The answer here is E.
This is not an LSAT question. I have searched and it is not. krishnakumarhod indicates that this is an older GMAT question from the paper tests.
This question is indeed an example of cause and effect. The effect is the thing that is observed and is not debatable. In this case we have observed that women win fewer elections. This is what needs to be explained. It says so right in the stimulus, "the reason there are so few women who win elections for these offices..." so you can see that we are trying to explain why women win few elections.
Now the cause it the thing that we want to weaken. In the stimulus they say the cause is that - and here the wording is very important "so few women want to run." So that is what they are saying that women do not want to run and that is why the do not win the elections. Now, the evidence for women not wanting to run is that only 15% of candidates for office are women.
Now we need to show a different reason, consistent with that evidence, that will explain why only 15% of the candidates are women. So we do not want to say that the women do not want to run for office but that there is another reason. The other reason is found in choice E -- the women may want to run but they do not because they cannot get adequate funding their campaigns. So this is a different cause and weakens the argument.
Choice B is not particularly relevant as it just says that the women do not run against other women. This is to be expected since there are only 15% of candidates that are women and so rather than explaining why so few women run it is a consequence of so few women running. It is not the cause but rather another effect and so cannot be the answer.