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power. A famous case arose in Massachusetts in the early nineteenth century when
the state legislature proposed a salamander-shaped electoral district in order to gain
electoral advantage. The governor of the state at that time was Elbridge Gerry, and
this practice became known as gerrymandering. See Lewyn ( 1993 ) for an interesting
description of gerrymandering cases.
To avoid political interference, many states have set up a neutral commission
to determine political boundaries satisfying a number of legislative and common
sense criteria. Depending on the country or jurisdiction involved, these criteria
may be enforced by legislative directive, judicial mandate, or historical precedent.
However, there is no consensus in political science, law, or geography on which
criteria are legitimate for the districting process, i.e., satisfy the neutrality condition.
Moreover, it is often unclear how they should be measured (Williams 1995 ). One
important issue at stake is population equality. To respect the principle of “one
man-one vote”, i.e., every vote has the same power, all districts should contain
approximately the same number of voters, i.e., be balanced. In the U.S., population
equality has been deemed by the courts to be very important, and as a result,
the total deviation of congressional districts from perfect balance was less than
1 % after the last census in 2000 (Webster 2013 ). In other countries, the allowed
deviations are usually higher (Handley and Grofmann 2008 ). Two other important
criteria always being mentioned are contiguity and compactness which both aim
at preventing gerrymandering. While contiguity is generally undisputed and easy
to verify, this is not the case for compactness. There is a broad discussion on how
to quantify this criterion adequately (Horn et al. 1993 ), and whether it is relevant
in the first place because an algorithm will never gerrymander on purpose as long
as it is does not use political data (Garfinkel and Nemhauser 1970 ). Moreover, if an
adequate minority representation is sought for, this may sometimes only be achieved
through non-compact districts (Dixon 1968 ). Other—often disputed—criteria are
the conformity to administrative boundaries, e.g., cities or counties, the preservation
of communities of interest, socio-economic homogeneity or a fair representation
of minority voters across the districts, the similarity with the previous electoral
districts, or the consideration of topological obstacles, like mountain ranges, lakes,
or rivers (cf. George et al. 1997 ;Parker 1990 ; Bozkaya et al. 2011 ). An excellent
review on typical criteria for political districting and their eligibility is given in
We b s t e r ( 2013 ).
When discussing automated procedures in the literature, it is always noted that
they are non-partisan and neutral as long as they do not use political data and, hence,
prevent gerrymandering. However, even if the computer does not gerrymander on
purpose, it may still do it accidentally, precisely because no political data is taken
into account. Therefore, Puppe and Tasnádi ( 2008 ) recently introduced the notion
of an (ex post) unbiased districting plan. In such a plan the number of districts won
by each party respects the relative strength of the party in the population as close
as possible. They focus on game theoretical aspects of the problem; see also Nagel
( 1965 ). However, one has to do a careful weighing up to avoid forthright politically
biased criteria that lead, in spirit, to gerrymandering.
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