Poll: 'Might' _____ the past tense of 'may'.
'Might' _____ the past tense of 'may'.
Many of the comments suggested with carved-in-stone certainty are quite specious because of the growing disuse and ignorance of the subjunctive forms in English. If the subjunctive WERE used more frequently we MIGHT/SHOULD/WOULD not be so confused.
You might have asked for past tense of 'may have' in which case I would have looked to choose 'might have'.