In 2008 a study was conducted in which participants were given a container with three "eggs" in it labeled X, Y or Z. All three "eggs" were the same in each container, so each container was all Xs or Ys or Zs. They were told that they would draw one egg from their container. Then after the experiment a computer would randomly select X, Y or Z. If the computer's selection matched their "egg" they would receive $30. Otherwise they received nothing. Participants were given the option to pay $1 to get a container with two "eggs" of the same letter and one different letter or $2 to get a container with all different letters. Otherwise they paid nothing to keep their container with all the same letter.
The important component of this study is that what the participant drew out of their container (and thus what was in the container) was completely irrelevant to their payout. The only component that affected their payout was whether the computer randomly matched their selected letter. Regardless of what letter was selected by a participant this probability would always be one third.
Despite this fact the majority of participants elected to pay to switch to a container with more than one letter inside. What possible explanation could there be for such behavior?
As it turns out there are several plausible explanations. Firstly, participants could simply be misunderstanding the math involved. It is very intuitive to say "I have all X eggs, what if the computer picks a Y egg? Then I can't win. I'll improve my odds of winning by getting a Y egg." However, this simply changes the equation without increasing odds of payoff. While the participant has given themselves a one third chance of winning if the computer picks Y they have also reduced their chance of winning by a third if the computer picks X. The net effect is no change except for the loss of the participants payment to change to another container.
People faced with uncertainty in which there is no clear best choice also tend to believe that diversity is better. While this is often true this mental shortcut could have led participants astray in this case. There is some evidence for this explanation as participants were much less likely to switch to a more homogeneous container from a more heterogeneous container in later experiments.
Participants may also have been attempting to avoid later regret. Imagine having an all Xs container and later being told the computer randomly selected Y. It's very natural to have the reaction that you should have paid to switch to a container with Y in it. Participants likely could have anticipated this reaction and acted to mitigate it by paying to include different letters in their container. When every letter is included participants can more easily ascribe their loss to luck rather than their decisions.
The core of this study is the idea that people often fall into the trap of false diversification. Simply paying for more heterogeneity is not enough. Diversification must increase return and lower risk. Otherwise it is simply a needless additional cost of investment.