MAPS AND DECISIONS, II:  Ambiguity.
Sandra L. Arlinghaus and William C. Arlinghaus

General Introduction

     Tournament level duplicate bridge is a card game that is a sport.  As is the case with sports, generally, there is an overseeing body:  in basketball it is the National Basketball Association (NBA); in bridge it is the American Contract Bridge League for North America (ACBL) and the World Bridge Federation (WBF) for all nations in the world.  The ACBL is a non-profit organization based in Memphis, Tennessee.  The ACBL has about 150,000 members in the U.S.A., Canada, and Mexico.  The WBF has more than 10 million members.  The ACBL owns two buildings in Memphis where they house a large staff to maintain records, databases, publications, and a host of other operations associated with this business in the entertainment/sports sector of the business world.  The second author of this work is currently a member of the Board of Directors of the ACBL.  This Board, as do equivalent boards of other corporations, sets policy for the organization, makes decisions that affect the entire population of ACBL members, and oversees the work of the Chief Executive Officer.  There are 25 Board members, each representing one geographical "district" of the ACBL.  Thus, the members of the Board of Directors are also referred to, even though their charge is to represent the interests of the entire ACBL, "District Directors." 

Ambiguity

     The second author is the District Director for District 12, including all of the lower peninsula of Michigan, part of the upper peninsula, and northwestern Ohio.  The map in Figure 1 shows the geographic extent of each of the districts with respect to the conterminous USA and suggests boundaries in Canada and Mexico (to see a full characterization, visit the ACBL website).  In addition, Figure 1 shows the count of members for each district as of March 2005, according to ACBL databases.  One reason for an individual district director to care about maps of all districts is individual district norms can be evaluated against national ones.  A national view may help to put local issues in perspective.  Decisions made at the national level affect individual districts.  The idea is a straightforward one employed in many arenas:  map the data at one scale in order to make cross-scale evaluations of various sorts.  As long as the data and maps work well together, the process works well.  When that mesh is not there, however, sometimes extra insight for decision-making comes from the mere process of mapping the data as the case below will show.

Figure 1.  ACBL membership mapped by District, based on March 2005 data.

     Each ACBL district is further subdivided into a number of "units."  The attached clickable map shows each district and its units for the conterminous USA.  Click on any unit and the corresponding part of the underlying database pops up showing district number for that unit, unit number, and number of ACBL members by unit.  This interactive map is a useful tool for getting a quick count on where there are concentrations of members and where there are not.  The former is important in considering where tournaments might best be located to serve large numbers of current members while the latter is important in looking for regions of potential recruitment (when coupled with other information such as density counts).  When the lower 48 of the US is mapped as a choropleth map on the number of members by unit the map in Figure 2 is the result.  The map was shaded in the GIS using shades of red; the light yellow areas are regions of no data (and these are identical independent of the method used to partition the data to produce the red regions).

     It might be plausible that there are units in rural California or eastern Oregon and Idaho with 0 members.  It is not reasonable, however, to believe that all of southeastern Michigan, including the entire Detroit metropolitan area and Ann Arbor contains no members.  A look back at the clickable map, at southeastern Michigan reveals the same situation (although it is much more evident in the single, static map below).  Is there a blunder in the record-keeping?  Take a closer look; it reveals far more.  What appears to be a single unit in Southeastern Michigan is in fact two units (from other ACBL data): 
One might wonder why there is this separation that belies, for example, the idea of standard metropolitan areas of various sorts; it is useful to employ census measures and such in relation to bridge territories, but this split makes that process difficult.  The reason for the separation is historical and is apparently based in perception issues of various sorts that are hopefully no longer part of the contemporary scene.  Some time ago, therefore, the ACBL allowed anyone living in the southeastern area of Michigan to choose which unit he or she wished to join.  Because the ACBL accumulates data by ZIP code and assigns member ZIP code to units in this and other databases, those in which members are allowed to choose units do not show up and are recorded as missing data:  there is no assignment algorithm that applies to these members.  There is ambiguity in choice:  one member in Detroit may choose the MBA and that member's next door neighbor (in the same ZIP code) may choose SOMBA.  In most other locales, all members in any given ZIP code are all assigned, with no choice, to a particular unit:  they show up in the database.  The mapping process made evident a densely populated region of the bridge database that has no count in decisions made using that database.

Figure 2.  Ambiguity:  note the light yellow area in southeastern Michigan.

Thanks to Jay Baum, ACBL CEO, Rick Beye, Carol Robertson, Richard Oshlag, and Ed Evers, ACBL, for providing the materials directly to Sandra Arlinghaus, who then created the map sets using GIS software (ESRI, ArcView 3.2) that forges a dynamic link between underlying database and outline base map.  Graphic adjusments of various kinds were made in Adobe PhotoShop or Adobe Illustrator.
Solstice:  An Electronic Journal of Geography and Mathematics, Institute of Mathematical Geography, Ann Arbor, Michigan.
Volume XVII, Number 1.
http://www.InstituteOfMathematicalGeography.org/