Militate is a verb that means to have a significant and influential part or effect. The verb is usually used with the word against and is therefore negative most of the time. Militate against is used to speak of halting or preventing things. It should be noted that militate does not have an object and is an intransitive verb.
When militate is used in the positive sense, it is usually paired with toward or towards. The prevalence of either is about equal, and both are extremely rare and should be used with caution.
Mitigate is a transitive verb, requiring an object, that means to lessen the degree of pain, severity, or harshness of something. It is commonly used in its adjective form mitigating, as in mitigating circumstances.
Other adjective forms for mitigate are mitigatory and mitigative. Noun forms can be either mitiation or mitigator.
Even thought mitigate against may seem like a logical phrase, it is more commonly seen as a confusion of militate and should be avoided.
According to her, the non-release of funds had continued to militate against effective implementation of projects. [All Africa]
“If history is a guide, these trends militate towards long-term expansion of freedom and rights.” [The New York Times]
A recent survey of 300 universities globally by the Asset Owners Disclosure Project found that 98 per cent were doing nothing to mitigate the damage caused by climate change, although they were major contributors to scientific research in helping climate change. [The Australian]