Okay, then. What do you think the problem is? Do you have any ideas for a solution?
Here's one problem, or question, anyway:
Does it make sense to allow any man to use a women's restroom, locker room or similar segregated space for women, simply by declaring that he wants to do so?
That's one of the proposals on the table, and I wouldn't mind your take on it.
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I think your third bathroom solves a separate but related problem: What to do for men who choose to present as women, and who are at risk of harassment or assault if they go into a men's bathroom.
Your solution is a bit of a compromise, which has been thoroughly discussed, so I won't re-hash it again.
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Another solution, that has some support in trans-advocacy circles, is that transwomen should be allowed to decide for themselves. Pre-op, post-op, presenting, not presenting, notional-only, any man at any time is entitled to declare trans status and use a women's restroom.
This solution very nicely avoids the problem of how to verify that a transwoman is "legitimate" without having to resort to "papers please" or some other form of social or official inspection. That's a really big problem. It's definitely an advantage of this solution that it solves that problem.
It does, however, raise other problems, or potential problems, that have not yet really been addressed. Maybe your compromise is the closest we can get.
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So.
Does it make sense to allow any man to use a women's restroom, locker room or similar segregated space for women, simply by declaring that he wants to do so?
What do you think?