The Muon Rules
muon2:
Quote from: Cardinal and IDS Legislator X, Tzar of Russia on December 05, 2014, 06:29:09 AM
I don't totally understand item 7, could you explain it a little more please, Muon?
The basic idea is that plans get sorted by chop (+ inequality) and erosity scores to determine which will go on to the commission (Item 3a or 3b). Any plan that beats another with in one score and does at least as well on the other knocks out the higher scoring plan (like golf low scores are desired). Population inequality is either used as a tie breaker if two plans are otherwise tied or combined with the chop score. The question is whether to use inequality strictly or to recognize that two plans with similar inequality remain statistically tied. That leads to the table in Item 7.
A while back I led some threads where a number of posters put together whole county plans to see how low the inequality could go, and applied the same idea to New England states with towns. The result was the graph I posted for Item 7. The fit is best when one uses the logarithm of the range rather than the actual range.
Next I wanted to use the fit line to see how repeated divisions would likely affect the range for a single state. When I total the number of counties and non-surrounded independent cities for non-New England states without AK and HI, there are 3023 for 42 states which is 71.97 counties per state. So a hypothetical average state has 72 counties.
Now if my hypothetical state has just 2 CDs, there would be an average of 36 counties for each, and the fit line predicts that the range would be 6. That corresponds to one chop of the state. A second chop of the state into 3 CDs average 24 counties for each and a predicted best range of 93. A third chop to 4 CDs gives a range of 379. Eventually a thirteenth chop predicts a range of 7656 which exceeds 1%. I took those predicted ranges for the number of state chops and rounded them off to get the table in Item 7.
One can think of each county chop as having one less whole county CD in a state, which is equivalent to having one less chop of the state as a whole. So, the table is another way of identifying when two plans have statistically equivalent ranges that would be expected for that number of whole county CDs or whole county groups of CDs.
muon2:
Definition: Geographic unit. A geographic unit is a contiguous geographic area used to build plans. States are divided into primary geographic units which cover the entire area and population of the state. Plans are built from a smallest geographic unit such as vote tabulation districts (VTD), census tracts or census blocks.
Definition: Subunit. Subunits are geographic subdivisions of a primary unit or other subunit. Examples include census defined subdivisions, townships, municipalities and unincorporated areas in an urban county, and recognized neighborhood regions in a city.
Item 8. The smallest geographic unit shall be the VTD. The primary geographic unit is the county (or parish in LA) except as identified below. Counties with populations in excess of ten times the maximum allowed range shall have identified county subunits. Subunits in excess of 10 times the allowed range may have identified subunits larger than the VTD.
Item 8a. Independent cities outside VA shall be treated as primary geographic units in their states (Baltimore, St Louis, Carson City). Independent cities in VA greater than 50K or that have annexed their entire county shall be treated as primary geographic units (Alexandria, Lynchburg, Richmond, Roanoke, Hampton, Suffolk, Chesapeake, Norfolk, Portsmouth, Virginia Beach, Newport News). Independent cities less than 50K shall be treated as subunits of the county they were created from.
Item 8b. Towns in the New England states (CT, ME, MA, NH, RI, VT) shall be the primary geographic units in their states except for counties that have unorganized areas. Counties with unorganized areas remain primary geographic units.
Item 8c. Minor county divisions (MCDs) recognized by the Census are subunits of the counties in those states not covered by Item 8b.
Item 8d. Incorporated cities and school districts in unincorporated areas are subunits of counties not otherwise covered in Items 8b or 8c.
muon2:
Definition: County Cluster. A connected set of counties sharing a common demographic feature. Connected means able to travel within the cluster to all counties on public roads or ferries without leaving the cluster. The size of a county cluster is the population of the cluster divided by the quota, and rounded up to the nearest whole number.
Definition: Cover. The cover of a cluster is the number of districts including all or part of any county in the cluster. The cover score for a cluster is the difference between the cover and the size of the cluster.
Definition: Pack. The pack of a cluster is the number of districts wholly contained within counties in the cluster. The pack score for a cluster is the difference between one less than the size and the pack of the cluster.
Definition: Urban County Cluster (UCC). A UCC is a county cluster where each county is within the same Census-designated Metropolitan Statistical Area (MSA), and has either an urbanized population of 25K or more, or an urbanized population of at least 40% of the total county population.
Definition: Minority County Cluster (MCC). An MCC is a county cluster where each county has 40% or more citizen voting age population (CVAP) for the same specific minority. Note that this is a more general statement than VAP, designed to be applicable for minority groups with substantial non-citizen populations including Latinos.
Item 9: A redistricting plan should avoid excess division of county clusters. The CHOP will increase by the cover score for each cluster. The CHOP will increase by the pack score for each cluster.
More discussion of the pack and cover and a specific application to the Omaha UCC in NE can be found in this thread.
muon2:
Definition: Chop. A single chop is the division of a geographic unit between two districts. A second chop divides the unit between three districts. In general the number of chops is equal to the number of districts in that unit less one.
Definition: Chop size. In units with a single chop, the size of a chop is the population of the smaller district within the unit. For districts with more than one chop, chop sizes are measured in order from the smallest populated district in the unit up to but not including the district with the largest population in the unit.
Definition: Microchop. A microchop is a chop that has a size that is 0.5% or less of the quota. Microchops do not count towards the number of chops in a unit.
Definition: Macrochop. A macrochop is one or more chops in a county that has a total size in excess of 5.0% of the quota. When a macrochop of a county occurs, the subunits of the county must be considered as if they were units as well. Note that macrochops may only apply to counties with a population of more than 10% of the quota, and must apply to counties with more than 105% of the quota.
Item 10: CHOP measures the integrity of geographic units in a plan. The CHOP score is the total of all county chops not including microchops. In counties with a macrochop, chops of county subunits are added to the CHOP score, however VTDs that span county subdivisions do not increase the CHOP score.
muon2:
The erosity rules were fleshed out per the discussion in this thread.
Principle: Each plan can be represented by a planar graph of nodes and links, where each node corresponds to a discrete area in the plan, each link corresponds to a connection between nodes, and each district corresponds to a subgraph with every node assigned to a subgraph.
Definition: Node. A node is a reference point for a geographic unit. For a political unit the node is the primary place of government for that unit.
Definition: Link. A link is a representation of a connecting path between two nodes. There is at most one link between nodes. For any type of connection, the connecting path between two nodes is considered to be the path that takes the shortest time as determined by generally available mapping software.
For example, here's a map of NC counties with a graph overlaid. The circles represent nodes for the county seats and need not be in the exact location of the county seats. The lines connecting the circles are links, and the color indicates the type of the link. As described in further posts, blue and green links are regional connections. Yellow, gold, and orange links are local connection without a regional connection. Pink links show contiguity without a local connection.
Item 10a: A macrochop of a geographic unit replaces that original unit with a set of subunits that cover all of the original unit. The original unit and its node and links are no longer considered in the plan. The subunits are treated as new units in the plan with their own nodes and links. (see Item 10.)
For example, Mecklenburg county NC is sufficiently large that it must be macrochopped to form congressional districts. The county node has been replaced by subunit nodes and links. Subunits are based on the 6 independent towns and 6 planning areas for Charlotte. Blue links are regional connections between counties. Gold links are local connections. Pink links are contiguous only.
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