The axiomatic foundation of social choice theory, established by Arrow and extended through a game-theoretic perspective by Gibbard and Satterthwaite, demonstrates that under an unrestricted set of preference profiles, only dictatorial outcomes are possible. In this study, we translated these axiomatic conditions into logic programming with Prolog to systematically investigate the logical structure of the basic model, a social choice function (SCF) involving two individuals and three alternatives with linear-order preference profiles. In particular, we examined the Gibbard-Satterthwaite-type SCF, a strategy-proof, non-imposed surjective function defined over a restricted preference domain, revealing its greater structural complexity compared to the Arrow-type SCF. By analyzing and visualizing dictatorial sequences that emeｍge as the domain expands, we identified interactions between cyclical components, designated as α-rings, γ-rings, and π-rings, which partition the unrestricted domain. We generated all maximal domains obtainable through systematic preference pair deletions (18 for Arrow-type SCFs and 54 for Gibbard-Satterthwaite-type SCFs) and ranked them according to the relative frequency of non-optimal outcomes for individual 1, referred to as the inequality index. Furthermore, we applied the concept of narratorial forms, parameterized oracles, to clarify the principles of covariation between these maximal γ-possible domains and their possible SCFs. Maximal γ-possible SCFs were generated by the narratorial form centered on symmetric pairs from π-rings in the case of symmetric pair deletion, and even when they deviate, they remain variants of this form. The extent of deviation from the narratorial form correlates with the inequality index and shifts toward dictatorial outcomes.

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In this study, we investigated the multifractality of intertrade durations (with a time resolution of 0.001 seconds) for bitcoin listed on Binance, the world's largest cryptocurrency exchange, over the period from 14:00 (UTC) on July 8, 2022, to 23:59 on March 22, 2023.We conducted multifractal detrended fluctuation analysis on the following four types of intertrade duration data: (i) Original data, consisting of approximately 1.6 billion entries collected. (ii) Zero-excluded data, which comprises approximately 600 million entries obtained by excluding instances of zero intertrade durations from the original data. (iii) Square root transformed data, which involves applying a square root transformation to the original data to approximate a gaussian distribution and mitigate the impact of long tails. (iv) Seasonally adjusted data, derived by removing non-stationary components caused by intraday seasonality from the original data. It was revealed that the original data exhibits multifractality. The multifractality strength of the zero-excluded data is nearly identical to that of the original data, indicating that zero intertrade durations have minimal impact on multifractality. In contrast, the square root transformed data was found to weaken multifractality. Approximately 30% of the multifractality in the original data is attributed to the power-law distribution, with its impact being particularly pronounced in the domain of small fluctuations. Furthermore, seasonally adjusted data was also found to weaken multifractality. About 20% of the multifractality in the original data is attributed to intraday seasonality, with its effects being especially prominent in the domain of small fluctuations.

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