Majority rule rejected by a majority

Psephomancy
Jul 4 · 6 min read

When discussing voting method reform, we often talk about concepts like the majority criterion, which requires that “If one candidate is ranked first by a majority (more than 50%) of voters, then that candidate must win”.

This seems like an obviously desirable quality, if you grew up with “democracy” being treated as a synonym for “majority rule”, but some people (like me) believe that it’s possible to do better than majority rule, which means that “failing” the majority criterion can actually be a good thing.

Majoritarian voting methods try to find the outcome that best pleases the majority, even if that comes at the expense of harming the minority. Better voting methods try to find the outcome that maximizes the consent/approval of all the voters. These are called “utilitarian” or “consensus” voting methods.

A blogger expressed this using a pizza-buying analogy:

Suppose you and a pair of friends are looking to order a pizza. You, and one friend, really like mushrooms, and prefer them over all other vegetable options, but you both also really, really like pepperoni. Your other friend also really likes mushrooms, and prefers them over all other options, but they’re also vegetarian. What one topping should you get?

Clearly the answer is mushrooms, and there is no group of friends worth calling themselves such who would conclude otherwise. It’s so obvious that it hardly seems worth calling attention to.

Yet some people do dispute this, and insist that majority rule is a necessary goal in and of itself. So I wanted to see how many actually feel this way, and made a few surveys.

I tried to keep the original “everyday” context of the scenario to avoid biasing people by making it sound too much like voting. The downside of making it too casual and realistic is that some people will just ignore what I’m really asking and choose their favorite pizza topping, or propose other solutions (picking off the pepperoni) that are fine in real life but don’t really answer the question.

I asked the question (except worded a little differently) on both Mechanical Turk and Reddit /r/samplesize. I also asked “Why did you choose this answer?” to see whether people were deciding based on utility vs majority, or just choosing for irrelevant reasons. I then ignored the answers that were made for reasons irrelevant to the question I was actually asking. (Such as “I’m a vegan”, “Who the hell prefers mushrooms over pepperoni?”, or “fk u”.) Obviously this is subjective and not the way a scientist would do it, but I’ve published all the raw data, and you can decide for yourself if those answers deserve deletion. (They don’t change the outcome much, anyway.)

Pizza results

For the Mechanical Turk and Reddit surveys, I asked this question:

Three hungry people are ordering a pizza to share. They can only afford one topping for the pizza, and the only choices are pepperoni or mushrooms.

2 of the 3 people love pepperoni, and like mushrooms (but not as much as they love pepperoni).

1 of the 3 people hates pepperoni, and loves mushrooms.

Which topping should they get?

Pepperoni

Mushrooms

Why did you choose this answer?

I got 61 responses and rejected 9. Of those remaining (who chose based on utility vs majority) 83% of respondents chose the utilitarian outcome:

Donut chart of 83% for the utilitarian option and 17% for the majoritarian option

Raw data here

Most respondents expressed support for a utilitarian outcome over a majoritarian one:

  • “they need to share and all of them should eat something that at least everybody likes”
  • “At least with mushrooms everybody gets something they can enjoy.”
  • “If mushrooms is selected everyone can eat the pizza without hating it.”
  • “With pepperoni, one person won’t want to eat the pizza. With mushrooms, everyone will be happy.”

Ironically, some actually used the word “majority” to argue against the majority rule option:

  • “I think mushrooms satisfies the majority better than pepperoni would.”
  • “The most of people like the mushrooms (Majority wise i will Choose the Answer)”

But a minority did still think the majoritarian outcome was correct:

  • “the majority of people in the group like pepperoni, so it makes the most sense to get pepperoni.”
  • “more people like pepperoni”
  • “Pepperoni would make the most people happy, and you can’t always please everyone.”
  • “Because majority rules.”

The reddit survey used the same question, and got similar responses, though the “Why” responses were a little more ambiguous. I got 119 responses, and rejected 13, and was not sure about 5 others. With all 18 removed, the answers were 98% in favor of the utilitarian outcome. With only the most egregious 13 removed, the answers were 93% in favor of utilitarian outcome:

Donut chart with 93% utilitarian, 7% majoritarian

Raw data here

Rationales were similar for the utilitarian outcome:

  • “I believe it’s better for 2 out of 3 people to be slightly disappointed than for 1 person to be extremely disappointed”
  • “Choosing mushrooms is enjoyable for the largest number of people”
  • “The total amount of happiness will be greater”
  • “If they are all paying for it they should get something they all like.”

And a few majoritarian fans:

  • “Only 1 loves mushrooms, but 2 love pepperoni.”
  • “More people like pepperoni.”

Restaurant ratings

Then I did another, more generic variation, asking about a group of people choosing a restaurant based on their numerical ratings:

3 people are going out to eat, and the only choices are Restaurant A and Restaurant B. All 3 people have eaten at these restaurants before, and have given them ratings on a 5-star rating scale:

• 2 of the 3 people rate A 5 stars, and B 4 stars

• 1 of the 3 people rates A 0 stars, and B 5 stars

Which restaurant should the group eat at?

Why did you choose this answer?

Table of ratings in the question

This time I got 83 responses, and rejected 2 for not understanding the part of the question that said they’d been there before, and 1 for a response I couldn’t make sense of. Of those left, 68% chose the utilitarian option. Significantly less than the other surveys, but it’s still a strong majority opposed to majority rule:

Donut graph with 68% supporting utilitarian outcome and 33% majoritarian outcome

Raw data here

Utilitarian rationales were similar:

  • “B is the one restaurant that everybody seems to like.”
  • “B had positive ratings from all three persons that ate there.”
  • “Seems to be rated better”
  • “Everyone will be happy with this choice, unlike A where one person would not be happy.”

as were majoritarian rationales:

  • “The majority rated A higher.”
  • “Because it was highest rated by the most people.”
  • “2 > 1 votes. Majority rules. Picking the restaurant is a group decision.”
  • “Majority rules.”

3-option restaurant survey

Reddit user lucasvb did a similar poll of Brazilian users in Portuguese:

Alice, Bob and Charlie go out for lunch together. Alice is vegetarian. Their options are: Indian food, steaks or pizzas.

• Alice loves Indian food, likes pizza, hates steaks.
• Bob loves steaks, would go for pizza, hates Indian food.
• Charlie loves steaks, likes pizza, would go for Indian food.

Given this, where do you think they should go out for lunch?

This is a similar scenario, where a 2/3 majority prefers an option that the minority hates, but there’s another option that everyone likes. Again, pollees overwhelmingly thought the utilitarian outcome was the best:

Raw data here

Previous Reddit reports:

Psephomancy

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*slaps roof of FPTP* this bad boy can fit so little democracy in it