The Efficient Siting of Noxious Facilities Under Majority
Rule Decisions
Timothy L. Hamilton
Amit Eynan
January 16, 2017
PLEASE DO NOT CITE WITHOUT AUTHOR PERMISSION
1
Introduction
A difficult and challenging decision facing policy makers is the allocation of goods that generate externalities. It is well known that markets forces alone will lead to inefficient outcomes.
Of particular interest in modern industrial societies is the task of choosing locations for
siting noxious facilities such as waste treatment facilities, landfills, or nuclear waste repositories. Such facilities are often associated with the NIMBY (Not In My BackYard) syndrome
(O’Hare et al., 1983). While such facilities are important parts of production economies,
individuals are averse to these facilities in their “backyard” because, all else equal, proximity
to such a noxious facility lowers utility. This last point is well documented in a large literature that indicates a negative relationship between proximity to such facilities and lower
housing prices (Farber, 1998; Ihlanfeldt and Taylor, 2004; McCluskey and Rausser, 2003).
Also note that while the discussion is often framed in terms of siting facilities, the idea is
equally applicable to allowing or not allowing particular activities at specific locations, such
as changes in land use or resource extraction.
1
The problem of siting noxious facilities challenges the allocative abilities of markets. One
question relates to which locality, among a number of choices, should host a proposed facility. Oates and Schwab (1988) show that efficiency results from a framework in which
communities compete for private and environmental production and make decisions using
a simple-majority rule. These results, however, are driven by the existence of homogeneous damages in any given locality, which implies full compensation. The standard market
solution- create a market in sites, and locate the facility in the locality that is willing to
serve as host for the lowest price- is likely to lead to efficient facility locations only if host
localities internalized all costs of the facility and were fully compensated for such. If so, then
the cheapest facility sites would be the most efficient, requiring the lowest cost to compensate
for damages. In the aggregate, the efficient number of noxious facilities will be constructed.
Similarly, Kunreuther and Kleindorfer (1986) develop a sealed-bid auction mechanism that
sites the facility in the winning location. Again, efficiency follows from a framework in which
aggregate willingness to pay reflects the preferences of a community. Minehart and Neeman
(2002) combine a bidding procedure with monetary transfers that act as both incentives and
compensation.
As shown by Ingberman (1995), the NIMBY syndrome implies that neither cost internalization nor full compensation result from a simple market siting process that is subject
only to approval of a locality. Thus, such market solutions are likely to lead to an aggregate
excess of facilities as well as inefficient site choices. A second question, therefore, pertains
to siting decisions on the part of individual localities. For competition between localities to
potentially serve as an efficient mechanism in the aggregate, it is reasonable to first determine whether a locality can make an efficient siting decision in isolation. Several studies
develop mechanisms that generate efficient siting decisions. One solution is proposed by
Perez-Castrillo and Wettstein (2002). An efficient solution is reached using a multibidding
mechanism that allows individuals to simultaneously bid different values for multiple potential projects. This process generalizes a siting decision by treating the proposed facility and
2
no facility as multiple projects.
As it seeks to determine the ability of localities to efficiently make siting decisions, this
research also contributes to issues surrounding fiscal federalism. Oates (1972) discusses the
theory of decentralization, in which efficiency is achieved when provision of local public goods
is the responsibility of local jurisdictions. Such jurisdictions are able to better capture the
demand of its residents. Closely related to our analysis is a change in the decision process for
siting nuclear waste storage facilities. Discussed in detail in Benjamin and Wagner (2006),
such decisions are now driven by the private sector and local jurisdictions, rather than the
U.S. Department of Energy. The basic principle of decentralization in fiscal federalism, which
states that decisions regarding public good provision should be belong at the lowest level of
government that includes the relevant cost and benefits (Oates, 1999), is open to criticism
in particular cases. One such case arises when the bounds of environmental impacts are not
perfectly aligned with those of political jurisdictions. We present a particular, though not
unlikely, specification of this property in our model where the relative size of the decisionmaking jurisdiction directly impacts the efficiency of the decision-making process.
