Honeybees do not use "quadratic voting." They use plain score voting.

By Warren D. Smith (PhD), May 2015.

The following highly misleading and wrong article appeared:

Rory Sutherland & Glen Weyl: Humans are doing democracy wrong. Bees are doing it right, The Spectator, 2 May 2015.

We will refute it, virtually entirely, from top to bottom. Their main claim is that "quadratic voting" is the method used by honeybees, which they contend is a better voting system. Here are the key quotes, with sentences numbered for easy reference, from the Sutherland/Weyl piece.

QUOTES: (1) The renowned biologist Thomas D. Seeley... was part of a team which discovered that colonies of honey bees look for new pollen sources to harvest by sending out scouts who search for the most attractive places. (2) When the scouts return to the hive, they perform complicated dances in front of their comrades.(3) The duration and intensity of these dances vary: bees who have found more attractive sources of pollen dance longer and more excitedly to signal the value of their location. (4) The other bees will fly to the locations that are signified as most attractive and then return and do their own dances if they concur. (5) Eventually a consensus is reached, and the colony concentrates on the new food source. (6) Of course, every bee wants credit for their own find. (7) So there needs to be a countervailing costly mechanism to prevent bees from simply over-promoting any pollen source they know. (8) Bees must spend a lot of energy to bring their fellows around. (9) 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. (10) 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.

OK, let's stop here and go through those crucial Sutherland/Weyl quotes pointing out what's wrong. Of the 10 sentences above, we will show that 1, 5, 6, 7, 8, 9, 10 – that's 70% – were false; the entire main thrust of the article is false; and their evidence is simply fabricated. Actually it is even worse than 70% because sentence 10 really contains several lies. The reader probably would have been better off flipping a coin, since that tends to yield 50% accuracy. In my opinion, anybody who publishes anything this false should not be a professional scientist, and if they want to try, then they must immediately publish an enormous retraction.

You can learn plenty about honeybee democracy from our web page on that topic. In fact I was the person who first realized the honeybee's voting system is essentially equivalent to plain score voting, i.e. each bee rates each candidate hive-location with a numerical score, and the highest average score wins. This realization came by seeing that a mathematical model involving eigenvalues, published by Mary Myerscough, could be interpreted in a much simpler manner.

However, all that is for the (generally once-yearly) election held for the purpose of determining where to locate the new year's beehive. It does not concern the question Sutherland & Weyl discuss of describing the location and quality of "pollen sources." Sutherland & Weyl are simply wrong about that. As anybody knows who has devoted more than slightest degree of effort to actually reading about bees: There is no "election" about pollen sources at all. There is no single "election winner." There is no voting. There is no "consensus reached." The colony does not "concentrate" on any single food source, because that would be stupid, because having a varied diet from many food sources, of course is superior.

The truth: "A bee uses dance sign language to tell its sisters about a food source's direction, distance, and quality." That's all. It is like you recommending a restaurant to some of your friends, who then may or may not individually visit it. This activity is not normally described by anybody as an "election" or "voting."

Was all this "discovered" by Thomas Seeley and his "team"? No, it was not. Seeley has indeed studied and written extensively about bees and their communications and democracy systems, including his book Honeybee Democracy (Princeton Univ. press 2010)... but the discoveries of those systems were made by Karl von Frisch (1886-1982) and his student Martin Lindauer (1918-2008) mostly before Seeley got out of kindergarten.

Are the quadratic growth claims in sentences 9 and 10 correct? No. The truth is the dance duration is linear in the food source attractiveness (quantitatively: caloric content). See figure 1 in this paper

Thomas D. Seeley: Honeybee foragers as sensory units of their colonies, Behavioral Ecology & Sociobiology 34 (1994) 51-62 (pdf). [Incidentally: Seeley gave me that paper and told me he did not recall ever making any quadratic claim.]

Is it true that bees must "spend a lot of energy" on these communication dances? No. Food-reporting "waggle dances" take place on the ground and last seconds to minutes – small energy expenditure compared to the cost of flying there, gathering food, and hauling it back.

