I hate the idea of mentioning something about men's rights and then looking like a fool because I was misinformed or missed important points in favor of the other side. Obviously I believe that my side is the right one, but who doesn't? Here's a list of ways to mitigate cognitive biases I came up with:

Contradictory evidence:

  • Acknowledge and don't filter out counter-evidence.
  • Be careful about assuming a trend exists too early; find more data points that disagree with your position as well as data points that agree with your position, and look for systematic reviews that try to establish a trend through statistical means.
  • Consider that the absence of contradictory evidence does not prove an assertion.
  • Consider even the most seemingly absurd counter-arguments.
  • Consider that the presence of absurd counter-arguments doesn't preclude the existence of more reasonable counter-arguments.

Overconfidence/Pessimism:

  • Interpret evidence in favor of your argument to their weakest conclusions, unless the evidence is particularly strong.
  • Don't assume you know what the other side is thinking, and ask them to elaborate.
  • Be careful with pessimistic predictions about the future. Be careful with assertions about the past, especially if they are "common knowledge" for people who hold the same opinion as you.
  • Assume the complexity of the issue and don't let overconfidence and hastiness mislead you into taking a stance too quickly.
  • Acknowledge your lack of knowledge and skill in a subject you were not trained in, particularly when it comes to statistics.

Non-factual influences:

  • Biased sources: Consider that your sources are inherently biased; look for sources that radically oppose your position as well as sources that have a more moderate view on the issue.
  • Recognize when you fall victim to the Halo Effect, that is "the tendency for positive impressions of a person, company, brand or product in one area to positively influence one's opinion or feelings in other areas" (Wikipedia).
  • Men – and, even more, women – have an innate emotional bias in favor of women. Check yourself consciously: is what I'm thinking rational and justified, or do I alter my claims in favor of women on the basis of their sex, however slightly? See Gamma Bias and Gender Empathy Gap.

Other:

  • Cherry picking: If you have multiple sources in your argument, but they contradict each other in some points, don't pick all the points that are in favor of your argument; look out for consistency. When debating someone, consider that there might be a truth to what they say, even if you don't agree with the majority of their points.
  • If defining a term makes the topic more confusing, stop using it, and instead say exactly what you mean. Many lies and errors hide behind bad definitions and vague terminology. Also consider that if a term causes friction with people who hold the opposite view that you do, it might be a good idea to not use it and instead paraphrase when discussing with them.
  • Bias bias: Recognize that you can also be too careful and be biased to doubt yourself. Sometimes you need to be confident in what you believe.

I hope this list can inspire a culture of rationality in this sub.