An answer (now deleted) at the new Islam.SE site made the following claim:
If one takes a look at society where polygamy is banned or discouraged, you will see that some men will always try to fulfill their need for more partners by illegal means; which gives rise to the ‘oldest profession in the world’: prostitution. Seldom has there been a demand for male prostitution in the annals of history.
The same claim is mentioned on this Islam site:
At this point, the apologist usually falls back on a defense of polygamy - claiming that it reduces prostitution, for example - while effectively conceding that men and women are equal in Islam except with[sic] they aren't.
And again in this news release (full article quoted, due to reports of unreliable paywall):
Kadyrov Says Polygamy Reduces Promiscuity
Chechen President Ramzan Kadyrov said Monday that he supports polygamy among Russian Muslims because it reduces sexual promiscuity and prostitution.
“That’s a tradition we’ve always had. God allows Muslims to do so,” Kadyrov, 33, said in an interview broadcast by state-run RT television. “Is it better to have 20 lovers rather than four lawful wives?”
Kadyrov said he was not asking federal authorities to the change law, which prohibits multiple marriages. Polygamy makes men accountable to their wives and reduces philandering, he said.
Kadyrov is “married with seven children,” according to his web site.
Is it true that polygamous behavior (specifically polygyny) leads to lower rates of marital infidelity and/or prostitution?