The flowers used in the experiment were artificial, made of a Plexiglass flower-top mounted on a tube, with a strip of fibreglass mesh to help the bee climb in and out. The tubes were of various lengths, from 4 to 10cm, and the tops were two-tone combinations of yellow, blue and white. Each artificial stalk led to a sucrose solution, with the longer tubes offering greater rewards.
After the bees had been taught to forage from these unusual plants, the experiments began, giving them the choice between paired specimens. The results showed that bees were generally indifferent to colour and the amount of sucrose delivered, but tended to prefer short flowers to long ones. When the shortest flower was paired with the longest, however, bees 3, 5 and 8 preferred the longer, despite having picked the shorter flower on earlier pairs.
For each individual bee, it is possible to determine an order of flowers such that weak stochastic transitivity is obeyed: in other words if A>B and B>C then A>C (where '>' means 'is preferred to'). But strong stochastic transitivity, demanding continuity in the strength of preferences (so that A>B and B>C implies A is very much preferred to C), is consistently violated by the three bees identified above.
The result shows that comparative evaluation of pairwise choices is not always determined by a simple utility function. The author says 'it is difficult to create situations where transitivity is regularly violated', though Hartston (unpublished data, 1994) claims it often happens in supermarkets.
The subject, H, was required to select after-dinner mints in a controlled environment (Sainsbury's) and given the choice of Matchmakers (M), Bendicks Bitter Mints (B) and After Eights (A). When these were presented in pairs, H had no hesitation in preferring A to M, and B to A giving, on each occasion, the explanation: 'It tastes better and is only a little more expensive.' Yet he preferred M to B on the grounds of expense.
Strong stochastic transitivity is maintained on scales of both taste and expense, but a more complex process is needed to explain the interaction between the two. That's probably why shopping takes so long and bees buzz so much.