On the size of minimum super arrovian domains

Published

Journal Article

Arrow's celebrated impossibility theorem states that a sufficiently diverse domain of voter preference profiles cannot be mapped into social orders of the alternatives without violating at least one of three appealing conditions. Following Fishburn and Kelly, we define a set of strict preference profiles to be super Arrovian if Arrow's impossibility theorem holds for this set and each of its strict preference profile supersets. We write σ(m, n) for the size of the smallest super Arrovian set for m alternatives and n voters. We show that σ(m, 2) = [2m/m-2] and σ(3, 3) = 19. We also show that σ(m, n) is bounded by a constant for fixed n and bounded on both sides by a constant times 2n for fixed m. In particular, we find that limn→∞ σ(3, n)/2n = 3. Finally, we answer two questions posed by Fishburn and Kelly on the structure of minimum and minimal super Arrovian sets.

Full Text

Duke Authors

Cited Authors

  • Dasgupta, S

Published Date

  • January 1, 1999

Published In

Volume / Issue

  • 12 / 4

Start / End Page

  • 524 - 534

International Standard Serial Number (ISSN)

  • 0895-4801

Digital Object Identifier (DOI)

  • 10.1137/S0895480198332521

Citation Source

  • Scopus