A pure theory of population distribution when preferences are ordinal

Oded Stark*, Grzegorz Kosiorowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We model an environment in which individuals prefer to be in a space in which their rank is higher, be it a social space, a geographical space, a work environment, or any other comparison sphere which we refer to in this paper, and without loss of generality, as a region. When the individuals can choose between more than two regions, we inquire: (i) whether a steady-state distribution of the population is reached; (ii) how long it will take to reach a steady state; and (iii) if a steady state obtains, whether at the steady state social welfare is maximized. Despite the fact that when there are three or more regions the mobility paths are more intricate than when there are only two regions, we prove that a steady-state distribution of the population across the regions is reached; we identify the upper bound of the number of time periods that it will take to reach the steady-state distribution; and we show that the steady-state distribution maximizes social welfare. This last result is surprising: even though the individuals act of their own accord, they achieve the socially preferred outcome.

Original languageEnglish
Pages (from-to)317-342
Number of pages26
JournalAnnals of Regional Science
Issue number2
StatePublished - Oct 2023
Externally publishedYes


  • Distaste for low rank
  • Inter-space mobility
  • Ordinal preferences
  • Social welfare
  • Steady-state population distribution
  • Three or more spaces


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