A general impossibility theorem and its application to individual rights

Abstract

Please cite this article as: Yi, J., Li, Y., A general impossibility theorem and its application to individual rights. Mathematical Social Sciences (2016), http://dx.This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Research highlights > We prove that it is impossible to find an incentive compatible social choice mechanism with finite social welfare losses > The impossibility also occur even if we replace incentive compatibility with approximately incentive compatibility. > We discuss the compatibility problems between incentive and individual rights. AbstractIn this paper, we generalize Green-Laffont's (1979) impossibility theorem to the following form: in quasi-linear environments, when the set of each agent's types is sufficiently rich, we can not find mechanisms that allow bounded deviations from the decisive efficiency, incentive compatibility and budget-balance at the same time. Hence, it is impossible to find an incentive compatible mechanism with minimum social welfare losses. Furthermore, we discuss the compatibility problems between incentive and individual rights in a quasi-linear environment (see Sen, 1970aSen, , 1970bDeb et al., 1997). Specifically, some new impossibility results are established. JEL Classification: C79; D82; D71.

Designing efficient and incentive compatible mechanisms is almost impossible in quasi-linear environments

“…Our impossibility theorem reveals that it is impossible to design incentive-compatible and efficient mechanisms in quasi-linear environments because budget constraints always exist in practical *Manuscript Click here to view linked References application. Furthermore, we prove that there is no efficient and incentive compatible mechanism satisfying (absolutely) budget boundedness over positive domains, which extends the results of Yi and Li (2016) to a class of restricted domains. Note that, our impossibility theorems imply: there does not exist an efficient and incentive compatible mechanism that satisfies absolutely or relative budget boundedness over both unrestricted and some restricted domains.…”

“…However, under unrestricted domains, Green and Laffont (1979) show that VCG mechanism does not satisfy budget-balance and hence there is waste or loss of efficiency. Yi and Li (2016) prove further that there is no decisively efficient and incentive compatible mechanism ( , ) that satisfies budget-boundedness. It means that VCG mechanism is infeasible in practice if the maximum loss that a society can afford is 0 ∈ (0, +∞).…”

“…However, when the general budget feasibility is replaced by absolute budget-boundedness, we have following impossibility Theorem 2, which is a generalization of Yi and Li (2016) We first show that ∑ (−1) #( ) ⊆ ( , − ′ ) is bounded over × .…”

“…Cavallo (2006), Guo and Conitzer (2009); Mehta et al, (2009); Moulin (2010) make attempts to estimate and minimize the budget imbalance. Yi and Li (2016) conclude that there is no VCG mechanism whose worst absolute loss of efficiency is finite over unrestricted domains. In addition, Moulin (2009) studies the relative boundedness of budget.…”

“…In this paper, we consider a class of general financial constraints of budget in which each constraint is given by a function that assigns a bound on the loss of efficiency to any profile of individuals' utilities. It is easy to check that our new budget constraints are weaker than the following requirements: budget balance (Green and Laffont, 1979;Walker, 1980), absolute budget boundedness (Yi and Li, 2016), individuals' budget constraint (Che and Gale, 1998, Laffont and Robert, 1996, Maskin, 2000Svensson, 2014, 2016), individual rationality requirement, and relative boundedness of budget (Moulin, 2009).…”