smc

As a consequence of the Triangle Inequality, we can form a quadrilateral from the four segments iff the sum of any three sides is greater than the sum of the fourth side. Thus, no segment can have a length $\ge \frac{1}{2}$. All other segment lengths are valid, so long as the inequality is satsified. Thus, our answer is $\boxed{\text{less than}\frac{1}{2}}$.