Once could be "way too often."

You believe that ruthless, manipulative people become leaders because those characteristics are commonly valued. I believe it happens because they disguise those qualities. That is another fundamental unresolvable difference of opinion between you and me.

No doubt, some people value ruthlessness and manipulativeness, but they are limited in number.

I'm not sure what you mean by "hardness." If it means the ability to make clear, firm decisions, then I am guilty. I consider that quality to be valuable in a leader.

I have never been in a leadership position. I have never had to select anyone to be in such a position. There is one exception. I was once elected to a position as a union steward. It was an accident. A friend was assigned the task of recruiting candidates. He asked me, and I agreed. I assumed someone would run against me and prevail. I assumed wrong. As the only candidate, I won the election. I held the position for years; I could not find anyone willing to replace me.

I was a very ineffective steward, just terrible. For some reason, my coworkers often claimed that I would make a good union president. I can't imagine why. I would tell them that if I were the president of the union, they would be disappointed. I would be just as corrupt as the rest of them and better at it.

I don't have enough experience with leadership to understand how one goes about leading effectively. I have no idea what problems a leader faces or how one addresses those problems. I cannot judge what qualities make one a good leader.

Here is an article I read recently describing what the author considers the qualities of a good leader. I can't disagree with him.

https://medium.com/@TobiasCharles/how-to-be-a-manager-everyone-wants-to-work-for-40490d1acba5

The research you quoted suggests that people look for different qualities in men than in women. That doesn't surprise me.