Measures of policy distance and inequality / disproportionality of votes and seats

Colignatus, Thomas (2018): Measures of policy distance and inequality / disproportionality of votes and seats.

Abstract

Let v be a vector of votes for parties and s a vector of their seats gained in the House of Commons or the House of Representatives. We use a single zero for the lumped category of "Other", of the wasted vote, for parties that got votes but no seats. Let V = 1'v be total turnout and S = 1's the total number of seats, and let w = v / V and z = s / S be the perunages (or per ten or percentages). Let d[w, z] be the inequality / disproportionality of votes and seats. This can be the angle between the vectors (AID) and the sine-diagonal (SDID) measure based upon this. Parties can also be scored with policy vector p, using a "left-to-right" policy scale [0, 10]. A common voter-legislative distance is the weighted average a = p' (z - w). With AID d[w, z] the present paper looks into the properties of d[p w, p z]. The latter term for variable w and z given p works as a disproportionality measure, and for variable p given w and z works as policy congruence. We can define an angular policy distance (APD) pd[w, z, p] that employs this d[p w, p z] properly. The APD is much more sensitive than the weighted average, but Sqrt[Abs[a]] has remarkably similar behaviour.

• Item Type: MPRA Paper
• Institution: Thomas Cool Consultancy & Econometrics
• Language: English
• Keywords: Votes, Seats, Electoral System, Policy Distance, Disproportionality, Angular Distance, Sine-Diagonal Inequality / Disproportionality, Loosemore-Hanby, Gallagher, Descriptive Statistics, Education
• Subjects: A - General Economics and Teaching > A1 - General Economics > A10 - General; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D72 - Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior

References

Colignatus is the name in science of Thomas Cool, econometrician and teacher of mathematics, Scheveningen, Holland, http://econpapers.repec.org/RAS/pco170.htm

This text is also available at https://www.wolframcloud.com/objects/thomas-cool/Voting/2018-02-02-PolicyDistance.nb

Colignatus, Th. (2017a), "Comparing votes and seats with cosine, sine and sign, with attention for the slope and enhanced sensitivity to disproportionality", https://mpra.ub.uni-muenchen.de/81389/

Colignatus, Th. (2017b), "One woman, one vote. Though not in the USA, UK and France", https://mpra.ub.uni-muenchen.de/82513/

Colignatus, Th. (2017c), "Statistics, slope, cosine, sine, sign, significance and R-squared", https://boycottholland.wordpress.com/2017/10/21/statistics-slope-cosine-sine-sign-significance-and-r-squared/

Colignatus, Th. (2018), "Comparing the Aitchison distance and the angular distance for use as inequality or disproportionality measures for votes and seats", https://www.wolframcloud.com/objects/thomas-cool/Voting/2018-01-18-Aitchison.nb

Golder, M. & Stramski, J. (2010), "Ideological congruence and electoral institutions", American Journal of Political Science, 54(1), 90-106, http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.606.8475&rep=rep1&type=pdf

Stokman, F., Knoop, J. van der & Oosten, R. C. H. van (2013), "Modeling collective decision making", in Nee, V., Snijders, T. A. B. & Wittek, R. (eds.) (2013), "Handbook of Rational Choice Social Research", Stanford University Press, p. 151-182. See also https://www.rug.nl/staff/f.n.stokman, while Dutch readers may look at http://decide.nl