Boolean functions whose Fourier transform is concentrated on the first two levels. (English) Zbl 1039.91014

This mathematical paper on Boolean functions has an interesting application in the study of neutral social choice functions. If the outcome (a strict social preference) of a neutral social choice function for random profiles is almost surely rational (transitive), then the social choice is approximately a dictatorship (the approximation being appropriately defined).
Reviewer: M. Salles (Caen)


91B14 Social choice
06E30 Boolean functions
Full Text: DOI


[1] Beckner, W., Inequalities in Fourier analysis, Ann. of math., 102, 159-182, (1975) · Zbl 0338.42017
[2] Bonami, A., Étude des coefficients Fourier des fonctiones de Lp(G), Ann. inst. Fourier, 20, 335-402, (1970) · Zbl 0195.42501
[3] Friedgut, E., Boolean functions with low average sensitivity, Combinatorica, 18, 27-35, (1998) · Zbl 0909.06008
[4] Hart, S., A note on the edges of the n-cube, Discrete math., 14, 157-163, (1976) · Zbl 0363.05058
[5] Kalai, G., A Fourier-theoretic perspective for the Condorcet paradox and Arrow’s theorem, Adv. appl. math., (2002), this issue · Zbl 1038.91027
[6] König, H.; Schütt, C.; Tomczak-Jaegermann, N., Projection constants of symmetric spaces and variants of Khintchine’s inequality, J. reine angew. math., 511, 1-42, (1999) · Zbl 0926.46008
[7] Latała, R.; Oleszkiewicz, K., On the best constant in the khinchin – kahane inequality, Studia math., 109, 1, 101-104, (1994) · Zbl 0812.60010
[8] Szarek, S.J., On the best constant in the Khinchin inequality, Studia math., 58, 2, 197-208, (1976) · Zbl 0424.42014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.