Skip to main content
SpringerLink
Log in

Electoral Reform and Social Choice Theory: Piecemeal Engineering and Selective Memory

  • Chapter
  • First Online:
Book cover Transactions on Computational Collective Intelligence XXXIV

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 11890))

  • 267 Accesses

Abstract

Most electoral reforms are dictated by recognized problems discovered in the existing procedures or - perhaps more often - by an attempt to consolidate power distributions. Very rarely, if ever, is the motivation derived from the social choice theory even though it deals with issues pertaining to what is possible and what is impossible to achieve by using given procedures in general. We discuss some reforms focusing particularly on a relatively recent one proposed by Eric Maskin and Amartya Sen. It differs from many of its predecessors in invoking social choice considerations in proposing a new system of electing representatives. At the same time it exemplifies the tradeoffs involved in abandoning existing systems and adopting new ones.

The author thanks the referees for numerous constructive comments.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is relatively straightforward to see how this conclusion is derived. To wit, suppose that there is a Condorcet loser, say x, in a profile consisting of n voters and k alternatives. This means that in each pairwise comparison, the maximum number of votes for x is strictly less than n/2. Hence x’s Borda score is less than \((k-1)\times (n/2)\). If all alternatives had the same or smaller Borda score than x (which would make x the Borda winner), the total number of Borda scores would be no larger than: \(k\times (k-1)\times n/2 \). Now this upper bound is strictly less than the sum total of Borda scores in any profile, viz. \( n \times (k^{2} - k)/2 = k \times (k-1) \times n/2\). (The number of pairwise comparisons involving different alternatives is \(k^2 - k\) with the sum of entry (i, j) and entry (j, i) being equal to the number of voters, n, for all alternatives i and j.) Therefore, in any profile there must be at least one alternative with a strictly larger Borda score than that of the Condorcet loser. Hence, the latter cannot be elected by the Borda count.

  2. 2.

    A strong Condorcet winner is an alternative ranked first by more than half of the electorate. Obviously, all procedures that elect a Condorcet winner also elect a strong Condorcet winner. The converse is not true, that is, there are procedures (e.g. plurality voting) that elect the strong Condorcet winner, but not necessarily a Condorcet winner.

  3. 3.

    Nanson’s argument to that effect is pretty similar to the one in footnote 1. It amounts to showing that the lower bound of the Borda score of a Condorcet winner is strictly larger than the average of the Borda scores.

  4. 4.

    The differences and similarities of Nanson’s and Baldwin’s rules are discussed in [7, 14, 15].

  5. 5.

    For example, let a three-person four-alternative profile be the following: 1 voter: ABCD, 1 voter: CBDA, 1 voter: DBAC. Here B is the Condorcet winner.

  6. 6.

    Moulin’s lower bound for the number of voters was 25. This bound has more recently been lowered to 12 by Brandt et al. [3]. A stronger variant of Moulin’s result has subsequently been proven by Pérez [19].

  7. 7.

    Table 8 also illustrates the vulnerability to the strong no-show paradox of several other Condorcet consistent procedures: Baldwin, Black, Copeland and Kemeny. For further discussion, see [8].

  8. 8.

    For a related discussion on the MS procedure, see [18].

References

  1. Baldwin, J.M.: The technique of the Nanson preferential majority system. Proc. Roy. Soc. Victoria 39, 42–52 (1926)

    MATH  Google Scholar 

  2. Black, D.: On the rationale of group decision-making. J. Polit. Econ. 56, 23–34 (1948)

    Article  Google Scholar 

  3. Brandt, F., Geist, C., Peters, D.: Optimal bounds for the no show paradox via SAT solving. Math. Soc. Sci. 90, 18–27 (2017)

    Article  MathSciNet  Google Scholar 

  4. De Grazia, A.: Mathematical derivation of an election system. Isis 44, 42–51 (1953)

    Article  Google Scholar 

  5. Felsenthal, D.S., Machover, M.: After two centuries should Condorcet’s voting procedure be implemented? Behav. Sci. 37, 250–273 (1992)

