My official position on the manner in which consenting adults choose to arrange their personal lives is: I don’t care. In reality, I faintly disapprove of almost everything everyone else does, generally for petty reasons of my own, hence the need to establish an official position. I want to be thought of as someone who is hard to scandalise.

The Men With Many Wives (Channel 4), a documentary about polygamy among British Muslims, should not have presented much of a challenge. Polygamy is illegal in Britain, but permitted under sharia law. There are by some estimates up to 20,000 polygamous marriages in Britain. Personally, I think polygamy is a bad look – belittling to women and hard to justify on any grounds, religious or otherwise – but if everybody involved is a willing participant, then officially, I don’t care.

I will, however, permit myself a bit of bewilderment: why? Who would be a polygamist?

“There are a lot of guys out there who are very well established, very successful men who can handle two, three wives easily,” said multiple-marriage broker Mizan Raja. “No problem, ’cos they got high libido rates, they sincerely want more children, you know, why not?”

Hasan, 32, tried to make it sound as if he were doing his soon-to-be third wife a giant favour. She doesn’t yet wear the niqab like his other two wives, so he’s gone down to the shops to pick one out for her. “This is the new one,” said the shopkeeper, holding up an example in black. I confess I was a bit surprised by that. I didn’t realise they were still coming out with new models.

Hasan’s third wedding was to be a low-key affair; he wouldn’t invite his other wives. “Even though they’re accepting of polygamy, you don’t want to rub their faces in it,” he said. This is the kind of thoughtful thing Hasan was prone to say, but when you watched him pick up his kids from nursery, take them home and give them their tea while his wife – well, one of his wives – was at work, you might be tempted to think: “As long as everyone’s cool with it, is polygamy really so terrible?” I don’t think that, though. I don’t think anything.

Omar, a physicist, met Raja with an eye toward acquiring a second wife. When asked why, he said: “No reason other than this is allowed.” His wife seemed just as keen. “I want to revive something that’s dying out,” she said. It is not my place to point out that these are both terrible reasons.

It fell to the marriage broker to explain the attraction for men. “For 80%, it’s a sexually driven thing,” he said. For the women, he said, it offers security. Many of his female clients are divorced with children, and are willing to become a second or third wife rather than be alone and unsupported. Shaheen is one such woman, who is now both a co-wife and a single mother – her husband hasn’t been around in months, and she is planning a sharia divorce.

After Hasan’s wedding, his new wife obediently donned the niqab. “Some people cover their cars,” he said. “In a similar way, my wife is being covered as protection for me.” At that point, I had to sort of remind myself that I didn’t care. He spent his wedding night at the house of one of his other wives. I guess you can’t really mess with the rota.

Up in Sheffield, Mohammed was keeping two families in separate houses, plus a third in Morocco, despite being unemployed. He has 11 children altogether, with some of his benefits going out to support his Moroccan family. I think I may disapprove of this. His British wives didn’t like it much either. It’s a shame, they were all constantly telling him, that they have to share him with two other wives. He held up his palms in self-exculpatory fashion. “This is Islam!” he said.

The Men With Many Wives was an unusually clear-eyed documentary that took all its subjects seriously and at face value. It was primarily a story of people struggling to keep relationships – lots of relationships – operative and afloat. More than anything else, it made one think about parallel hypocrisies in western marriage traditions. That’s what I’ll be thinking about for the rest of the week.

The programme ended with Hasan in his car, driving from one wife to another. “They say absence makes the heart grow fonder, isn’t it,” he said. A postscript told us that Hasan and his new wife have now separated. Were I in a position to care, I’d say she was well out of it.