The Ig Nobel Prize is given out by a group called Improbable Research, which celebrates "achievements that first make people laugh,
and then make them think. The prizes are intended to celebrate
the unusual, honor the imaginative — and spur people's interest in science,
medicine, and technology."  The 2010 awards were handed out on September 30th, and one one of the doctoral students I work with, Isaac Waisberg, pointed out that one of the prizes was awarded to a simulation that demonstrated — if the Peter Principle is true — organizations would be better off promoting employees randomly rather than promoting people until they they reach their level of incompetence.  Isaac knew I was interested in The Peter Principle as I wrote the foreword to the 40th Anniversary edition. Here is a link to the PDF of the article and here is the abstract:

The Peter Principle Revisited: A Computational Study

Authors:
Alessandro Pluchino,
Andrea Rapisarda,
Cesare Garofalo

In the late sixties the Canadian psychologist Laurence J. Peter advanced an
apparently paradoxical principle, named since then after him, which can be
summarized as follows: {\it 'Every new member in a hierarchical organization
climbs the hierarchy until he/she reaches his/her level of maximum
incompetence'}. Despite its apparent unreasonableness, such a principle would
realistically act in any organization where the mechanism of promotion rewards
the best members and where the mechanism at their new level in the hierarchical
structure does not depend on the competence they had at the previous level,
usually because the tasks of the levels are very different to each other. Here
we show, by means of agent based simulations, that if the latter two features
actually hold in a given model of an organization with a hierarchical
structure, then not only is the Peter principle unavoidable, but also it yields
in turn a significant reduction of the global efficiency of the organization.
Within a game theory-like approach, we explore different promotion strategies
and we find, counterintuitively, that in order to avoid such an effect the best
ways for improving the efficiency of a given organization are either to promote
each time an agent at random or to promote randomly the best and the worst
members in terms of competence.

This is just a simulation, not an empirical test. But the virtues of randomness are also found in an earlier experiment that showed groups that randomly selected leaders performed better than those that were asked to selected a leader from among their peers.  Here is the summary I wrote in Weird Ideas That Work:

Further evidence for the virtues of
making random decisions comes from a pair of experiments in Australia by S.
Alexander Haslam and his colleagues. Their experiments compared the performance of
small problem solving groups (3 to 5 people) that were asked to select their
own leaders with groups that were randomly assigned a leader (i.e., a person
whose name appeared either first or last in the alphabet).  These experiments involved 91 groups that
worked on one of three closely related group decision-making exercises, the
“winter survival task,” the “desert survival task,” or the “fallout survival
task.”  Each of these small groups of
college students developed a strategy for ranking potentially useful items for
the particular task,  and their decisions
were scored relative to expert ratings. 
Both experiments showed that groups
that had randomly assigned leaders performed significantly better than those
that had selected their own leaders. 
Random assignment was shown to be superior to groups that had used
either an informal  process where they
selected leaders by “whatever means you see fit” or a formal process where each
group member completed 10 self-report questions on a leadership skills
inventory that had been shown to predict managerial success in prior
studies.  Leaders who scored the highest
on the inventory were assigned to lead groups that used the formal process.
There were no significant differences between groups that used an informal or a
formal process.  Both had inferior
performance to groups with randomly selected leaders. 

Haslam and his colleagues believe that
the process of selecting a leader in these experiments focused attention on
differences between group members, which undermined the group’s sense of shared
identity and purpose, which in turn, undermined performance.  Instead of thinking about how to solve the
problem together, or having a “united we stand, divided we fall” mentality,
they thought about differences between them that were unrelated to the task —
like who had more prestige in the group and why.  My interpretation is similar.  I would add that the leaders who are given a
mandate to be in charge of a group often – without realizing – start imposing
their individual will too strongly, which can stifle the range of ideas that
are seriously considered by the group. 
The researchers admit that they have suggested only one possible
explanation for these findings, and acknowledge that a random process of
selecting a leader is probably inferior to a systematic process for groups that
do other tasks.  But these findings are
intriguing because they force many of us – both practitioners and researchers
–  to see an old problem in a new way,
they spark the “vu ja de” mentality. 
They suggest our assumptions about how to select
a leader may, at least at times, be flawed.

I am not arguing that we ought to give-up and start selecting and promoting leaders randomly.  But it is interesting to consider randomness because doing so challenges our assumptions about the rationality of what we do in life  Indeed, speaking of randomness, last year I heard that Nobel Prize winner Daniel Kahneman (he won the real prize, not to Ig) was running a simulation that seemed to show that if the CEOs of Fortune 500 companies were randomly reassigned to different companies, there would be no significant impact on firm performance.  I don't know what happened to that research, or even how accurate that rumor is, all I can find is this WSJ article where he chimes in on the subject.  If anyone knows more, please comment.

P.S. The reference for the experiment is
Haslam, S. A, C. McGarty, R. A. Eggins, 
B. E. Morrison, & K. J. Reynolds, “Inspecting the Emperor’s Clothes:
Evidence that Randomly Selected Leaders can Enhance Group Performance”,  Group
Dynamics: Theory, Process and Research 2 (1998): 168-18

P.P.S. For another post on randomness, check out this one about decision-making among the Nasakpai Indians.