Skip to main content

2015 | OriginalPaper | Buchkapitel

The Choice of Voting Rules Based on Preferences over Criteria

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The community of voting system experts is largely divided on the issue of the best voting rule. Some – perhaps a majority – of the community stresses the performance related to Condorcet’s intuition, while others take a more “positional” view of the voting rules. This paper approaches the choice of the rule from the viewpoint of the individuals that will subsequently be applying the chosen rule in solving opinion aggregation problems. Our first starting point is that each individual has a preference ranking over the criteria. This starting point reduces the rule selection into the classic social choice problem. Using the Borda count one is able to construct a vector of weights that reflects the importance that the individuals assign to various criteria. Using the analytic results on the compatibility of various rules and criteria we can then associate each rule with a value that reflects the aggregated opinion of the importance criteria. Hence, the choice of the rules gets its justification from the views that the individuals have on the significance of the criteria. Our second starting point is based on weights that individuals associate with the criteria. The collective weights are then determined as in range voting. Again a justification of the chosen rules can be expressed in terms of the importance that individual assign to criteria.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
The impromptu nature of the proceedings is reflected by the somewhat light-hearted brainstorming debate preceding the vote as well as by the fact that the voters were not asked to reveal anything else but their approved systems. Several weeks after the meeting the participants were asked to disclose their reasons for voting the way they did, but at this time many didn’t recall the systems they approved of, much less the reasons for doing so. Thus, we do not know how much the election outcome depends on the aggregation system adopted [10].
 
2
The problem of ‘optimal’ decision rule has, of course, a much longer history. See e.g. [22].
 
3
The method was invented already in the 15’th century by Nicholas of Cusa, but arguably he did not emphasize the particular problem related to the plurality voting, viz. that it may result in the election of a candidate that would lose the pairwise contests against any other candidate (see [9, 12]).
 
