Re: What percentage of title fights...
I suspect that before ~1920, many of them were fixed. Boxing was just getting out from underground and shady characters were running everything in broad daylight -at least until the cops kicked the doors in to the warehouse. Perhaps 5-10% were not completely on the level.
After it got more organized and the modern era was ushered in but before Valachi turned and blew the cover of La Cosa Nostra, Blinky Palermo and co. weren't quite running things in broad daylight, but their presence was known and felt by everyone. They were strong in the shadows and behind straw men. I'd hazard that 1-3% of title fights were tainted.
Since then, I think that fixes are happenstance and ****omous. Too much risk of exposure. In '93, Ray Mercer tried to bribe his way to a win over Ferguson during the bout and suddenly he was in the New York Times. Overall, another factor may be better purses... the temptation is less.