    Article  Google Scholar 

  6. Felsenthal, D.S., Nurmi, H.: Monotonicity Failures Afflicting Procedures for Electing a Single Candidate. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51061-3

    Book  Google Scholar 

  7. Felsenthal, D.S., Nurmi, H.: Monotonicity violations by Borda’s elimination and Nanson’s rules: a comparison. Group Decis. Negot. 27(2018), 637–664 (2018)

    Article  Google Scholar 

  8. Felsenthal, D.S., Nurmi, H.: Voting Procedures Under a Restricted Domain. An Examination of the (In)Vulnerability of 20 Voting Procedures to Five Main Paradoxes. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12627-8

    Book  Google Scholar 

  9. Fishburn, P.C., Brams, S.J.: Paradoxes of preferential voting. Math. Mag. 56, 207–214 (1983)

    Article  MathSciNet  Google Scholar 

  10. Maskin, E., Sen, A.K.: How majority rule might have stopped Donald Trump. The New York Times, 28 April 2016 (2016). https://www.nytimes.com/2016/05/01/opinion/sunday/how-majority-rule-might-have-stopped-donald-trump.html

  11. McLean, I., Urken, A.B.: Classics of Social Choice. University of Michigan Press, Ann Arbor (1995)

    Book  Google Scholar 

  12. Moulin, H.: Condorcet’s principle implies the no-show paradox. J. Econ. Theory 45, 53–64 (1988)

    Article  MathSciNet  Google Scholar 

  13. Nanson, E.J.: Methods of elections. Trans. Proc. Roy. Soc. Victoria 19, 197–240 (1883). McLean, I., Urken, A.B. (eds.) Classics of Social Choice, Chapter 14, pp. 321–359. University of Michigan Press (1995)

    Google Scholar 

  14. Niou, E.M.S.: A note on Nanson’s rule. Public Choice 54, 191–193 (1987)

    Article  Google Scholar 

  15. Nurmi, H.: On Nanson’s method. In: Borg, O., Apunen, O., Hakovirta, H., Paastela, J. (eds.) Democracy in the Modern World. Essays for Tatu Vanhanen, series A, vol. 260, pp. 199–210. Acta Universitatis Tamperensis, Tampere (1989)

    Google Scholar 

  16. Nurmi, H.: Voting Paradoxes and How to Deal with Them. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-662-03782-9

    Book  MATH  Google Scholar 

  17. Nurmi, H.: Reflections on two old Condorcet extensions. Trans. Comput. Collective Intell. XXXI, 9–21 (2018)

    Google Scholar 

  18. Nurmi, H.: Voting theory: cui bono? Politeia 91, 106–121 (2018)

    Article  Google Scholar 

  19. Pérez, J.: The strong no show paradoxes are a common flaw in Condorcet voting correspondences. Soc. Choice Welfare 18, 601–616 (2001)

    Article  MathSciNet  Google Scholar 

  20. Saari, D.G.: Capturing ‘The Will of the People’. Ethics 113, 333–349 (2003)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Contemporary History, Philosophy and Political Science, University of Turku, Turku, Finland

    Hannu Nurmi

Authors
  1. Hannu Nurmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hannu Nurmi .

Editor information

Editors and Affiliations

  1. Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, VIC, Australia

    Ryszard Kowalczyk

  3. WSB University in Wroclaw, Wroclaw, Poland

    Jacek Mercik

  4. WSB University in Wroclaw, Wroclaw, Poland

    Anna Motylska-Kuźma

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer-Verlag GmbH Germany, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nurmi, H. (2019). Electoral Reform and Social Choice Theory: Piecemeal Engineering and Selective Memory. In: Nguyen, N., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXIV. Lecture Notes in Computer Science(), vol 11890. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60555-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-60555-4_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-60554-7

  • Online ISBN: 978-3-662-60555-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation