Electoral inequity
| Author | Nicolas Boccard |
| DOI | http://doi.org/10.1177/09516298231162047 |
| Published date | 01 April 2023 |
| Date | 01 April 2023 |
| Subject Matter | Articles |
Electoral inequity
Nicolas Boccard
Economics Department, University of Girona, Girona, Spain
Abstract
Ideally, a representative democracy awards a genuine vote to each adult. We study this issue in
competitive democracies with an election model combining district apportionment and propor-
tional representation. Four classic seat allocation rules, including d’Hondt, are reframed as
Dutch auctions, allowing important properties to be easily derived. The pros and cons of these
methods are stated in terms of economic inequality; Sainte Laguë’s is shown to best carry the genu-
ine vote ideal, both for elections and for apportionment. We next expound the interplay between
these two components in generating an inequitable treatment of voters and develop the scale-free
index of inequity best fitted to their concern. We apply it to 40 countries for the apportionment
of electoral districts. Lastly, we compute the same inequity index for recent parliamentary elec-
tions in 80 countries, finding that the majority system mistreats electors, thus putting a ‘price’
on government stability.
Keywords
Apportionment; d’Hondt; disproportionality; divisor method; election; equity; Sainte Laguë
1. Introduction
To radical political activists Wilkes (1776) and Mirabeau (1789), an ideal parliament
arising from elections should be a ‘spitting image’of the nation,
1
a view properly synthe-
sized by Mill (1861) as ‘the pure idea of democracy is the government of the whole
people by the whole people, equally represented’, so that ‘a majority of the electors
would always have a majority of the representatives; but a minority of the electors
would always have a minority of the representatives’(Section 7, emphasis added).
2
The now ubiquitous universal franchise in competitive democracies has achieved the
first part of this proportional representation (PR) ideal
3
but as far as the delicate
Corresponding author:
Nicolas Boccard, Edifici Econòmiques, Campus Montilivi, C/ de la Universitat de Girona, 10, 1 7003, Girona, Spain.
Email: nicolas.boccard@udg.edu
Article
Journal of Theoretical Politics
2023, Vol. 35(2) 100–125
© The Author(s) 2023
Article reuse guidelines:
sagepub.com/journals-permissions
DOI: 10.1177/09516298231162047
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balance highlighted in the second part is concerned, there remains many instances where
sizable and well-delineated minority opinions or groups are left without political
representation, sometimes at the hand of an abusive majority employing dilution strat-
egies (aka debasement).
Although constitutions profess the political equality of citizens with respect to legis-
lative representation, they only emit proportionality guidelines for apportionment and
elections, leaving the task of implementation to governments and oversight to courts.
This arises from the complexity of obtaining and compressing millions of opinions
into a small number of elected candidates that shall govern and legislate. Whereas the
majority is easily identified and served its due, every other grouping is but a minority.
Whichever contour it assumes (e.g. geographical, religious), its fair representation will
be a subjective matter and its implementation a fierce political struggle. Political philoso-
phers Grotius (1625), Locke (1695) and Rousseau (1755) thus advocated for majoritar-
ianism whereby the majority faction in parliament holds an absolute right to govern, ‘at
will’, unencumbered by opposition.
4
In hindsight, Popper (1988) adds a further quality to
majoritarianism, the ability to swiftly dismiss a ‘bad’government.
5
This framework has
thus endured in many countries, only surrendering a slice of PR to vocal minorities
without however appeasing all their qualms.
In recent decades, buoyed by growing individualism and liberalism, aggrieved citizens
of advanced economies have successfully challenged electoral laws in constitutional
courts on the ground that every vote should weigh equally upon the election result if pol-
itical rights are to be truly equal among citizens. In several cases discussed in Section 3.1.,
landmark rulings have mandated governments making sure their citizens were endowed
with what has been alternatively termed, an effective, genuine or worthy vote. Our aim
here is to measure electoral worth, theoretically and then empirically, across many coun-
tries over recent decades. For that task, we conceptualize electoral inequity as the statis-
tical dispersion of individual electoral worthiness.
The literature around the issue of electoral equality (or equity) has concentrated on
representatives (members of parliament (MPs)) and territories rather than citizens (cf.
classics by Duverger (1951), Rae (1967), Monroe (1994), Lijphart (1994), Samuels
and Snyder (2001) or more mathematical studies by Taagepera and Grofman (2003),
Schuster et al. (2003), and Karpov (2008)). We summarize the methods involved
Section 2.5., noting they mostly abstain from eliciting a moral criteria and then finding
the optimal rule to satisfy it (within the whole-numbers limit). In the next section, we
build the notion of a ‘worthy vote’from an intuitive approach. We then synthetically
model apportionment and election so as to contain both pure majoritarianism and pure
proportionality, as well as some classical PR methods whose equity properties are
derived to allow a clear-cut comparison. Sainte Laguë will be shown to be most equitable.
The appendix offers two detailed examples of inequity computation. The third empirical
section assesses an almost exhaustive sample of competitive democracies, firstly for the
latest apportionment of representatives among states/regions/provinces, highlighting the
deeply unequal treatment of residents according to non-constitutional details. Next, we
collect the results of some 500 general elections held since 1990 to compute the effective
electoral influence of voters.
Boccard 101
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