Optimal preference satisfaction for conflict-free joint decisions

Shinkawa, Hiroaki; Chauvet, Nicolas; Bachelier, Guillaume; Röhm, André; Horisaki, Ryoichi; Naruse, Makoto

doi:10.48550/arxiv.2205.00799

Cited by 1 publication

(8 citation statements)

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“…Those previous studies aimed to maximize total cumulative rewards by making conflict-free decisions. Conversely, the present research, as well as the related former work [5], exclude external factors such as rewards. Instead, the focus is on how to accomplish the maximization of preference satisfaction; that is, how well the player's preference is reflected in the joint decision.…”

Section: Introductionmentioning

confidence: 65%

“…In this section, we review the problem settings of the conflict-free probabilistic preference satisfaction proposed in Ref. [5]. Suppose that two players, player A and B, have probabilistic preferences over N options (N ≥ 2).…”

Section: Preference Satisfaction By Conflict-free Joint Decisions a P...mentioning

confidence: 99%

“…In this section, we review principal theorems on the optimal joint selection probability matrix from [5] and clarify two problems associated with them. We define a score called the popularity, which represents how much each option is favored by the players.…”

Section: B Optimal Joint Selection Probability Matrixmentioning

confidence: 99%

“…In the previous study, we extended the preference from a deterministic to a probabilistic one and mathematically discussed how a joint selection that satisfies players' probabilistic preferences should be made [5]. In uncertain situations, people in the real world or agents in reinforcement learning are often torn between the desire to choose the best current option and the desire to explore other options [6].…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [5], a joint selection probability matrix that maximizes the satisfaction of the probabilistic preferences of two players is mathematically derived. However, as we will confirm later, two concerns exist.…”

Section: Introductionmentioning

confidence: 99%

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Conflict-free joint sampling for preference satisfaction through quantum interference

Shinkawa¹,

Chauvet²,

Röhm³

et al. 2022

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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 conflictfree joint sampling methods through 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.

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Section: Introductionmentioning

confidence: 65%

Section: Preference Satisfaction By Conflict-free Joint Decisions a P...mentioning

confidence: 99%

Section: B Optimal Joint Selection Probability Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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