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Group Decision and Negotiation

Erschienen in:

01.01.2015

Strategic Voting and the Degree of Path-Dependence

verfasst von: Aki Lehtinen

Erschienen in: Group Decision and Negotiation | Ausgabe 1/2015

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Abstract

This paper generalises Enelow (J Polit 43(4):1062–1089, 1981) and Lehtinen’s (Theory Decis 63(1):1–40, 2007b) model of strategic voting under amendment agendas by allowing any number of alternatives and any voting order. The generalisation enables studying utilitarian efficiencies in an incomplete information model with a large number of alternatives. Furthermore, it allows for studying how strategic voting affects path-dependence. Strategic voting increases utilitarian efficiency also when there are more than three alternatives. The existence of a Condorcet winner does not guarantee path-independence if the voters engage in strategic voting under incomplete information. A criterion for evaluating path-dependence, the degree of path-dependence, is proposed, and the generalised model is used to study how strategic voting affects it. When there is a Condorcet winner, strategic voting inevitably increases the degree of path-dependence, but when there is no Condorcet winner, strategic voting decreases path-dependence. Computer simulations show, however, that on average it increases the degree of path-dependence.

Vorheriger Artikel Introduction to the Theory of Intersubjective Management

Nächster Artikel Studies on Interval Multiplicative Preference Relations and Their Application to Group Decision Making

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There is a sense in which the vast literatures on the uncovered set (Miller 1977) and the Banks set (1985) study related questions: they endeavour to determine the set of possible outcomes under agendas when voters are strategic. Given, however, that these approaches are based on complete information, they will not be further discussed here.

Although the indexing methods apply with literally any number of alternatives, in practise, given that the model is based on computer simulation, the results can be computed with 8 alternatives at most if one runs all the parameter values in one simulation. Some results are reported with 10 alternatives below. With 11 or more alternatives, the combinatorial explosion becomes unbearable for ordinary supercomputers. For example, there are n!/2 different agendas. The number of different agendas is 2520 with 7 alternatives. With 10 alternatives, there are 3628800 different agendas and with 11, the number is 39916800. With almost 80 million different preference orderings, the matrices seem to become too big for the memory of the supercomputer I am using.

The appendix can be downloaded from http://www.mv.helsinki.fi/home/alehtine/. Upon request, I can provide a reasonably well-documented FORTRAN code. In order to run the simulations, one needs access to a fairly new supercomputer and to IMSL libraries.

See Ordeshook (1986), Ordeshook and Schwartz (1987) and Miller (1995) for a discussion of different agendas.

Note that the model does not require that voters are able to make interpersonal comparisons in order to formulate their signals. The difference in the sums of utilities is used as a rough proxy for estimating other voters’ behaviour. Lehtinen (2008) also provides a signal model for plurality and approval voting which is based on sums of utilities. I refer to this paper for further justifying arguments for this assumption.

It is obvious that \(E\left[ \varDelta \left( j,k\right) \right] =0\).

See the special issue on path-dependence in Political Analysis 2012, 20(2) for incomplete information accounts of path-dependence in non-voting contexts.

The total number of agendas n! is divided by 2 so as remove behaviourally indistinguishable agendas. For example, agenda (123) is behaviourally identical to (213) because alternatives 1 and 2 are put to a vote against each other in the first round. Only the labelling of the alternatives is different. Each pair of alternatives thus always has two behaviourally indistinguishable agendas.

Corrado Gini was one of the first to apply it for studying the inequality of the distribution of income. Carnap (1952, pp. 65–68) discussed it under the name ‘degree of order’. Carnap also used the terms ‘homogeneity’ and the ‘uniformity of the world’. Patil and Taillie (1982) show various applications (e.g., biodiversity, industrial concentration) for the functional form used here and related forms. Political scientists are perhaps best acquainted with the so called ‘effective number of parties’ (Laakso and Taagepera 1979).

The figures report C values in the range of 50–100 because parameter C was implemented with another parameter b in the computer code: b =100 \(*\) C.

Banks J (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welf 1:295–306CrossRef

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Titel: Strategic Voting and the Degree of Path-Dependence
verfasst von: Aki Lehtinen
Publikationsdatum: 01.01.2015
Verlag: Springer Netherlands
Erschienen in: Group Decision and Negotiation / Ausgabe 1/2015
Print ISSN: 0926-2644
Elektronische ISSN: 1572-9907
DOI: https://doi.org/10.1007/s10726-014-9381-y

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