Results related to fiscal decentralization suggest that local public good provision should
be the responsibility of local jurisdictions. Moreover, bidding mechanisms indicate a means of
generating efficient outcomes at the local level. A single decision-maker may be left to make
a siting decision for a locality but would require the willingness to pay of each citizen to do so
efficiently. The mechanism developed by Perez-Castrillo and Wettstein (2002) accomplishes
this when individuals are able to accurately provide their true preferences. More often,
however, locality decisions are made on the basis of a vote, in which individuals only have
the option to vote for or against a facility based on their individual preferences, rather than
providing any magnitude of their values. While the use of an approval voting structure may
be inferior, it is typically dictated by political constraints. The purpose of this paper is to
investigate the possibility that such a voting procedure can be used to make efficient siting
decisions. Specifically, we seek to determine a criteria for passing siting decisions within the
3
majority-rule voting process, primarily by correcting the features of local majority rule that
lead to inefficiency.
The following subsections present the general mechanism that drives inefficiency in majorityrule voting, followed by examples of voting on siting decisions. In section 2 we develop a
functional model to generalize damage functions and population distributions. Section ??
discusses inefficient siting decisions in the context of our model and Sections 4 and 5 provide
potential solutions to such inefficiencies under different model assumptions. We provide an
empirical exercise that parameterizes the population distribution function in Section 6 to
illustrate the magnitude of potentially inefficient decisions. Finally, Section 7 concludes with
a discussion of our results and caveats of our analysis to be explored in further research.
1.1
The Inefficiency of Market Siting
To establish intuition, it is useful to understand why inefficiencies result from relying on
markets to site noxious facilities.1 Following Ingberman (1995), consider a firm that seeks to
site a facility in one of a number of localities. Each locality consists of a uniformly distributed
population on an otherwise featureless plane. Given that markets are used to choose sites,
the host locality must be offered compensation in the form of a host fee that leads it to agree
to host the facility.2 Assume that localities use simple majority rule to make their decisions.3
Due to the decision facing the owner of the noxious facility, the locality that requires the
lowest host fee will host the facility.
There are two fundamental attributes of noxious facilities that drive the inefficiencies of
this market siting process. First, individuals in the host locality want any facility it hosts to
be sited as far away as possible, in an effort to avoid damages associated with proximity to
the facility. Second, the benefits of hosting a facility (host fees) stop at the host locality's
border, while the disamenities of the site can cross borders. While the latter problem of
cross-boundary spillovers is an important aspect of siting decisions and a significant source
of inefficiency across the entire landscape, this paper is concerned with the former problem.
4
Absent any spatial externalities outside of the locality, plausible assumptions lead to a situation in which simple majority rule siting decisions will generate inefficiencies within the
host locality. More specifically, the majority will accept the facility at a host fee that is
strictly less than the total disamenity the facility imposes on the locality. This result implies
that host localities will accept facilities at a price lower than their disamenities, so that an
aggregate surplus of noxious facilities will be constructed and thus generate an excessive
amount of environmental damages.
Ingberman (1995) establishes the inefficiency of siting based on majority rule by presenting the case of a square-shaped locality with residents distributed uniformly across space.
We impose a flexible structure on the model to make several contributions. First, we generalize the results of Ingberman (1995) to create a model that is more closely aligned with
the nature of localities. Second, our quantitative structure enables calculation of a voting
rule that would achieve efficient siting. Such structure also allows us to explore the characteristics of population distributions that mitigate or exacerbate the problem and offers the
opportunity for empirical analysis.
We show that inefficient siting can be eliminated by requiring a supermajority for siting
decisions: i.e. a requirement that some percentage more than 50% of the population must
agree to host the facility. For example, given a particular shape of the locality and facility
disamenities that linear in distance and everywhere positive, a supermajority of 5/9 will
equate the locality's aggregate disamenity with the host fee needed to elicit voluntary agreement. If the facility disamenities are convex in proximity or if disamenities go to zero within
the locality, then 5/9 supermajority rule – while an improvement over simple majority rule
– still leads the locality to voluntarily accept a facility at a host fee that lies strictly below
the aggregate disamenity imposed on the community. We therefore address these potential
5
extensions of the baseline model.
1.2
Applications
The primary model of this paper is one in which localities use a majority rule vote to
determine whether or not a noxious facility or activity should be allowed to site within the
community s boundaries. While some siting decisions are the result of top-down decisions
or free market purchases of land, there are many scenarios in which majority rule at the
locality level may determine siting.
There are two prominent cases of majority-rule criteria applied directly to the siting of
noxious facilities in Canada. In 1984 a private firm sited a hazardous waste treatment facility
in the community of Swan Hills, located in Alberta. The decision concluded a four-year
process that saw a list of potential communities narrowed down to a single town, followed by
town meetings and informational campaigns run by the Environmental Council of Alberta.
