Zahavi's handicap principle is an argument for sexual selection in which the costliness of the male character, such as a peacock's tail for example, is positively useful to the female. The argument, originally suggested by the biologist Amotz Zahavi runs as follows:
In a population in which males vary in their quality, some of the males possess a handicap - a costly or deleterious character which reduces survival. If only males with high quality genes can survive possessing a handicap, a female who mates preferentially with handicapped males will only mate with males with good genes.
Provided the advantage through the superior genes outweighs the cost of the handicap then the net quality of the choosy female's offspring will be higher than those of the randomly mating female.
The handicap acts as an indicator of genetic quality and has to be costly to guarantee that signalling is honest: otherwise low quality males could equally well advertise and females would be unable to distinguish between them.