Conflict-Free Joint Sampling for Preference Satisfaction through Quantum Interference

Abstract

Collective decision making is vital for recent information and communications technologies. In our previous research, we mathematically derived conflict-free joint decision making that optimally satisfies players' probabilistic preference profiles. However, two problems exist regarding the optimal joint decision-making method. First, as the number of choices increases, the computational cost of calculating the optimal joint selection probability matrix explodes. Second, to derive the optimal joint selection probability matrix, all players must disclose their probabilistic preferences. Now, it is noteworthy that explicit calculation of the joint probability distribution is not necessarily needed; what is necessary for collective decisions is sampling. This study examines several sampling methods that converge to heuristic joint selection probability matrices that satisfy players' preferences. We show that they can significantly reduce the above problems of computational cost and confidentiality. We analyze the probability distribution each of the sampling methods converges to, as well as the computational cost required and the confidentiality secured. In particular, we introduce two conflict-free joint sampling methods through the quantum interference of photons. The first system allows the players to hide their choices while satisfying the players' preferences almost perfectly when they have the same preferences. The second system, where the physical nature of light replaces the expensive computational cost, also conceals their choices under the assumption that they have a trusted third party.

Asymmetric quantum decision-making

“…Quantum approaches have been extensively studied to solve uncertain problems 8 – 13 . The quantum properties of photons can aid in solving the problem of decision conflicts in collective decision-making 5 , 14 , 15 . Two previous studies developed quantum systems enabling conflict-free decision-making between two players.…”

“…Two previous studies developed quantum systems enabling conflict-free decision-making between two players. The first study utilized the Hong–Ou–Mandel effect of orbital angular momentum (OAM) 14 , 15 , whereas the second one utilized entangled photons 5 .…”

Asymmetric quantum decision-making

“…Quantum approaches have been extensively studied to solve uncertain problems [8][9][10][11][12][13] . The quantum properties of photons can aid in solving the problem of decision conflicts in collective decision-making 5,14,15 . Two previous studies developed quantum systems enabling conflict-free decision-making between two players.…”