlikely that it would elect a Condorcet loser.
  • The method (sort of) inherits other attractive features of ranking systems, like the mutual majority criterion.
  • Few assumptions are made about the relative distances between locations on the rating scale.
  • The strategic incentives to exaggerate preferences are low (unlike vanilla score voting).

You’re familiar with


=/ The strategic incentives to exaggerate preferences are low (unlike vanilla score voting). /=

Why on earth does just about everybody believe that “vanilla” score would, after a very few election cycles, induce voters to exaggerate preferences? Where did they all learn this nonsense? That is not what would happen.

The voters would instead utilize the hedge strategy to defeat the two-party system that has been continually exploited by the ruling political class (the modern elite mandarins) to lock them into voting for the lesser of two evils. So they might grant (10) votes to a Nader, and (8) or (9) votes to a Gore, so as to reduce the likelihood of the election of a Bush. Then, the Nader could perhaps receive the most votes, and thus actually win.

Another problem with this Copeland-cardinal hybrid method is shared with the STAR method – At the end of the election, the candidate with the strongest score, or with the Copeland-cardinal strongest approval rating, could very possibly still lose an election. And this result would be a sure-fire trigger for a massive social upheaval, or even a possible insurrection. A “plain vanilla” (or “simple”) score method would side-step extra vote information trafficking since it would be strictly summative, with no extra complications.


I am. That’s where I got the idea for an approval threshold. I like the way 3-2-1 has a simple, understandable scale, a relatively simple algorithm, and a runoff at the end. There are a few things I don’t love about it, though.

I don’t think it lends itself well to elections with large numbers of candidates, particularly when there is an imbalance between the number of candidates per party. The 3-candidate cutoff could limit the field to a single party, and it would not necessarily be the party of the majority of voters.

Also, I think a 4 or 5 level scale might make more sense when most candidates and most voters are aligned with one of two parties. Then each voter can have two hierarchies per party. With only three levels, some voters would use the middle level for less-preferred candidates of their party, while other voters would use it for lesser-evil candidates of the opposing party. Others might not use the middle level at all. It seems to me that different voting groups would use it very differently under different circumstances, which seem likely to produce some weird results on occasion.


Thanks for the input, rkjoyce! To your question of why everybody believes that score would induce voters to exaggerate preferences - I don’t exactly believe that. What I said in my post is simply that the incentives exist. How voters would actually behave, in aggregate, I can’t really say. I wish we could try it and find out!


It seems like your method still fails LNH, which means that FailVote will never support it. I really get the sense that trying to compromise with FailVote is impossible.

One thing that has always bugged me about both your idea (hedge voting) of Score voter behavior and the IRV propagandists’ idea (bullet voting) is How do you know or expect that voters will ACTUALLY choose to behave that way?

Explain how this is a problem again?


Oh, yeah, I wasn’t planning on trying to present this to them. Their dogmatic, rigid defense of IRV completely baffles me. I am optimistic that if approval voting can win in a few more places (fingers crossed for St. Louis) then all conversations around voting reform will open up. And maybe then there would be room to talk more realistically about my method.

Regarding LNH - yes, my method fails that criterion. That said, because the method relies on rankings, it seems pretty unlikely to me that this would matter much. The data I’ve seen suggest that Condorcet winners exist in the vast majority of elections, so I would strongly prefer a method that elects them as often as possible. The main situations where including a ranking for less-preferred candidates could hurt more-preferred candidates involve majority rule cycles, which happen pretty infrequently. Anyway, I don’t think I need to tell you about all the shortcomings of IRV.


Dividing distinct election systems into ‘cardinal’ and ‘ordinal’ categories creates a misleading dichotomy. Penguins and hawks are both birds, but they have very little in common. It is vastly more elucidative to divide each particular system into phases of ‘ballot design’ and ‘tabulation method’ with consideration of ‘expressiveness’ for the former, and ‘responsiveness’ for the latter. Both are required.

What truly needs to be accomplished is effective disruption of the two-party lock-in which the elite mandarins depend upon to surreptitiously subjugate the commonalty.

The single-select (‘plurality’) and approval voting methods are woefully deficient in ballot expressiveness. And they are crippled by spoiler effect pathology of the former, and double bind effect pathology of the latter.

The ranked-choice-voting (‘IRV’/‘RCV’) method(s) is a mandarin-sponsored impending disaster. The ‘ordinal’ ballot design provides very poor expressiveness. But much worse still is the profoundly illusory tabulation method, in which the results are initially summed, the weakest candidate is ‘eliminated’, and then every single ballot (or each of millions of ballot combinations) is painstakingly readjusted to move second choices forward (as if they were chess pieces). Each summation, elimination, and mass readjustment (termed a ‘round’) must be repeated until an artificial (not autochthonous) ‘majority’ is produced. The resulting combinatorial explosion creates massive information traffic which is indecipherable to the common voter, and thus the whole system settles back into effective two-party lock-in.

Then there are systems such as STAR voting which embellish simpler ones such as score voting, which somewhat increase information traffic, while making it difficult for the common voter to utilize the hedge strategy. And this obviously causes increased difficulty in overcoming the two-party lock-in, and thus the mandarins are thereby better positioned to win, and the commoners more prone to lose the elections.

So why not just use (1) to (10) (or even just (5) to (10)) score voting (perhaps with an ‘abstention’ option, if you prefer), so the vast numbers of common voters can finally defeat the tiny numbers of sociopathic mandarin manipulators?


To NoIRV: You mentioned:

=/ One thing that has always bugged me about both your idea (hedge voting) of Score voter behavior and the IRV propagandists’ idea (bullet voting) is How do you know or expect that voters will ACTUALLY choose to behave that way? /=

Well just between you and me, I cannot actually predict how they will actually behave. They can be stupid and ‘bullet vote’, or they can be smart and ‘hedge vote’. Frankly, I have thus far failed to develop any system that would overcome voter stupidity.