Due to activities leading up to the vote, including information meetings relating to technical
and regulatory matters of the facility, it is reasonable to assume a well-informed population
with knowledge of the potential dangers. The town of Swan Hills conducted a referendum
in which approximately 80% of the town's citizens voted in favor of siting the facility. The
plant officially opened in 1987. At the time of its opening, the facility offered no host fees or
tax revenues. Benefits were presumably only in the form of economic activity (Harris, 1994).
A similar process took place in Montcalm, Manitoba, in which a hazardous waste treatment facility was successfully sited in 1991. After several rounds in which communities
3
There is a large literature that advocates exactly the opposite conclusion, namely that markets would be
efficient in siting facilities. See, for example, Mitchell and Carson (1986), Kunreuther et al. (1987), Sullivan
(1990), or O’Sullivan (1993). The conclusion that markets are efficient siting mechanisms, however, relies on
two key assumptions: 1) political jurisdictions fully internalize the disamenities of facilities, and there are
no spillovers across borders or other externalities, and 2) the majority will never accept a facility at a price
that reduces total economic surplus in the jurisdiction as a whole. As shown by Ingberman (1995), these
assumptions are often implausible in equilibrium.
3
For evidence of the prevalence and magnitude of host fees, see Jenkins et al. (2004), in which the authors
compile a datset of 37 solid waste landfills that paid host fees to local jurisdictions in 1996. The average
host fee among these 37 landfills was approximately $1.5 million.
3
See the discussion in the following section for instances where simple majority rule applies to siting
decisions.
6
expressed interest in hosting the plant, the list of potential sites was narrowed down to four
communities. Majority-rule referenda in two of the communities rejected the proposal. A
third community, Winnipeg, was deleted as a potential site due to its high population density. The fourth community, Montcalm, became the focus of open houses and informational
meetings put on by both the proposed facility's owners and local government and environmental groups. More than a year after evidence of initial support, the local government of
Montcalm held a referendum in which 67.1% (618 citizens) voted to “support the location
of a hazardous waste management facility by the Manitoba Hazardous Waste Management
Corporation in the Rural Municipality of Montcalm (Castle, 1993).
While there have not yet been any direct votes yet, an obvious candidate for a referendum
is a nuclear waste storage facility. Such facilities are difficult to site in communities and the
surrounding debate has become increasingly contentious. Efforts to locate storage facilities
in the United States have met an enormous degree of opposition from states, local communities, and environmental groups (Kraft, 2007). Furthermore, the possibility of referenda has
entered the public discourse in both Russia and Taiwan.
Perhaps the strongest possibility for a majority-rule referendum is the opening of lands for
hydraulic fracturing. Hydraulic fracturing, commonly referred to as “fracking”, involves the
process of injecting fluids into the ground, thereby creating fractures in the earth that allow
for easy extraction of natural resources. It is most commonly used for extraction of natural
gas. The economic benefits of fracking are obvious, stemming from economic activity and
access to a larger supply of energy resources. However, the procedure itself poses significant
environmental and health risks. While the impacts are still imperfectly understood, the
U.S. Environmental Protection Agency (EPA) has reported initial findings of increased air
pollution and contamination of ground and surface water.4
Due to the potential health and environmental risk, fracking has become a target for
4
For EPA analysis of fracking see http://www2.epa.gov/hydraulicfracturing.
For EPA analysis of the impact of fracking on drinking water see http://www2.epa.gov/sites/production/files/201506/documents/hf es erd jun2015.pdf.
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policy concerning whether or not to allow such activity. Shale basins that serve as potential
fracking sites are spread throughout the United States, with large plays concentrated in New
York, Pennsylvania, West Virginia, Ohio, and Michigan. Recent years have seen the use of
state-wide referendum as a tool for a number of social issues. This suggests that a push for
fracking resolutions on state ballots can be expected. Already in Michigan, the Committee
to Ban Fracking in Michigan is gathering signatures to put a proposal to ban fracking on a
statewide ballot.5
Previous to a statewide ban on fracking in New York, there were 141 bans or moratoria on
fracking at the municipality level in the state. Popular movements for a ban or moratorium
existed in an additional 82 municipalities.6 While it is unclear how many of these resolutions
were passed as a result of a direct vote, all municipalities operate according to a democratic
process. It is therefore reasonable to assume that these local political decisions are driven by
majority-rule. In both Peters, PA and Warren, PA, however, fracking was approved in late
2011 by popular referenda (Bosco, 2011; The Times Observer, 2012). As indicated by the
level of current activity, fracking is a high-profile issue surrounded by an engaged citizenry.
