TY - JOUR

T1 - A pure theory of population distribution when preferences are ordinal

AU - Stark, Oded

AU - Kosiorowski, Grzegorz

N1 - Publisher Copyright:
© 2022, The Author(s).

PY - 2023/10

Y1 - 2023/10

N2 - 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.

AB - 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.

KW - Distaste for low rank

KW - Inter-space mobility

KW - Ordinal preferences

KW - Social welfare

KW - Steady-state population distribution

KW - Three or more spaces

UR - http://www.scopus.com/inward/record.url?scp=85144698693&partnerID=8YFLogxK

U2 - 10.1007/s00168-022-01194-y

DO - 10.1007/s00168-022-01194-y

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AN - SCOPUS:85144698693

SN - 0570-1864

VL - 71

SP - 317

EP - 342

JO - Annals of Regional Science

JF - Annals of Regional Science

IS - 2

ER -