A Condorcet winner may not be a true consensus candidate. Approval voting can find consensus with a simpler ballot.
Three friends are trying to decide on a restaurant for dinner. Two of them really love pizza, but the third is a vegan. The full rankings of the three friends are as follows:
| Number | 1st Choice | 2nd Choice | 3rd Choice |
|---|---|---|---|
| 2 | Pizza Palace | Veg n’ Go | Burger Barn |
| 1 | Veg n’ Go | Burger Barn | Pizza Palace |
The vegan obviously loves the vegan restaurant, and Burger Barn at least has vegan options, unlike Pizza Palace, so the vegan prefers Veg n’ Go > Burger Barn > Pizza Palace. The two pizza lovers are really craving pizza, and they had burgers for lunch, so they prefer Pizza Palace > Veg n’ Go > Burger Barn.
Marquis de Condorcet would decree that the true consensus option is Pizza Palace, because a majority of voters have it as their first choice, and thus it defeats every other option. Majority rule, after all, is the most fundamental principle of democracy. Or is it?
When I was in grad school, I had a friend who was vegan, and he convinced me to give Veg n’ Go a try. I was skeptical at first, but I loved it! It may not be my first choice on any given day, but I was always perfectly happy to eat there, despite not being a vegan myself. Its proximity to our office combined with the fact my friend was a vegan made it a great compromise that we went to regularly.
If both pizza lovers find Veg n’ Go to be 99% as good as Pizza Palace, then Veg n’ Go is a choice that literally 100% of voters would be content with, while Pizza Palace would result in the minority being unable to eat anything at all. Which of these sounds like the compromise to you?
This example highlights my major issue with the Condorcet criterion.
The Condorcet winner is the candidate who would win a head-to-head matchup against every other candidate. A voting system satisfies the Condorcet criterion if it always elects the Condorcet winner when one exists.
Many Condorcetists will argue that if you don’t elect the Condorcet winner, then you are not electing the true compromise of the electorate. But I think this is a complete fallacy and misunderstanding of what a compromise is.
The Condorcet winner is something defined by ordinal preferences. That is, it only looks at a comparison of orderings of candidates by the voters. Why should consensus be defined by ordinal preferences?
When we talk about compromise, or negotiation, or consensus, we don’t evaluate things simply by how many people prefer one option to another, or even necessarily by majority rule. We tend to try to find an agreement that allows everyone to leave feeling like they got something out of the deal, even if it wasn’t their first choice.
Knowledge that one person prefers Pizza Palace to Veg n’ Go tells us nothing about whether or not they would be willing to compromise and eat at Veg n’ Go. The order tells us nothing about that intensity or distance between the two options. This is important information entirely lost when we ask a voter to submit a ranked ballot. A ranked ballot is simply not a good tool for determining consensus.
In the example above, the Condorcet winner is Pizza Palace, but the true compromise is Veg n’ Go. If we were to take a majority rule comparison between the two, Pizza Palace would win 2-1. But if we simply ask “who is okay with Pizza Palace?” the answer is “only 2 out of 3 people.” If we ask “who is okay with Veg n’ Go?” the answer is “all 3 people.” How is that not the truest consensus option?
| Option | Approval Count |
|---|---|
| Veg n’ Go | 3 (100%) |
| Pizza Palace | 2 (66.7%) |
| Burger Barn | 0 (0%) |
It sure looks like we found the compromise candidate, even if we know that underneath this data Pizza Palace would have defeated Veg n’ Go in a head-to-head matchup. But everyone is at least content with the outcome, and is that not the point of compromise?
Majority rule and ordinal preferences are a decent option when we have a very large group of voters, especially if no single option is going to make a majority of voters content with the outcome. But equating majority rule with compromise is a complete fallacy.
I have previously argued that if you collect ordinal data, then the Condorcet winner is the only candidate for which it makes sense to elect. Because without that intensity, all we can gather from ordinal preferences is that if we move from a non-Condorcet winner to the Condorcet winner, then a majority of voters will be happier. But that doesn’t mean the entire electorate will be happier overall. Just because it’s the only choice that makes sense, when we use that specific type of ballot, doesn’t make it the right choice.
Moving from Veg n’ Go to Pizza Palace would make two voters happier, objectively. And only one voter would be less happy. But we go from three voters being satisfied to only two voters being satisfied, and one voter now being actively unhappy. And, I don’t know about you, but watching my friend starve to death while two of us eat pizza is not going to make me feel like we found a compromise, even if I got my best outcome.
I’d rather more people be content with the outcome than to be forced to make a choice between which two options I prefer. Even if Veg n’ Go is only 40% as good as Pizza Palace to me, I might still be willing to eat there if it means that all of my friends can have a good time, and the menu actually has something each person can eat.
