Editing Gerrymandering (section)

===Objective rules to create districts===
Another means to reduce gerrymandering is to create objective, precise criteria with which any district map must comply. Courts in the United States, for instance, have ruled that congressional districts must be contiguous in order to be constitutional.<ref>[[wikisource:Reynolds v. Sims|Reynolds v. Sims]] states that "a state legislative apportionment scheme may properly give representation to various political subdivisions and provide for compact districts of contiguous territory if substantial equality among districts is maintained." See also [[Reynolds v. Sims|the Wikipedia article]].</ref> This, however, is not a particularly effective constraint, as very narrow strips of land with few or no voters in them may be used to connect separate regions for inclusion in one district, as is the case in [[Texas's 35th congressional district]].

Depending on the distribution of voters for a particular party, metrics that maximize compactness can be opposed to metrics that minimize the efficiency gap.  For example, in the United States, voters registered with the Democratic Party tend to be concentrated in cities, potentially resulting in a large number of "wasted" votes if compact districts are drawn around city populations.  Neither of these metrics take into consideration other possible goals,<ref>{{cite web|url=https://fivethirtyeight.com/features/hating-gerrymandering-is-easy-fixing-it-is-harder/|title=Hating Gerrymandering Is Easy. Fixing It Is Harder.|last=Wasserman|first=David|date=25 January 2018|website=[[FiveThirtyEight]]}}</ref> such as proportional representation based on other demographic characteristics (such as race, ethnicity, gender, or income), maximizing competitiveness of elections (the greatest number of districts where party affiliation is 50/50), avoiding splits of existing government units (like cities and counties), and ensuring representation of major interest groups (like farmers or voters in a specific transportation corridor), though any of these could be incorporated into a more complicated metric.

====Minimum district to convex polygon ratio====
{{More citations needed section|date=February 2022}}
[[File:Polygons of Georgia Districts 8 and 10.png|thumb|upright=1.3|Smallest possible convex polygons drawn around the [[Georgia's 8th congressional district|8th]] (left) and [[Georgia's 10th congressional district|10th]] congressional districts in Georgia, 2012. To avoid penalizing large areas, the measure is the ratio of the area of the district to the area of the polygon. District 8 will get a lower score than District 10.]]
One method is to define a minimum district to [[convex polygon]] ratio.{{Definition needed|date=July 2016}} To use this method, every proposed district is circumscribed by the smallest possible convex polygon (its [[convex hull]]; think of stretching a rubberband around the outline of the district). Then, the area of the district is divided{{explain|date=December 2015}} by the area of the polygon; or, if at the edge of the state, by the portion of the area of the polygon within state boundaries.

The advantages of this method are that it allows a certain amount of human intervention to take place (thus solving the Colorado problem of [[#Shortest splitline algorithm|splitline districting]]); it allows the borders of the district to follow existing jagged subdivisions, such as neighborhoods or voting districts (something isoperimetric rules would discourage); and it allows concave coastline districts, such as the Florida gulf coast area. It would mostly eliminate bent districts, but still permit long, straight ones. However, since human intervention is still allowed, the gerrymandering issues of packing and cracking would still occur, just to a lesser extent.

====Shortest splitline algorithm====
The [[Center for Range Voting]] has proposed<ref>{{cite web|url=http://www.RangeVoting.org/GerryExamples.html|title=Gerrymandering and a cure—shortest splitline algorithm|publisher=RangeVoting.org|access-date=5 August 2009}}</ref> a way to draw districts by a simple [[algorithm]].<ref>{{Cite web|url=https://www.rangevoting.org/|title=RangeVoting.org – Center for Range Voting – front page|website=www.rangevoting.org}}</ref> The algorithm uses only the shape of the state, the number {{var|N}} of districts wanted, and the population distribution as inputs. The algorithm (slightly simplified) is:

# Start with the boundary outline of the state.
# Let {{var|N}}=A+B where {{var|N}} is the number of districts to create, and A and B are two whole numbers, either equal (if {{var|N}} is even) or differing by exactly one (if {{var|N}} is odd). For example, if {{var|N}} is 10, each of {{var|A}} and {{var|B}} would be 5. If {{var|N}} is 7, {{var|A}} would be 4 and {{var|B}} would be 3.
# Among all possible straight lines that split the state into two parts with the population ratio A:B, choose the ''shortest''. If there are two or more such shortest lines, choose the one that is most north–south in direction; if there is still more than one possibility, choose the westernmost.
# We now have two hemi-states, each to contain a specified number (namely {{var|A}} and {{var|B}}) of districts. Handle them recursively via the same splitting procedure.
# Any human residence that is split in two or more parts by the resulting lines is considered to be a part of the most north-eastern of the resulting districts; if this does not decide it, then of the most northern.

This district-drawing algorithm has the advantages of simplicity, ultra-low cost, a single possible result (thus no possibility of human interference), lack of intentional bias, and it produces simple boundaries that do not meander needlessly. It has the disadvantage of ignoring geographic features such as rivers, cliffs, and highways and cultural features such as tribal boundaries. This landscape oversight causes it to produce districts different from those a human would produce. Ignoring geographic features can induce very simple boundaries.

