I suspect that democracy is actually a driver here. I think that it's possible that the calculation is that "fans" will vote for a representative who backs the stadium where as most other voters will not care about the issue, and will switch off when it's raised as it's a "sports" thing. If you don't back the stadium then your opponent's will and you'll be out! Also I guess this falls into the "any publicity is good" bucket - so you back the stadium and the rich folks driving it will ensure that you are at events where the TV cameras are running and your face is on the screen.