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

Thomas Colignatus ()

MPRA Paper from University Library of Munich, Germany

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 (search for similar items in EconPapers)
JEL-codes: A10 D63 D71 D72 (search for similar items in EconPapers)
Date: 2018-02-02, Revised 2018-02-02
New Economics Papers: this item is included in nep-pol
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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