Create a space in this interface specifically for providing links to research, so that it's easier to make our case.

In some cases, a petition might require knowledge that an ordinary person reading the petition might not have. Furthermore, 800 characters can go by fast when there are, say ten links in the description, and the argument seems absurd. The necessity of providing research for one's arguments should be clarified, and accommodated, further than it currently is.
So, by providing extra space for links and research, arguments can be fully expressed, and people can feel that they have not been rejected without cause.