While most districts produced by the method will be fairly compact and either roughly rectangular or triangular, some of the resulting districts can still be long and narrow strips (or triangles) of land.

Like most automatic redistricting rules, the shortest splitline algorithm will fail to create majority-minority districts, for both ethnic and political minorities, if the minority populations are not very compact. This might reduce minority representation.

Another criticism of the system is that splitline districts sometimes divide and diffuse the voters in a large metropolitan area. This condition is most likely to occur when one of the first splitlines cuts through the metropolitan area. It is often considered a drawback of the system because residents of the same agglomeration are assumed to be a community of common interest. This is most evident in the splitline allocation of [[Colorado]].<ref>{{Cite web | url = http://www.rangevoting.org/SSHR/co_final.png| title = Untitled | website = rangevoting.org| access-date = 30 June 2021}}</ref>
However, in cases when the splitline divides a large metropolitan area, it is usually because that large area has enough population for multiple districts. In cases which the large area only has the population for one district, then the splitline usually results in the urban area being in one district with the other district being rural.

As of July 2007, shortest-splitline redistricting pictures, based on the results of the 2000 census, are available for all 50 states.<ref>{{cite web|url=http://www.RangeVoting.org/SplitLR.html|title=Splitline districtings of all 50 states + DC + PR|publisher=RangeVoting.org|access-date=5 August 2009}}</ref>

====Minimum isoperimetric quotient====
{{See also|Compactness measure of a shape|Polsby–Popper test}}
It is possible to define a specific minimum [[isoperimetric quotient]],<ref name="siam.org">{{cite journal |last1=Case |first1=James |title=Flagrant Gerrymandering: Help from the Isoperimetric Theorem? |journal=SIAM News |date=November 2007 |volume=40 |issue=9 |url=https://archive.siam.org/news/news.php?id=1237 }}</ref> proportional to the ratio between the area and the square of the perimeter of any given congressional voting district. Although technologies presently exist to define districts in this manner, there are no rules in place mandating their use, and no national movement to implement such a policy. One problem with the simplest version of this rule is that it would prevent incorporation of jagged natural boundaries, such as rivers or mountains; when such boundaries are required, such as at the edge of a state, certain districts may not be able to meet the required minima. One way of avoiding this problem is to allow districts which share a border with a state border to replace that border with a polygon or semi-circle enclosing the state boundary as a kind of virtual boundary definition, but using the actual perimeter of the district whenever this occurs inside the state boundaries. Enforcing a minimum isoperimetric quotient would encourage districts with a high ratio between area and perimeter.<ref name="siam.org" />

====Efficiency gap calculation====
{{Main|Efficiency gap}}
The efficiency gap is a simply-calculable measure that can show the effects of gerrymandering.<ref name="TheNewRepublic">{{cite magazine|url=https://newrepublic.com/article/118534/gerrymandering-efficiency-gap-better-way-measure-gerrymandering|title=Here's How We Can End Gerrymandering Once and for All|magazine=The New Republic|author=Nicholas Stephanopoulas|date=3 July 2014|access-date=8 May 2018}}</ref> It measures wasted votes for each party: the sum of votes cast in losing districts (losses due to cracking) and excess votes cast in winning districts (losses due to packing).  The difference in these wasted votes are divided by total votes cast, and the resulting percentage is the efficiency gap.

In 2017, Boris Alexeev and Dustin Mixon proved that "sometimes, a small efficiency gap is only possible with bizarrely shaped districts". This means that it is mathematically impossible to always devise boundaries which would simultaneously meet certain Polsby–Popper and efficiency gap targets,<ref>{{cite journal|title=An Impossibility Theorem for Gerrymandering|journal=[[American Mathematical Monthly]]|volume=125|issue=10|year=2018|last1=Alexeev|first1=Boris|last2=Mixon|first2=Dustin G.|pages=878–884|doi=10.1080/00029890.2018.1517571|arxiv=1710.04193|s2cid=54570818}}</ref><ref>{{cite web|url=https://news.osu.edu/you-cant-tell-a-gerrymandered-district-by-its-shape/|title=You can't tell a gerrymandered district by its shape|date=25 October 2017|work=news.osu.edu|publisher=[[Ohio State University]]|access-date=16 September 2020}}</ref><ref>{{cite web|url=https://www.quantamagazine.org/when-math-gets-impossibly-hard-20200914/|title=When Math Gets Impossibly Hard|last=Richeson|first=David S.|date=14 September 2020|work=[[Quanta Magazine]]|access-date=16 September 2020}}</ref>

Given such theoretical difficulties, a robust, however sub-optimal, anti-gerrymandering rule may be as simple as identifying all maps satisfying a rough efficiency measure, like expected outcome matching voter affiliation proportions, then choosing the one most compact.