Men tend to want the woman they see in front of them, while women want the man other women see:
Are women more interested in men who are already in a relationship? Female and male participants who were single or in a relationship viewed information about an opposite-sex other and indicated their interest in pursuing this target. Half of the participants were told that the target was single and half read that the target was currently in a relationship. The results showed that only single women were more interested in pursuing an attached target rather than a single target. …
According to a recent poll, most women who engage in mate poaching do not think the attached status of the target played a role in their poaching decision, but our study shows this belief to be false. …
Across ten world regions, 57% of men and 35% of women indicated they had engaged in an attempt at mate poaching, … people who mate poach are more likely to be low in agreeableness and conscientiousness than those who do not. …. Research on animal mating (e.g., fish, birds) has shown that female animals are more likely to choose a male that has already been chosen by other females … Research on human preferences does show that women rate men as more desirable when they are surrounded by other women, compared to being alone or surrounded by other men. Conversely, men rate women as less desirable when they are surrounded by other men, compared to being alone or surrounded by other women.
Yet another way in which we don’t know why we do what we do.
This study was of college undergraduates ONLY. Cute study, but essentially worthless as to what [all] women want/desire. College kids are generally more promiscuous - which this study may confirm.
It can be helpful, when reading results like these and thinking about certain human dynamics, to pretend there are really three genders: Females, Alpha males and Beta males.
In most human societies until the advent of birth control and hygeinic abortion, about 80-90% of women reproduced in each generation, whereas around 40-50% of men did. (You have many more female ancestors than you have male ancestors.) As long as a woman is healthy, she is deemed a candidate for reproduction, whereas a man has to meet much higher standards to get a woman to commit the serious resources it costs her to bear and care for children.
A man with another woman is more likely to be Alpha, very obviously. The best reproductive strategy for a woman is to get the committmentt of a Beta male, and the sperm of an Alpha. Her children will be cared for by the Beta and her sons will be more likely to be Alpha themselves and therefore reproduce. This is genetically and economically maximal.
It's very risky socially, of course. If the ruse is discovered, she risks ostracization and maybe even death (via jealous husband). So this acts as a cap on female behavior of this kind, but the rewards for this behavior are also very high and so it remains as a viable strategy.
It's an even better strategy if women remain utterly baffled as to their own behavior. Hence the proliferation of just-so stories that justify women's poaching instincts, or explanations which manage to shift the blame for poaching behavior back onto the man, or "self-esteem issues" or other betes-noires.