Recently I participated in an interesting discussion on the internet. The main topic was how some people reject scientific evidence if it contradicts their religious or ideological commitments, but the example was the nexus of evolutionary biology, male and female reproductive strategies, and differences between men and women.
It seems rather self-evident that males of nearly every species can potentially, if they are lucky and pursue the "right" strategy to achieve that end, have many more children than females. That is, after all, how female is defined in biology: it is the sex that makes the greater investment in offspring, usually at a minimum by producing a few large, immobile gametes, while the male is defined as the sex that makes the lower investment into each individual potential descendant, usually at a minimum by producing many small, mobile gametes. On top of that many species have layered additional female investment into the developing offspring, be it by giving live birth (or its botanical counterpart of producing seeds instead of spores), producing milk, or providing paternal care.
It is at this stage that the situation can, rarely, be flipped, e.g. by male sea-horses taking over the pregnancy, or male ratites raising the young; or paternal care can be shared by the sexes. But for most species, the female is the bottleneck, so to speak: How many offspring a female and a male can have is capped by the female's fertility.
It follows logically that a male can increase its number of offspring by being promiscuous, while a female cannot. The conclusion for reproductive strategies is that males in your modal species should evolve to be non-discriminating with regard to sexual encounters, and to maximise the number of partners. Females, on the other hand, do not get anything out of such behaviour. (Unless other considerations come into play, such as earning money with prostitution, or using casual sex as social glue, as it said the bonobos do.)
Whether, for example, human men are more interested in having many partners or more willing to cheat than women is a testable hypothesis. But the answer to that question is not really what I want to dwell on.
What interested me was that a lot of people who argue from reproductive strategies as discussed above write things on the lines of "men cheat more than women" or "men are more promiscuous than women". Also quite interestingly, rarely somebody will pop up who argues the opposite, claiming that "women cheat more than men". Honestly I do not understand the logic for that latter claim, as it does not even have the advantage of making sense from an evolutionary biology perspective; the idea that it is based entirely on misogyny is at least not easily dismissed.
But really for present purposes both claims can be treated as equivalent: I think both of them are, equally, mathematically impossible.
Yes, perhaps it can be shown that men are wired to seek more partners; maybe that is even biological as opposed to cultural. But that does not mean that they will be successful at having more partners, and that is unfortunately what being promiscuous means. Wishing is not doing.
Assume equal numbers of men and women, and disregard homosexual pairings, as neither of these factors are what those who claim "[gender] cheats more than [other gender]" are concerned with. Make a row of female circles on the left and a row of male circles on the right. Now draw lines between female and male circles to indicate pairings.
You can end up with very different network structures, of course. You could have three quarters of all men unpaired, while a quarter of them is paired with four women each, a harem scenario. You could first have each man paired with one woman, and very women also paired with lots of men, a prostitution / men cheat a lot scenario.
But it is simply impossible to have more average promiscuity on the left than on the right, or vice versa, because obviously all connections start on the left and end on the right, meaning that promiscuity is in all cases = number of people of that gender / connections, and we assumed equal numbers of men and women.
Arguments could perhaps be made about the median, but that is not what people intuitively mean or understand when somebody says, for example, "women cheat more than men". Claims like those just don't make any sense, and one doesn't even have to collect evidence on that. They fail right out of the gate, on basic logic.