We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the sampling cos
ts, and one important question is how many to sample for optimal gain (worth minus costs). If, in addition, the assessment of worth for each sample is associated with some measurement error, the perceived best out of $n$ might not be the actual best, complicating the issue. Situations like this are typical in mate selection, job hiring, and food foraging, to name just a few. We tackle the problem by standard order statistics, yielding suggestions for optimal strategies, as well as some unexpected insights.
We introduce a basic model for human mobility that accounts for the different dynamics arising from individuals embarking on short trips (and returning to their home locations) and individuals relocating to a new home. The differences between the two
modes of motion comes to light on contrasting two recent studies, one tracking the geographical location of dollar bills cite{brockmann}, the other that of mobile cell phones cite{gonzalez}. Trips introduce two characteristic time scales; the time between trips, $theta$, and the duration of each trip, $tau$, and relocations introduces a third time scale, $T$, for the time between relocations. In practice, $Tsim{rm years}$, $thetasim{rm months}$, and $tausim{rm days}$, so the three time scales are widely separated. Traditionally, studies incorporating human motion assume only a single mode, using a generic rate to account for all types of motion.