Majority rule decisions appear to offer the most accessible means of addressing concerns.
2
A Model of Majority Rule Decisions
2.1
Siting Decision
To simplify the exposition, we examine only the firm’s decision to site a single facility in one
locality.
7
The facility creates local disamenities and, aside from any host fees paid to the
host locality, creates no local benefits. While this appears to be an extreme assumption, it
corresponds to the case of tax revenues and/or economic growth that are evenly distributed
across the population. Majority agreement will require compensation in the form a host fee,
5
6
http://www.letsbanfracking.org/
http://www.fractracker.org/map/us/new-york/moratoria/
8
of which residents receive equal per capita shares.
Locality residents experience some level of disamenities (costs) that increase with proximity to the facility. That is, define d as a voting household's distance from the proposed
facility and define disamenity (cost) function c(d) as the disamenity experienced by residents
who are located at distance d from the facility.
We assume that the disamenity function c(d) is (weakly) convex: c0 < 0, c00 ≥ 0. This
common assumption can be interpreted more generally as a localized disamenity, in the sense
that the damages increase at an increasing rate as one becomes closer to the facility. Such
a specification also serves as the basis for much of the empirical literature that estimates
damages through the impact on housing values.
The decision on the part of a locality to accept a facility is determined by a simple
majority rule. For any facility to be sited, a majority of voters in the host locality must
agree to host. Voters vote “yes” whenever they are at least as well off accepting the facility
as they are when rejecting the offer. Profit maximizing firms will offer the minimum host
fee that still achieves acceptance of the facility.
2.2
Equilibrium Compensation with Simple Majority Rule
Suppose a locality will serve as host. Ingberman (1995) shows that a majority prefers to site
the facility on its border when localities are square shaped and have population uniformly
distributed across the land area. A corner location minimizes the disamenity of the facility
to the population. Therefore the firm and the majority have a joint incentive to choose a
corner location. Thus, undercompensation of the host locality in the case of a corner location
is sufficient to conclude that host fees are inefficiently low.
Since the firm wants to minimize costs, it offers a host fee that makes the voter who
is median distance from the facility indifferent between hosting or not. Given such a host
fee offer, those voters who are more than median distance must strictly prefer to serve as
7
This corresponds to the first-stage optimal choice for each possible site when looking at competition
among localities.
9
host for the offered fee (since they bear lower disamenity but receive the same share of the
host fee benefit). In the model of Ingberman (1995) mean distance from the facility, which
determines the minimum host fee offered, is strictly less than the median distance. There
are two properties that cause mean distance to be less than median distance. The first is
a disamenity function that is decreasing in proximity. The second involves the distribution
of distance to the proposed facility across the population. A uniformly distributed (across
space) population generates a probability distribution of distance in which there is a higher
density of voters at farther distances.
The model assumes no bargaining power on the part of the locality, a reasonable assumption when there is potential competition with other localities. It is also assumed that
the firm’s location decision is driven entirely by the required host fee, rather than other
amenities within the locality. The equilibrium described above will exist if the minimum
aggregate host fee is less than the expected profit from siting the facility. If the minimum
required aggregate host fee is larger than expected profit, the facility will not be established.
We extend these results to examine the case of a non-uniform distribution of the population across space in a non-square locality. We assume that the locality’s geographic
boundaries encompass a convex set of points and that the spatial population distribution
is a unimodal bivariate distribution.8 In equlibrium, the profit-maximizing firm will choose
a location on the border to maximize median distance from its facility. Importantly, this
location will result in mean distance that is less than median distance, leading to a host fee
that is less than average damages.
As a firm seeks to minimize host fees, it locates a facility away from areas with high population density. Such behavior generates a distribution of distance that is negatively skewed,
generating mean damages that are greater than median damages. While there may exist
localities with particular geographic shapes and spatial distributions for which a negative
skew does not arise, our empirical application and specified parametric distribution in what
8
The bivariate distribution corresponds to the geographic coordinates in 2-dimensional space.
10
follows are able to capture a variety of potential population distributions that demonstrate
the prevalence of inefficient siting.
