  Maximality, interval dominance, and E-admissibility are three well-known
criteria for decision making under severe uncertainty using lower previsions.
We present a new fast algorithm for finding maximal gambles. We compare its
performance to existing algorithms, one proposed by Troffaes and Hable (2014),
and one by Jansen, Augustin, and Schollmeyer (2017). To do so, we develop a new
method for generating random decision problems with pre-specified ratios of
maximal and interval dominant gambles. Based on earlier work, we present
efficient ways to find common feasible starting points in these algorithms. We
then exploit these feasible starting points to develop early stopping criteria
for the primal-dual interior point method, further improving efficiency. We
find that the primal-dual interior point method works best. We also investigate
the use of interval dominance to eliminate non-maximal gambles. This can make
the problem smaller, and we observe that this benefits Jansen et al.'s
algorithm, but perhaps surprisingly, not the other two algorithms. We find that
our algorithm, without using interval dominance, outperforms all other
algorithms in all scenarios in our benchmarking.
