Pollsters keep track of the gender of the people they call. This means that any poll can be broken down into two polls with entirely separate sets of respondents. The private polling firm Research2000 reported the gender breakdowns for all 795 [Note: This number was wrong earlier] of their weekly tracking poll questions done for dailykos.
These two separate smaller polls may look similar if men and women have similar opinions, but there is no overlap in respondents, so the precise % numbers are completely unrelated.
This means that if an odd-number percentage of men are “FAV”, it does not have any bearing on whether an odd or even % of women say “FAV”.
That said, we can look at all the questions that Research2000 asked, and count how often the men’s results and the women’s matched in being even or odd. For each question, there are four possible combinations:
Because the results come independently, each of these combinations is equally likely. So for the 795 weekly questions, we should have roughly 199 of each. Here are the actual tallies:
(Among “FAV” responses in questions with 3 possible responses asked in state polls only.)
How likely is this to happen by chance?
Well, this is roughly the equivalent of flipping two different coins 795 times, and only getting different results twice. It should happen by chance approximately:
One time in