4
For explanation of the criteria, see e.g. [16]).
 
5
A few adaptations notwithstanding, the PROMETHEE description given here essentially follows that of [2, 11].
 
Literatur
1.
Zurück zum Zitat Barbera, S., Jackson, M.: Choosing how to choose: self-stable majority rules and constitutions. Q. J. Econ. 119, 1011–1048 (2004)CrossRef Barbera, S., Jackson, M.: Choosing how to choose: self-stable majority rules and constitutions. Q. J. Econ. 119, 1011–1048 (2004)CrossRef
2.
Zurück zum Zitat Brans, J.-P., Mareschal, B.: Promethee methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 163–196. Springer, Berlin (2005) Brans, J.-P., Mareschal, B.: Promethee methods. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 163–196. Springer, Berlin (2005)
3.
Zurück zum Zitat Buchanan, J., Tullock, G.: The Calculus of Consent. Logical Foundations of Constitutional Democracy. The University of Michigan Press, Ann Arbor (1962) Buchanan, J., Tullock, G.: The Calculus of Consent. Logical Foundations of Constitutional Democracy. The University of Michigan Press, Ann Arbor (1962)
4.
Zurück zum Zitat Dietrich, F.: How to reach legitimate decisions when the procedure is controversial. Soc. Choice Welfare 24, 363–393 (2005)CrossRef Dietrich, F.: How to reach legitimate decisions when the procedure is controversial. Soc. Choice Welfare 24, 363–393 (2005)CrossRef
5.
Zurück zum Zitat Diss, M., Merlin, V.: On the stability of a triplet of scoring rules. Theor. Decis. 69, 289–316 (2010)CrossRef Diss, M., Merlin, V.: On the stability of a triplet of scoring rules. Theor. Decis. 69, 289–316 (2010)CrossRef
6.
Zurück zum Zitat Felsenthal, D.: Review of paradoxes afflicting procedures for electing a single candidate. In: Felsenthal, D., Machover, M. (eds.) Electoral Systems: Paradoxes, Assumptions, and Procedures, pp. 19–91. Springer, Heidelberg (2012)CrossRef Felsenthal, D.: Review of paradoxes afflicting procedures for electing a single candidate. In: Felsenthal, D., Machover, M. (eds.) Electoral Systems: Paradoxes, Assumptions, and Procedures, pp. 19–91. Springer, Heidelberg (2012)CrossRef
7.
Zurück zum Zitat Felsenthal, D., Machover, M. (eds.): Electoral Systems: Paradoxes, Assumptions and Procedures. Springer, Heidelberg (2012) Felsenthal, D., Machover, M. (eds.): Electoral Systems: Paradoxes, Assumptions and Procedures. Springer, Heidelberg (2012)
8.
Zurück zum Zitat Fishburn, P.: Condorcet social choice functions. SIAM J. Appl. Math. 33, 469–489 (1977)CrossRef Fishburn, P.: Condorcet social choice functions. SIAM J. Appl. Math. 33, 469–489 (1977)CrossRef
9.
Zurück zum Zitat Hägele, G., Pukelsheim, F.: The electoral systems of nicholas of cusa in the catholic concordance and beyond. In: Christianson, G., Izbicki, T., Bellitto, C. (eds.) The Church, the Councils & Reform: The Legacy of the Fifteenth Century, pp. 229–249. The Catholic University of America Press, Washington, DC (2008) Hägele, G., Pukelsheim, F.: The electoral systems of nicholas of cusa in the catholic concordance and beyond. In: Christianson, G., Izbicki, T., Bellitto, C. (eds.) The Church, the Councils & Reform: The Legacy of the Fifteenth Century, pp. 229–249. The Catholic University of America Press, Washington, DC (2008)
10.
Zurück zum Zitat Laslier, J.-F.: And the loser is..plurality voting. In: Felsenthal, D., Machover, M. (eds.) Electoral Systems: Paradoxes, Assumptions and Procedures, pp. 327–351. Springer, Heidelberg (2012)CrossRef Laslier, J.-F.: And the loser is..plurality voting. In: Felsenthal, D., Machover, M. (eds.) Electoral Systems: Paradoxes, Assumptions and Procedures, pp. 327–351. Springer, Heidelberg (2012)CrossRef
11.
Zurück zum Zitat Macharis, C., Brans, J.-P., Mareschal, B.: The GDSS PROMETHEE procedure. J. Decis. Syst. 7, 283–307 (1998) Macharis, C., Brans, J.-P., Mareschal, B.: The GDSS PROMETHEE procedure. J. Decis. Syst. 7, 283–307 (1998)
12.
Zurück zum Zitat McLean, I., Urken, A. (eds.): Classics of Social Choice. The University of Michigan Press, Ann Arbor (1995) McLean, I., Urken, A. (eds.): Classics of Social Choice. The University of Michigan Press, Ann Arbor (1995)
13.
Zurück zum Zitat Meskanen, T., Nurmi, H.: Distance from consensus: a theme and variations. Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice, pp. 117–132. Springer, Heidelberg (2006)CrossRef Meskanen, T., Nurmi, H.: Distance from consensus: a theme and variations. Mathematics and Democracy: Recent Advances in Voting Systems and Collective Choice, pp. 117–132. Springer, Heidelberg (2006)CrossRef
14.
Zurück zum Zitat Niemi, R., Weisberg, H. (eds.): Probability Models of Collective Decision Making. Charles E. Merrill, Columbus (1972) Niemi, R., Weisberg, H. (eds.): Probability Models of Collective Decision Making. Charles E. Merrill, Columbus (1972)
15.
Zurück zum Zitat Nitzan, S.: Some measures of closeness to unanimity and their implications. Theor. Decis. 13, 129–138 (1981)CrossRef Nitzan, S.: Some measures of closeness to unanimity and their implications. Theor. Decis. 13, 129–138 (1981)CrossRef
16.
Zurück zum Zitat Nurmi, H.: Voting Systems under Uncertainty. Springer, Heidelberg (2002)CrossRef Nurmi, H.: Voting Systems under Uncertainty. Springer, Heidelberg (2002)CrossRef
17.
Zurück zum Zitat Nurmi, H.: Assessing Borda’s rule and its modifications. In: Emerson, P. (ed.) Designing an All-Inclusive Democracy: Consensual Voting Procedures for Use in Parliaments, Councils and Committees, pp. 109–119. Springer, Heidelberg (2007)CrossRef Nurmi, H.: Assessing Borda’s rule and its modifications. In: Emerson, P. (ed.) Designing an All-Inclusive Democracy: Consensual Voting Procedures for Use in Parliaments, Councils and Committees, pp. 109–119. Springer, Heidelberg (2007)CrossRef
18.
Zurück zum Zitat Plott, C.: Individual choice of politico-economic process. In: Niemi, R., Weisberg, H. (eds.) Probability Models of Collective Decision Making, pp. 83–97. Charles E. Merrill, Columbus (1972) Plott, C.: Individual choice of politico-economic process. In: Niemi, R., Weisberg, H. (eds.) Probability Models of Collective Decision Making, pp. 83–97. Charles E. Merrill, Columbus (1972)
19.
Zurück zum Zitat Rae, D.: Decision rules and individual values in constitutional choice. Am. Polit. Sci. Rev. 63, 40–56 (1969)CrossRef Rae, D.: Decision rules and individual values in constitutional choice. Am. Polit. Sci. Rev. 63, 40–56 (1969)CrossRef
20.
Zurück zum Zitat Richelson, J.: A comparative analysis of social choice functions. IV, Behav. Sci. 26, 346–353 (1981)CrossRef Richelson, J.: A comparative analysis of social choice functions. IV, Behav. Sci. 26, 346–353 (1981)CrossRef
21.
Zurück zum Zitat Suzuki, T., Horita, M.: How to order the alternatives, rules and the rules to choose rules: when the endogenous procedural choice regresses. In: Kami\(\rm \acute{n}\)ski, B., Kersten, G.E., Shakun, M.F., Szapiro, T. (eds.) GDN2015. LNBIP, vol. 218, pp. 47–59. Springer, Heidelberg (2015) Suzuki, T., Horita, M.: How to order the alternatives, rules and the rules to choose rules: when the endogenous procedural choice regresses. In: Kami\(\rm \acute{n}\)ski, B., Kersten, G.E., Shakun, M.F., Szapiro, T. (eds.) GDN2015. LNBIP, vol. 218, pp. 47–59. Springer, Heidelberg (2015)
22.
Zurück zum Zitat Tangian, A.: Mathematical Theory of Democracy. Springer, Heidelberg (2014)CrossRef Tangian, A.: Mathematical Theory of Democracy. Springer, Heidelberg (2014)CrossRef
Metadaten
Titel
The Choice of Voting Rules Based on Preferences over Criteria
verfasst von
Hannu Nurmi
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-19515-5_19