Unfortunately, it's not just elected officials that are problematic for prediction markets. The Secretary of War, for instance is not an elected official nor are leaders of the armed forces and there is definitely a prediction market for war. Multiply this by every powerful appointee and every career bureaucrat and see what kind of picture that paints.
If we're not going to ban prediction markets, we could at least make it a requirement that all bets are public and associated with a real identity.
That'd go a long way towards curbing the corruption of these things, while preserving (or even greatly enhancing) their "predictive power."