Further results on dictatorial domains
- 263 Downloads
This paper generalizes the results in Aswal et al. (Econ Theory 22:45–62, 2003) on dictatorial domains. This is done in two ways. In the first, the notion of connections between pairs of alternatives in Aswal et al. (2003) is weakened to weak connectedness. This notion requires the specification of four preference orderings for every alternative pair. Domains that are linked in the sense of Aswal et al. (2003) with weak connectedness replacing connectedness, are shown to be dictatorial. In the second, the notion of connections for alternative pairs is strengthened relative to its counterpart in Aswal et al. (2003). However, a domain is shown to be dictatorial if the induced graph is merely connected rather than linked. This result generalizes the result in Sato (Rev Econ Design 14:331–342, 2010) on circular domains.
I am deeply indebted to my supervisor Arunava Sen for guiding me in writing this paper. I am very thankful to Sarvesh Bandhu, Debasis Mishra, Hans Peters, Souvik Roy, James Schummer, Shigehiro Serizawa, William Thomson, Rakesh Vohra and two anonymous referees for very useful comments and suggestions. I am also thankful to the seminar participants at the 2014 Society for Social Choice and Welfare meeting for their helpful comments. An earlier version of this paper forms a chapter of my Ph.D. dissertation, submitted to the Indian Statistical Institute, New Delhi in 2014. All remaining errors are my own.