Logic and Social Choice (RLE Social Theory) by Yasusuke Murakami

Author:Yasusuke Murakami [Murakami, Yasusuke]
Language: eng
Format: epub
Tags: Social Science, Sociology, General
ISBN: 9781317651567
Google: wpiQBAAAQBAJ
Publisher: Routledge
Published: 2014-09-19T05:58:02+00:00

where x′ is an outcome of the individual decisions R′1, R′2, …, R′n.

This definition is a slight modification of M. Dummet and R. Farquharson’s formulation and, in a wider perspective, a variation of stability concepts developed in the theory of games. The interested reader should refer to R. D. Luce and H. Raiffa’s noted book Games And Decisions.

Let us first consider a simple majority voting based on pairwise comparison, and ask if such a social decision-making rule is stable. The following seemingly unstable example may be useful for understanding the present problem. Let us suppose that three individuals have the following individual preferences concerning an issue composed of three alternatives called La, Li and Con.

The first individual prefers La to Li and Li to Con.

The second individual prefers Li to Con and Con to La.

The third individual prefers Con to Li and Li to La.

Simple majority voting on the pair (La, Li) results in a social preference of Li to La. Similarly, Li is socially preferred to Con. Li is the most preferred alternative so that it is an outcome of sincere individual decisions.

Then let us suppose that the third individual does not vote according to his preference, and tries to manipulate the result in his favour. For this purpose, on the pair (La, Li) he votes for La against his preference. On the pair (La, Con) he votes for Con according to his preference. Simple majority votings on the pair (La, Li) and the pair (La, Con) result in the following social decision: Con is socially preferred to La and La is socially preferred to Li. Now Con seems to be the most preferred alternative or the new outcome, which, moreover, the third individual prefers to Li, the original outcome. The original outcome as a consequence of sincere votings seems to be unstable.

However, this is not the case. For, once the society votes on another pair (Li, Con), the society prefers Li to Con; any strategic move on the side of the third individual cannot alter this result. It can now be seen that the social decision as a whole is intransitive, so that there exists no most preferred alternative, that is, no outcome. Therefore, the third individual’s strategic move cannot produce the new outcome which is to replace the original outcome. Then, by definition, the original outcome of the sincere individual decisions is stable.

This example teaches us two lessons. In the first place, the minority’s—in the above example, the third individual’s—decision can be adopted as a ‘social decision’, if simple majority voting is not undertaken on all possible pairs of alternatives or, in other words, if the so-called round robin process is not completed. As an actual example, the procedural regulation in the U.S. House of Representatives restricts a number of the rounds of voting so that the minority opinion may possibly be adopted through the ingenious manoeuvre on the side of minority. The completion of the round robin process may be considered as essential to pairwise simple majority voting, if we want to avoid the minority rule under a possibility of insincere votings.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.