Electing candidates is not the same as picking a restaurant for dinner, but I see no reason to redefine what a “compromise” is. Even if my preference is Pizza Palace over Veg n’ Go, I want to be able to signal that I would be satisfied either way. By providing the additional information that I have an ordinal preference of Pizza Palace over Veg n’ Go, I can actually obscure the compromise in the ballot data.
The two tables above are two different perspectives on the same underlying preferences. But the ranked data, while surely more detailed, actually makes it harder to see which option is actually the consensus choice. More data does not necessarily mean better data, and in this case, the ranked ballot data is actually worse for determining consensus than simply tallying up approvals.
I am thus left with two propositions:
Fortunately for me, there is a simple solution: Approval voting.
Approval voting is a voting system where voters can approve of as many candidates as they like, and the candidate with the most approvals wins.
In Approval voting, I do not have to express that I technically prefer Pizza Palace to Veg n’ Go. Instead, I can express that I would be satisfied with either outcome. And if a consensus option like Veg n’ Go racks up approvals from all voters, then it will win without anyone being any the wiser about the fact that there was a polarizing Condorcet winner that would have left fewer people overall satisfied.
You see, approval is actually, provably, a two-tiered Condorcet method which never runs into a paradox where no Condorcet winner exists. The Approval winner is always the Condorcet winner induced by the ballot data. But it is not beholden to pick the true ranked Condorcet winner if that candidate is less acceptable to the electorate than another candidate. To explain why, let’s look back at the first example with just three voters.
The number of voters who approved of Veg n’ Go but not Pizza Palace is 1. The number of voters who approved of Pizza Palace but not Veg n’ Go is 0. Therefore, Veg n’ Go actually defeats Pizza Palace in a head-to-head matchup of approvals, as two voters declared indifference. Similarly, Veg n’ Go also defeats Burger Barn in a head-to-head matchup of approvals, three to zero. Therefore, Veg n’ Go is the Condorcet winner of the approval data, even though Pizza Palace is the Condorcet winner of the ranked data. This always happens in Approval: the Approval winner is the Condorcet winner of the approval data, but it may not be the Condorcet winner when you consider the ranked data underlying those approvals.
Approval, therefore, gives us the best of both worlds. It can select the true compromise candidate while also giving the winner absolute legitimacy, by being the Condorcet winner of the ballot data. It does this without being beholden to the ranked Condorcet winner, which may not be the ultimate compromise choice.
There are things I like about Condorcet methods, but what really pushes me towards Approval voting is the practical consideration of how we run each election. It’s simply far easier to run an Approval election than a Condorcet election, particularly when we’re trying to find a consensus for a much larger group. We can simply ask each voter to raise their hand for each option they would be happy with, and the option with the most raised hands wins. We don’t need to collect ranked ballots from every voter and then run pairwise comparisons between every candidate to find the Condorcet winner, or run a majority rule election for all three matchups. We can just count approvals and be done with it.
The Condorcet winner and approval winner generally coincide. However, when they don’t, there is usually good reason. The 1985 Institute of Management Sciences (TIMS) election is a good example where they potentially didn’t. See this post where I discuss it in more detail.
In this election, they collected both approval and ranked data. The approval winner won by over a hundred approvals. The supposed Condorcet winner was inferred to be strictly preferred over the approval winner by a single vote (901 to 900 of those who expressed some type of preference), while 27 voters abstained–leaving it very ambiguous. That’s not exactly a strong legitimate claim. Approval broke that ambiguity: the approval winner earned 1,038 approvals to the “Condorcet winner’s” 908 approvals.
Would a 901 to 900 majority really give as much legitimacy to the Condorcet winner as the 1,038 to 908 majority that Approval voting gave to its winner? I don’t think so. Instead, we can definitively conclude that many of the voters who said they preferred the Condorcet winner to the Approval winner explicitly approved of both candidates. You can have an ordinal preference but still be perfectly happy with either candidate. To pretend this is some sort of impossibility, and that tiny ordinal distances make a non-Condorcet winner somehow “fringe”, is to completely misunderstand the nature of compromise and acceptability.
The lesson is simple: majority preference and broad consent are not the same thing, and a voting system should make room for both. Condorcet logic captures pairwise legitimacy, but it can still miss the candidate most people can genuinely agree on. Approval voting closes that gap by letting voters signal acceptable outcomes directly, while still preserving a coherent notion of legitimacy in the ballot data. It is easier to run, easier to explain, and often yields the same winner when the Condorcet case is clear, yet it behaves better when preferences are close, ambiguous, or weakly held. If our goal is not just to crown a winner but to produce outcomes people can accept as fair, then approval voting is the better compromise between mathematical rigor and democratic reality.
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