Stephen Roman responds to a post from Professor Bainbridge, which was a response to Wolfers and Zitzewitz' question about Manipulation in their 5 Open Questions About Prediction Markets paper. That paper didn't bring up insider trading; the manipulation section focused on attempts to change outcomes by changing prices. Bainbridge's approach is to ask how bad insider trading could be since firms don't seem to have prohibited it on their own.
Roman tries to address the question of whether there is ever a reason for a prediction market exchange to ban insider trading. His answer is that it's never in the interest of the exchange or any of the participants to refuse admission to anyone. This argument leaves out an important part of the argument, though. The reason people keep asking the question is that they thought they learned from stock markets that it was important to prevent it. If stock markets are right to ban insiders from trading, what's the difference, and what does that imply for prediction markets?
The reason insiders are banned from trading on stock markets isn't because of their effect on prices or information, it's because having something to gain from the company's losses might give them reason to act against the company's interests. (In the insurance field, this is called "moral hazard".) The reason the major stock markets publicize and help enforce the ban is because the companies are their customers, and the exchanges and the companies share an interest in making the market appear to be free of that influence.
Another rationale for the ban is to prevent insiders from profiting from early access to information, but I think that is a secondary concern. If the moral hazard created by allowing people to trade against their employer's interests weren't present, it would be much harder to figure out where to draw the line to say who has unfair early access to information.
In the absence of such rules from the exchange, it would still make sense for companies to make and enforce explicit rules prohibiting employees from taking positions against the interests of companies when they have privileged access to information. This might clearly apply to some specific prediction market contracts, but companies would probably find it more effective to make a general rule than to try to maintain an explicit list of forbidden contracts or topics.
In the end, I agree with Stephen that prediction markets shouldn't ban insider trading. But it's not because all insider trading is benign, it's because insider trading is a net benefit in these markets, and the conflicts of interest can be handled closer to where they occur. And the answer to Bainbridge's question is that companies haven't done anything voluntarily because the stock exchanges already prohibit it. I think you have to look somewhere other than publicly traded companies to find examples of voluntary enforcement.