Is it true that "Of course, every bee wants credit for their own find"? I am not aware of any evidence about what bees "want" of this nature, and especially not that there is any "credit" ever assigned to anybody by anybody else. Indeed, bees will happily listen to and respond to even intentionally-wrong food-reporting instructions provided by a robotic pseudo-bee, who (if this were true) would never have had any "credibility." if bees kept track of their sisters remembering who was who and who had more credibiity credit, then they'd probably have good enough recognition that they would not listen to a robot who was not one of their sisters at all, in fact not even a bee at all. And most of the bees doing all this dancing are not reporting about "their own find" anyhow, so even if they were somehow able to get and want discovery-credit, that would be irrelevant.

There is no known need for a "countervailing costly mechanism to prevent bees from simply over-promoting any pollen source they know." That is because worker bees (who forage, dance, and observe dances) do not reproduce. That means their sole Darwinian motivation is to make the hive as a whole succeed, which means they are motivated to report honestly. They are not motivated to "over-promote." (Perhaps Sutherland, a professional advertising man, was unable to comprehend this concept.) There actually are very rare circumstances where a worker bee does try to lay eggs and reproduce, although if she is caught doing so, she is killed. But even a rare reproducing worker again has no motivation to lie about food sources, because such lying would only hurt, not help, her offspring.

Wait – there is more. Sutherland and Weyl falsely claim (sentence 10 above) that "quadratic voting" involves paying a cost proportional to the square of the candidate-attractiveness score you provide in your vote. This is a false description of what "quadratic voting" is, perhaps caused by the fact that Weyl in his original paper was unable to figure out how to do quadratic voting in elections with more than 2 candidates, and it was I who had to discover that in my paper, which Weyl and Sutherland were allergic to since it was highly critical of Weyl's. (Note: bees usually have more than 2 food sources, and more than two candidate hive locations.) What is the correct description? Quadratic vote buying really involves paying a cost zero if your score for some candidate (that you cast as part of your ballot) concerns any candidate other than the ultimate election winner (call him W) or second-placer (call him S). If, however, you are scoring S or W, then that does cost you, and the cost is the square of the difference between the scores you provide for S and for W.

The bees, even in their real election about hive-location (and that really is an "election," involving "voting" and with a "single winner" and in which a "consensus" really is reached), do not do this. They could not even if they wanted to, because they do not know ahead of time what either W or S will be. (Which ignorance, of course, is why they need to have an election!) I suppose you could try to argue that paying cost V2 to cast a score V for each candidate-hive-location would be the best approximation the bees could provide to the correct quadratic-vote-buying cost function (given their inability to predict the future)... except that the bees simply do not pay V2, based on actual observed data.

Now here are a few more quotes from the Sutherland/Weyl piece.

QUOTE: Thus, it is the total passion of the bees, not simply [their] numbers alone, that ultimately carries the day... If you want a better system of voting, the bees have it.

The bees use score voting. They do not use quadratic voting. I agree score voting is a superior voting system, and it indeed attempts to compute the "total passion," although that wording is highly misleading when applied to the bee voting system because although it is true the bee system is score voting, the algorithm they use ultimately converts "highest average score" into "highest number of bees" causing the two concepts to lose their separate identities. I have been saying score voting (without any payment required to cast your vote – voting is free) is better for about 15 years now, and I had the advantage over Sutherland and Weyl that I actually knew about what the bees were doing, correctly, not wrongly, and in fact was the discoverer of its correct mathematical interpretation of what they were doing, well before either Sutherland or Weyl even knew that quadratic voting even existed.

QUOTE: In fact, Glen Weyl's statistician co-author Steven P. Lalley has shown mathematically that QV is the only pricing rule that gives individuals an incentive truthfully to report their preferences.

Sorry, that statement is false. See my 2-year-old report on monetized score voting systems (which Weyl was fully aware of) for counterexamples.

Conclusion: Of course, unethical and/or foolish people like Sutherland and Dr.Weyl are motivated to over-promote their own so-called discoveries while showing zero regard for the truth nor performing any kind of fact checking. There needs to be a countervailing costly mechanism to prevent that. Perhaps this web page will be able to draw attention to their behavior and thus serve as that corrective mechanism. Let us hope so. The bees do indeed have useful lessons to provide, but only if one actually pays attention to facts, rather than merely one's personal self-promotion agenda.


Other social insects


Monetizing schemes for score voting

Clarke-Tideman-Tullock monetized voting

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