First thought, is the amount of one third of ownership you are thinking of sufficient to run an aircraft one third of price? If so, seriously take a second thought - an old 25,000 C172s usability is not far from a newer 75,000 C172 and you would not have the hazzle with other people (pilots have a tendency to not really be the best in such close groups). Even a 250,000 C172 will give you only glass, a 40 percent increase in fuel burn for 10 percent more knots and reduced usable load, compared to an old 20,000 C172.
Avoid fractional ownership, if your fraction would suit a smaller aircraft run on your own.
If you talk one third of a budget plane and it is your only chance to stay airborn, look for a group of people without friendship. It helps to be professional.