2.3
Functional Model
To demonstrate the degree of inefficiency in majority rule siting decisions and to generate an
efficient solution, we specify a functional form for the distance distribution. Conceptually,
we are concerned with the distribution of the population throughout the locality, across a
two-dimensional plane. Mechanically, however, the actual variable of interest is “distance to
the facility”, a scalar measure. Any bivariate distribution of coordinates in two-dimensional
space can be transformed to a univariate distribution of the Euclidean distance between
each point and a single point representing the location of the proposed facility. We focus
on the measure of distance, retaining generality in terms of the shape of the locality and
the explicit distribution of the population across space. We continue to assume that the
proposed location of the facility is in the point of the locality that minimizes the necessary
host fee.
To model the distribution of a voter's distance to a proposed facility we use the Beta
distribution, Beta(α, β). This distribution has support [0,1], making it ideal for modeling
a distance variable that is positive with an upper limit defined by the size of the locality.
Without loss of generalization, we simply normalize the maximum distance to 1. Moreover,
the Beta distribution is very flexible, as parameter combinations can generate probability
density functions that are increasing, decreasing, or nonmonotonic, along with different
degrees of concavity and convexity. Using the Beta distribution, the density function of
distance d is defined as
f (d; α, β) =
1
dα−1 (1 − d)β−1 ,
B(α, β)
11
(1)
where B(α, β) is the beta function9 ,
Z
B(α, β) =
1
xα−1 (1 − x)β−1 dx.
(2)
0
The cumulative distribution function is
F (d; α, β) =
B(d; α, β)
B(α, β)
(3)
Equilibrium siting decisions made through majority rule mechanisms with offered hosts
fees may result in distance distributions that are negatively skewed. As seen in Ingberman
(1995), the special case of a square locality with spatially uniform population distribution
results in a negatively skewed distribution of distance to the optimally located facility. This
is also true for the more general case of any locality whose borders encompass a convex set
of points.10
We concentrate on two subsets of parameters (α, β) that generate negatively skewed
distributions and thus describe potential equilibrium solutions. The first subset is β =
1, α ∈ [2, ∞], which generates a density of distance function that it strictly increasing and
weakly convex. This subset implies a population that is increasingly concentrated away
from the potential facility. The second subset is β = 3, α ∈ (3, ∞]. This subset generates
a density of distance in which the population concentrates around a particular point within
the locality. Such a point can be interpreted as a central business area or an amenity that
provides benefits with proximity. It is important to note that this point of concentration
remains at a far distance from the proposed facility and thus creates a distribution that is
negatively skewed. If this point of concentration was located close to the facility (positively
skewed distribution), that proposed facility location would not be optimal for the firm, as
they could find a location with a lower necessary host host fee. There are other possible
9
The beta function may also be defined from the gamma function, B(α, β) =
10
See Appendix ??.
12
Γ(α)Γ(β)
Γ(α+β)
parameter combinations that work within the context of our model's equilibrium, given more
variation in β, but these subsets add little to the discussion.
To demonstrate the role of the Beta distribution in capturing potential spatial distributions, it is helpful to see that potential localities can be described with a parameterized Beta
distribution. For example, a quarter-circle locality with a uniform distribution leads to an
equilibrium in which a facility is sited at the corner where the radii meet. The distribution of
distance to the facility is defined as Beta(2,1). Equilibrium siting in a square locality with a
uniform spatial distribution, as in Ingberman (1995), generates a density function of distance
to the facility that is negatively skewed and can be approximated by the Beta distribution
with α ≈ 2.63 and β ≈ 2.38. Different shapes and spatial distributions will then lead to
distance distributions characterized by concentrations of households at different distances
that can still be approximated with a beta distribution. From a Beta(3,2) distribution, an
increase in the first parameter models a population that is concentrated further from the
facility. Alternatively, an increase in the second parameter models a population that is more
highly concentrated around a particular distance. Overall, the beta distribution serves as a
flexible way to capture the scalar variable of interest, which is the distribution of distance
to a facility.
In addition to the distance distribution, we define a flexible function for the cost function,
c(d) = dγ (1 − d)δ .
(4)
We are primarily concerned with cost functions that are decreasing in distance and weakly
convex. The special case in which γ = 0 and δ = 1 results in a linear damage function in
which marginal (over distance) damages are constant. The cost function becomes convex as
γ decreases from 0 and as δ increases from 1. When γ decreases, the convexity manifests
as a very sharp decrease in costs at close proximities, implying a disamenity that causes
considerable damages concentrated at very close proximity. The cost function is also convex
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for values of δ greater than one. As δ increases, the cost function flattens out at farther distances. One interpretation here is that damages approach 0 within the locality and, beyond
this point, increased proximity to the site causes very little damage: i.e. if an individual
lives at least x miles from the facility, damages will not decrease (increase) significantly if
she moves further away (closer). We focus on creating a convex cost function by decreasing γ
and return later to the role of δ in generating potentially interesting disamenities. In general,
the functional form in Equation (4) is quite flexible and capable of generating a variety of
damage function properties. We begin by assuming that disamenity costs are positive for all
residents within the locality. We relax this assumption later on.
