Your behavior seems to be formulated as if there is a huge issue of "false" accusations going on within the metoo movement. I haven't seen anything to make me think that there is a serious risk of being falsely accused.
Chance need not be huge. Anything times negative inf is negative inf. Your career will be hurt by any false accusations, no matter how unlikely. Your family won't care how unlikely the accusation that ended their livelihood was.
In that case, I wholeheartedly disagree that mentoring people, especially very talented ones, be they women or men has little or no value for one's career and/or life.
Staying in your own little homogeneous bubble and avoid contact with anyone not like you or doing anything outside what objectively gives you direct, measurable value seems like a surefire way to stagnate your career.
And the chance of a false accusation has always been around. So to act so indignant now seems more to throw water on the movement than to truly be worried about your personal career progress.
I mentor plenty of people, women included, thank you very much. I am always willing to help.
What I am not willing to do is stick my and my families' neck on the line and take unnecessary career risks. I don't run in fear of women, I just take necessary precautions when dealing with a hazard.
I didn't create this environment where males, especially white middle-class males, are morally wrong for simply existing. And where any comment you say could be posted on twitter and you have a mob of people who say such nice things as "kill white people" are ready to harass you until you lose your job and everything you worked for. I am just reacting to it in a way that prevents me from falling victim to what I see as a threat to my career and protects my livelyhood and family.
Twenty years ago, I never felt like being alone with a woman in the office was a danger. Now, I feel like if I am not taking active measures, I could be crucified by HR, females, and the twitter / internet mob in the blink of an eye for simply making a comment that was taken the wrong way.
Ok. It has a lot of value. A lot is finite. Negative inf is still overpowering in that equation. That's the point OP made that you seem to be trying very hard to avoid addressing.
Because "negative infinity" is just hyperbole in this case. Some careers have been harmed or even destroyed, but we aren't seeing accused men wondering the streets homeless just yet (or whatever you want to equate to the most terrible outcome).
Most that have been reported in the news are wealthy enough to retire in comfort already. Beyond that, I'm not sure there is a huge number of non-public people losing their jobs over accusations (especially false ones).
If we assume that all accusation are true unless proven in a court of law, and all ""false"" accusations to be false unless proven in court, then the risk is very small.
Otherwise the rate that I tend to see in articles about it is estimated to be around 10-33% based on game theory.
ExpectedValueOfSaidMentoring = -inf * chanceFalseAccusation + negligiblySmall * (1 - chanceFalseAccusation)
This is what OP meant.
Chance need not be huge. Anything times negative inf is negative inf. Your career will be hurt by any false accusations, no matter how unlikely. Your family won't care how unlikely the accusation that ended their livelihood was.