Measures of policy distance and inequality / disproportionality of votes and seats
Measures of policy distance and inequality / disproportionality of votes and seats
Didactics and routines using Mathematica
Thomas Colignatus
http://thomascool.eu
February 2 2018
http://thomascool.eu
February 2 2018
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.
Keywords
Votes, Seats, Electoral System, Policy Distance, Disproportionality, Angular Distance, Sine-Diagonal Inequality / Disproportionality, Loosemore-Hanby, Gallagher, Descriptive Statistics, Education
MSC2010
00A69 General applied mathematics
28A75 Measure and integration. Length, area, volume, other geometric measure theory
62J20 Statistics. Diagnotics
97M70 Mathematics education. Behavioral and social sciences
28A75 Measure and integration. Length, area, volume, other geometric measure theory
62J20 Statistics. Diagnotics
97M70 Mathematics education. Behavioral and social sciences
JEL
A100 General Economics: General
D710 Social Choice; Clubs; Committees; Associations,
D720 Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
D630 Equity, Justice, Inequality, and Other Normative Criteria and Measurement
D710 Social Choice; Clubs; Committees; Associations,
D720 Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
D630 Equity, Justice, Inequality, and Other Normative Criteria and Measurement
Contents
Contents
Start (evaluate this subsection for the initialisation packages)
Start (evaluate this subsection for the initialisation packages)
1. Introduction
1. Introduction
2. Inequality / disproportionality measures of votes and seats
2. Inequality / disproportionality measures of votes and seats
3. Before and after (half) elections
3. Before and after (half) elections
4. Properties and first distinctions
4. Properties and first distinctions
5. Basics of the Angular Policy Distance (APD)
5. Basics of the Angular Policy Distance (APD)
6. Properties and application of the APD
6. Properties and application of the APD
7. Focusing on d[p w, p z] (APT)
7. Focusing on d[p w, p z] (APT)
8. The weighted average policy distance (WA)
8. The weighted average policy distance (WA)
9. Relation of the WA to ALHID and APD
9. Relation of the WA to ALHID and APD
10. Conclusion
10. Conclusion
Appendix A. Using d[w, p] and d[z, p]
Appendix A. Using d[w, p] and d[z, p]
Appendix B. d[p w, p z] for ALHID
Appendix B. d[p w, p z] for ALHID
Appendix C. Combining WA with the RPM
Appendix C. Combining WA with the RPM
Appendix D. ||p - p’|| on top of d[w, z]
Appendix D. ||p - p’|| on top of d[w, z]
References
References