Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 60

• One-to-one ownership: One family owns a single parcel of land, often
in a suburban area and elsewhere when land is plentiful and land
values are relatively low.
• Many-to-one ownership: Many families own a single parcel or build-
ing. This style of ownership is often “condominium” or “cooperative”
ownership. In the landscape, it is evident mostly in more densely
populated areas or where land values are relatively high.
• One-to-many ownership: One family owns many residences. This par-
ticular situation, not represented as a mathematical function but only
as a relation, is perhaps not as common as the two above. Typically,
one might expect families with excess wealth to own more than one
residence. Our colleague John Nystuen asked where, in the situation
with multiple residences, such individuals cast votes. We explore the
dynamics of that situation below.
3.1.1.3 Composition of transformations
If one were to map the relations listed above for home ownership, a figure
similar to Figure 3.3 would be the result. When voting is added on, the situa-
tion becomes more complicated, given that voting is done and counted locally
and not nationally.
• In the one-to-one situation, the homeowner registers to vote from his
or her single address and there is no difficulty counting the vote.
• In the many-to-one situation, the homeowners register to vote from
their unique, single address and there is no difficulty counting the
vote. All go to the same polling place to vote.
• In the one-to-many situation, however, a person who owns property
in Michigan and in Florida, for example, might attempt to vote in two
places even though he/she is only entitled to one vote.
Figure 3.4 shows that when only a single vote is cast, as it should be, the
system remains closed, bounded, and manageable (in some sense). In Figure
3.4a , voter x owns three residences, y 1 , y 2 , and y 3 and casts the one legal
vote, z , to which he/she is entitled. Voter a owns three residences, b 1 , b 2 , and
b 3 and casts one legal vote c 1 (from residence b 1 ) and two illegal votes (from
residences b 2 and b 3 ), c 2 , and c 3 . Note that the legal case is visually manage-
able in some sense while the illegal case sprawls across the map and is more
difficult to track. When more than one vote is cast, the system may rapidly fall
out of order, especially when there are thousands or hundreds of thousands
of people who own more than one residence from which they might vote.
When home ownership and voting become more complicated ( Figure 3.4b ) ,
the closure and sprawl issues, referred to above, become more evident. Some
sort of nationalized database on voter registration and residency makes the
problems easier to deal with.