If you do that poll repeatedly, over many groups and many industries and many times and many subsets, and in every case the men are paid more (whether 5% or 23%), there is either an actual statistical difference, or Maxwell's social justice demon is out to get you.
And if there is an actual statistical difference, the question is why. Are men more valuable to the market?
That's a great idea! Someone should do that study one of these days instead of just relying on the aggregate BLS statistics that the 77% number is drawn from. Sadly, I doubt it'll happen...
And if so, why? Maybe men and women work equally hard, all else being equal, but in a society where a man's income is used to determine his worth as a person to a greater extent that a woman's income is used to determine her worth, a man will spend more time focusing on improving his income, and thus work in ways that provide more value by sacrificing quality of life (while a woman in such a society would focus on increasing what ever attributes the society judges her worthiness based upon). In such a case, there is clearly sexism, but unequal pay is not the cause, only a symptom, and thus equalizing pay will only cover up a symptom of the deeper problem (and perhaps even exaggerating the problem).
The sexes are NOT the same and should not be treated the same. In fact it is quite ironic how the libertarian leaning HN crowd manages to fit the conflicting facts of just markets and wage discrimination in their collective heads.
If you want to be particularly devil's advocate about it, there was a time when the "gender pay gap" was 90%+ because the majority of women didn't work at all. It's a rather recent invention that everyone should work, and yet more recent that everyone should work all the time and still not be able to make ends meet.
Which is to say, I'm not sure why advocating for this particular devil is constructive. Do you believe that a well-functioning society should have women being less valuable to the free market than men?