Global IIA, Sen’s Impossibility Theorem and State-salient Decision Rules

[Somdeb Lahiri]

Dear All:

At the link below is a paper I had written more than a year ago, but requested a peer review report a few days ago.
https://www.preprints.org/manuscript/202410.1435/v1
The following is the review report on which no final decision is available as yet. However the comments may be worth some thought for those interested in the topic.

Regards.

Somdeb.

The paper is a ‘simple proof” in the context of “Pareto property, Global Independence of Irrelevant Alternatives. and State-salient Decision Rules”, appealing to “Sen’s Impossibility Theorem”. A critical evaluation of such proofs is out of place in view of the legendary mathematical certainty: if the premises are correct, the conclusion will necessarily be correct. However, I have a few open suggestions that the author/editor is free to reject or accept.

One of the essential contributory qualities of a research (journal) article (whether review, empirical or theoretical) is that it be informative. Usually with serious researchers, review or empirical articles are mostly so, very explicitly. The theoretical ones are information/innovation-rich, but the reach of that richness remains sometimes restrictive: some of these may be meant for only a small group of peers, but some are for a larger group, with an additional instructive orientation for enhanced accessibility. Such articles are structured and presented with a view to making the information not only available but also accessible to a larger readership. The article under review belongs to the first genre, meant for a limited set of peers, especially since it is only a proof. Even then, there is of course every scope of enhancing the reach of its intellectual richness, by restructuring and presenting it in an accessible framework (as in the original works of Arrow or Sen or in the interpretative textbook of Kelly, among others) for the benefit of the journal readers at large. It requires an interpretative language, instead of the present terse language of core mathematical logic. Besides, the paper must be a self-contained one; for example, even about the motivation for the proof and the mathematical framework, the paper says:

The motivation for the framework of this paper i.e., decision making with state (or criteria) dependent strict rankings of alternatives, can be found in Lahiri (2019). Our mathematical framework is the same as that of mathematical voting theory originating in the work of Pattanaik (1970), although our interpretation (as in Lahiri (2019)) is different.

I feel that it would be worthwhile to let most of the journal readers read and understand directly the motivations and the similarities and differences from a self-contained paper.

Moreover, the title of the paper appears a bit inappropriate, as the paper gives only a proof in the context of certain concepts, and not a direct study of the concepts as such. A title somewhat like the following may be appropriate: Pareto Property, Global Independence of Irrelevant Alternatives. and State-salient Decision Rules: A Simple proof appealing to Sen’s Impossibility Theorem.