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Females are unable to assess directly the quality of the males.
Instead, males advertise their quality via a display of some sort, for example a long tail or bright plumage or a heavy rack of antlers. Suppose, moreover, that it is easier for a high quality male to produce a handicap than for a low quality male to do so. In this situation, high quality males will choose to produce large handicaps, to ensure that they are chosen as mates by females. Low quality males will not be able to afford to produce large handicaps and will produce small or no handicaps. Females will choose males with larger handicaps, because these are the higher quality males, and thus the handicap serves as an honest signal of male quality.