  We all have preferences when multiple choices are available. If we insist on
satisfying our preferences only, we may suffer a loss due to conflicts with
other people's identical selections. Such a case applies when the choice cannot
be divided into multiple pieces due to the intrinsic nature of the resources.
Former studies, such as the top trading cycle, examined how to conduct fair
joint decision-making while avoiding decision conflicts from the perspective of
game theory when multiple players have their own deterministic preference
profiles. However, in reality, probabilistic preferences can naturally appear
in relation to the stochastic decision-making of humans. Here, we theoretically
derive conflict-free joint decision-making that can satisfy the probabilistic
preferences of all individual players. More specifically, we mathematically
prove the conditions wherein the deviation of the resultant chance of obtaining
each choice from the individual preference profile, which we call the loss,
becomes zero, meaning that all players' satisfaction is perfectly appreciated
while avoiding decision conflicts. Furthermore, even in situations where
zero-loss conflict-free joint decision-making is unachievable, we show how to
derive joint decision-making that accomplishes the theoretical minimum loss
while ensuring conflict-free choices. Numerical demonstrations are also shown
with several benchmarks.
