Preferences and Coalitions

  • Thomas Kämpke
  • Franz Josef Radermacher
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 679)


Redistribution of income is assumed to require the vote of at least 50 % of all individuals with income and each of them insists to be a winner from the redistribution. When inequality is to be increased in the interest of some, coalition partners must be found by compensation schemes. Compensation minimization is shown to lead to coalition partners being either a connected or a disconnected income group. When inequality reaches certain critical levels, disconnection becomes unavoidable. For one-parametric income distributions, the critical levels are denoted as bifurcation points.

Values of bifurcation points are computed numerically for several one-parametric distributions. For income distributions with two or more parameters the bifurcation point is replaced by a bifurcation function.


Loss Function Income Distribution Pareto Distribution Lorenz Curve Bifurcation Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Barnett WA, He Y (1999) Center manifold, stability, and bifurcations in continuous time macroeconometric systems. In: The winter meetings of the Econometric Society, New YorkGoogle Scholar
  2. Bolton GE, Ockenfels A (2000) ERC: a theory of equity, reciprocity, and competition. Am Econ Rev 90:166–193CrossRefGoogle Scholar
  3. Congleton R (2002) The median voter model. In: Rowley RK, Schneider F (eds) The encyclopedia of public choice. Kluwer, New YorkGoogle Scholar
  4. Crosen R, Konow J (2009) Social preferences and moral hazard. MPRA, Munich University Library.
  5. Grandmont J-M (2006) Fiscally stable income distributions under majority voting and bargaining sets. Adv Math Econ 8:215–230CrossRefGoogle Scholar
  6. Grossmann V (2003) Income inequality, voting over the size of public consumption, and growth. Eur J Polit Econ 19:265–287CrossRefGoogle Scholar
  7. Hale JK, Kocak H (1996) Dynamics and bifurcations. Springer, New YorkGoogle Scholar
  8. Herlyn E (2012) Einkommensverteilungsbasierte Präferenz- und Koalitionsanalysen auf der Basis selbstähnlicher Equity-Lorenzkurven. Springer Gabler, WiesbadenCrossRefGoogle Scholar
  9. Kämpke T (2012) Income distribution and majority patterns. Int J of Computational Economics and Econometrics 2:155–178CrossRefGoogle Scholar
  10. Kämpke T, Radermacher FJ (2011) Analytische Eigenschaften von Equity-Lorenzkurven. FAW Working Paper, UlmGoogle Scholar
  11. Lee C-S (2005) Income inequality, democracy, and public sector size. Am Sociol Rev 70:158–181CrossRefGoogle Scholar
  12. Parker AE, Gedeon T (2004) Bifurcation structure of a class of S N-invariant constrained optimization problems. J Dyn Differ Equ 16:629–678CrossRefGoogle Scholar
  13. Rutström EE, Williams MB (2000) Entitlements and fairness: an experimental study on distributive preferences. J Econ Behav Organ 43:75–89CrossRefGoogle Scholar
  14. Scilab, The free platform for numerical computation,
  15. Sen A (2001) Development as freedom. Oxford University Press, OxfordGoogle Scholar
  16. Vigdor JL (2006) Fifty million voters can’t be wrong: economic self-interest and redistributive politics. Working Paper 12371. National Bureau of Economic Research, CambridgeGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Thomas Kämpke
    • 1
  • Franz Josef Radermacher
    • 2
  1. 1.Research Institute for Applied Knowledge Processing (FAW/n)UlmGermany
  2. 2.Department of Computer ScienceUniversity of UlmUlmGermany

Personalised recommendations