Square Dancing Bees and Quadratic Voting

It’s well known that bees dance to convey where useful resources are located but how do bees convey the quality of the resource and what makes this information credible? Rory Sutherland and Glen Weyl argue that the bees have hit upon a key idea, quadratic dancing or as I like to put it, square dancing.

Seeley’s research shows that the time they spend on dances grows not linearly but quadratically in proportion to the attractiveness of the site they encountered. Twice as good a site leads to four times as much wiggling, three times as good a site leads to nine times as lengthy a dance, and so forth.

Quadratic dancing has some useful properties which can be duplicated in humans with quadratic voting.

Under Quadratic Voting (QV), by contrast, individuals have a vote budget that they can spread around different issues that matter to them in proportion to the value those issues hold for them. And just as with Seeley’s bees, it becomes increasingly costly proportionately to acquire the next unit of influence on one issue. This approach highlights not only frequency of preferences but also intensity of preferences, by forcing individuals to decide how they will divide their influence across issues, while penalising the single-issue fanatic’s fussiness of putting all one’s weight on a single issue. It encourages individuals to distribute their points in precise proportion to how much each issue matters to them.

They offer a useful application

Consider a firm that wants to learn whether customers care about particular product attributes: colour, quality, price, and so on. Rather than simply ask people what they care about — which leads to notoriously inaccurate results, often where people affect strong views just to maximise their individual influence — a business, or a public service, could supply customers with budgets of credits which they then used to vote, in quadratic fashion, for the attributes they want. This forces the group of respondents, like the swarm of bees, to allocate more resources to the options they care most about.

Weyl’s paper with Eric Posner is a good introduction to quadratic voting and here are previous MR posts on quadratic voting.


Hi Tyler,

Whats the significance of quadratic voting in terms of communication for bees? I get that quad voting in terms of prices for humans in collectives helps to balance the interests of people with different intensity of views by varying costs, but bees are not in competition with each other. It doesn't benefit an individual bee if the location he is gunning for is selected by the rest, so it isn't clear this even an economics problem, i.e there are costs and payoffs for individuals in competition with each other, etc.

Maybe this occurs due to efficiency of communication in a crowded space? Aka, in a two-dimensional crowd of bees on the surface of a hive, vision doesn't work, the communication is tactile and pheromonal, so a dance that increases in size by the square contacts a linearly-increasing number of other bees. Much more direct explanation, to me at least.

Great question, I would like to know the answer.

Possibly the quadratically increasing cost of getting extra weight for your views allows the hive to give less weight to bees that are mistaken?

That's interesting, we don't think of hive minds as having to deal with unreliability but of course they do even if not actual malice.

Not a fan of the quadratic voting (as applied to elections, etc).
There would still be those 'fanatic' voters who would put all of their budget onto a single candidate, over-reinforcing that candidate. That would be putting 100% budget on one whereas other voters would spread around their budget, having the effect of voting for their front-runner at a price a fraction of the fanatic's front-runner - if I am understanding QV correctly in this context.
We want to nurture a culture of voters who know what they like but also know what their options are and what they like less - not a culture of my way or the highway. So, this could mean having every vote require a 1,2,3,4 ranking to either all or a specified minimum number (perhaps half of all candidates on ballot plus one). The 1 would be worth 10-20% more than 2 would be worth 10-20% more than 3 and so on… Failure to put all rank numbers would invalidate the vote. Using percentages instead would mean having to add the total to 100 or whatever - probably burdensome.
And by the way, why can't we vote at ABM bank machines of the Big Banks (say the top 7)? - at their branch-only machines - nothing is more secure than those machines (in the G7 anyway).

Who knew that the birds and the bees (and people) put more effort into things they value more highly?.

Voters always make similar subjective value/effort judgements; for example, skipping primaries and routine local/state elections in favor of bigger stakes in gubernatorial, Congressional and Presidential races. Voter turnout statistics indicate which elections voters personally value with their time and effort.

But formal voting is just one of the many forms of communication in human society. Bees have very little to communicate -- human society has huge numbers of complex issues in play.

Cool, but Range voting is a better way to go

But for simplicity and to promote consensus, approval voting is superior.

You get to "approve" of every candidate you would accept as serving in the best interest of all, including yourself.

The winning candidate will be the one who has the highest confidence from all voters. It is highly unlikely that winning candidate will be strongly objected to by any faction that actually believes in republican governance, as opposed to authoritarian rule by an elite, which is that faction.

The more a candidate attacks opponents or factions in society, the larger the number of voters who will refuse to approve. The candidates who seek to embrace all and seek common ground and compromise is likely to get approval from most who do not want minority rule.

Most important, no vote is "thrown away".

I'd include one automatic ballot option: "none of the above" which if it got 51% would force a new election with an entirely new slate of candidates as the campaign must have convinced most voters they were picking the least bad from a batch of bad candidates.

I don't think either system is ideal. The challenge is to encourage voters to express their true preferences while still making use of them in some way. With approval voting, most voters would probably only approve of the same candidate they would vote for in a first-past-the-post system. If we were more honest, we would always vote none of the above, but that is a de-facto vote to keep the current incumbent in office which is even worse.

Do you we really need to give rich people the ability to buy even more voting power? I'm too young to remember a time when the left cared about the working class. Posner and Weyl claim it will help protect minorities from the "tyranny of the majority." Wonder which minorities it would "protect?" Blacks? Mexicans? Native Americans? All no, as they don't have the money to waste on vote buying schemes. It would "protect" Eric Posner's people, who contribute half of the money to the Democrat Party and a quarter of the money to the Republican Party.

It doesn't necessarily have to be real money. You could give a certain number of credits to each registered voter. They'd vote by spending those credits. If you really care about one issue, you spend all your credits on that issue, and lose the ability to vote on other things.

I really appreciate article like this. It's very informative and I learned something from here. Thanks for sharing and I will definitely share this to my friends.

The government stole my shoes and burned them.


Better to have a simple easy to understand voting system, and have checks and balances against power. The more complex a voting system the more chance you have of people not bothering to vote. Given that its not really worth voting anyway (as the chance your vote makes a difference is very small), anything that makes it more difficult is going to reduce further participation, so only the fanatics vote. There is no apparent correlation anyway between systems of voting and prosperity of a nation, so what is the problem being fixed here?

The Sutherland/Weyl bees piece is virtually entirely refuted here:

Previous work by Weyl and others on quadratic voting was refuted here:

(Unethical self-promotion behavior by Weyl & pals is also pointed out along the way.)
So far I have never seen a retraction by Weyl of any of his baloney.

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