A difficulty in Arrow’s impossibility theorem

Abstract

Purpose

The purpose of this paper is twofold. First, it evaluates the impossibility proposition, called the “Arrow impossibility theorem” (AIT), which is widely attributed to Arrow’s social choice theory. This theorem denies the possibility of arriving at any collective majority resolution in any group voting system if the social choice function must satisfy “certain natural conditions”. Second, it intends to show the reasons behind the proliferation of this impossibility impression.

Design/methodology/approach

Theoretical and philosophical.

Findings

Arrow’s mathematical model does not seem to suggest or support his impossibility thesis. He has considered only one voting outcome, well known by the phrase “the Condorcet paradox”. However, other voting results are equally likely from his model, which might suggest unambiguous majority choice. This logical dilemma has been created by Arrow’s excessive dependence on the language of mathematics and symbolic logic.

Research limitations/implications

The languages of mathematics and symbolic logic – numbers, letters and signs – have definite advantages in scientific argumentation and reasoning. These numbers and letters being invented however do not have any behavioural characteristics, which suggests that conclusions drawn from the model merely reflect the author’s opinions. The AIT is a good example of this logical dilemma.

Social implications

The modern social choice theory, which is founded on the AIT, seems to be an academic assault to the system of democratic governance that is dominating current global village. By highlighting weaknesses in the AIT, this paper attempts to discredit this intellectual omission.

Originality/value

The paper offers a counter example to show that the impossibility of social choice is not necessarily implied by the Arrow’s model. Second, it uses Locke’s theory of human understanding to explain why the concerned social scientists are missing this point. This approach is probably entirely novel in this area of research.

Citation

Qudrat-I Elahi, K. (2017), "A difficulty in Arrow’s impossibility theorem", International Journal of Social Economics, Vol. 44 No. 12, pp. 1609-1621. https://doi.org/10.1108/IJSE-02-2016-0065