  Suppose that females choose males based on attributes that do not signal any
genetic quality that is not related to the choice itself. Can being choosy
confer selective advantage in this situation? We introduce correlated
strategies, which means that females, when making their choice, may take into
consideration external and independent random factors that are known to be
observable by all. Individual-based simulation is used to show that, in this
case, choosiness can emerge against the cost of over 25\% when pitted against
randomly mating females. Moreover, after being established in the population,
it can sustain costs of over 35\% .
  While such costs are not biologically plausible, they demonstrate
unequivocally that sexual choice is a strong evolutionary force. Thus,
correlated strategies are shown to be an evolutionary tool that channels
randomness from the environment into genetic diversity. In addition, it turns
out that a higher number of attributes in the ornament makes the choice more
advantageous, which may result in a runaway complexity of sexual traits.
Implications for the evolution of (female) cognitive abilities and speciation
are discussed.