3
Inefficiency of Majority Rule Siting
Siting inefficiency is defined here as the equilibrium in which mean damages are greater than
median damages, leading to a decision that generates greater aggregate costs than aggregate
benefits in the form of a host fee. While siting a facility may not be the optimal choice
in terms of the size or nature of the facility, we are only considering the choice of allowing
or rejecting the facility and measuring whether this is an aggregate welfare improvement.
To demonstrate the inefficiency of majority rule siting, we establish mean costs and median
costs in the context of the previously discussed function forms.
Mean disamenity costs, c̄, are calculated as
Z
1
c̄ =
c(x)f (x)dx.
(5)
0
As shown in 1Appendix Appendix A:, mean costs are easily calculated as the ratio of two
beta functions,
c̄ =
B(Θ, Φ)
,
B(α, β)
14
(6)
where
Θ = α + γ and Φ = β + δ.
(7)
Median disamenity costs, denoted cM , are found directly using median distance from the
proposed facility. Since the cost function is a monotonic transformation of distance, the
individual that is median distance from the facility will suffer median costs and thus be the
pivotal voter. Median distance, dm , in the Beta distribution is implicitly defined as
0.5 =
B(dm ; α, β)
,
B(α, β)
(8)
Median costs are then calculated as
cM = c(dm ) = dγm (1 − dm )δ
(9)
For the negatively skewed Beta distribution (justified by optimal firm behavior) median
distance from the proposed facility will be greater than mean distance. Specifically, mean
distance in the beta distribution is defined as
mated by
α−1/3
,
α+β−2/3
α
,
α+β
while median distance can be approxi-
so that mean distance is smaller for the previously discussed cases where
α ≥ β. In the case of linear damages, c(d) = (1 − d), smaller mean distance from the facility
implies that mean disamenity costs are higher. As the cost function becomes more convex,
costs become more concentrated around the facility, exacerbating the inefficiency. In our
model, an increase in convexity is achieved through a decrease in γ or an increase in δ. As
shown in Appendix Appendix B:, both changes in the cost function increase mean costs more
than median costs, causing aggregate costs to increase more than the potentially successful
host fee.
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4
Siting Efficiency
It becomes clear that aggregate damages will be greater than the required host fee (enough on
average to satisfy the pivotal voter) by seeing that the voter who suffers mean costs is closer
to the proposed facility than than the voter who suffers median costs. A skewed distance
distribution and convex disamenity costs each contribute to this inefficiency. To correct the
emergence of excessive costs, an efficient supermajority can be defined as M , which is equal
to some percent of the population that must agree to site a facility in a particular location
such that the aggregate host fee is equal to aggregate disamenity costs. Such a mechanism
will lead to higher host fees that generate compensation for disamenity costs, and prevent
siting in the case of host fees that do not cover aggregate costs. The efficient supermajority
M should generate a pivotal voter that suffers mean costs. Define d∗ as the distance at which
mean costs are incurred so that
c̄ = d∗ γ (1 − d∗ )δ ,
(10)
M = 1 − F (d∗ ; α, β).
(11)
To find the efficient supermajority, we find the distance of the voter who suffers mean costs
and calculate the cumulative distance distribution at this point, F (dc̄ ). This implicitly
defines the necessary supermajority to avoid excess costs. Without a general closed-form
expression for d∗ , there is no general closed-form solution for M . Rather, we derive M for
the specific cases in which d∗ can be found analytically and use numerical methods to find
d∗ in other cases, at which point M is easily found using Equation (11).
5
The Efficient Supermajority
The required voting supermajority that will ensure an aggregate host fee that compensates
for aggregate disamenity costs is dependent on the parameters of the model. While a closedform expression that defines the supermajority as a function of model parameters does
16
not generally exist, there are general results related to specific distributional assumptions.
Special cases of model parameters help to isolate the impact of convexity in costs and the
distribution of the voting population. We first present the case of linear costs to examine the
role of population concentration. We then present specific distance distributions to examine
the role of convex costs and the interaction of the two properties. Finally, we consider the
special, but plausible, case in which the cost function becomes zero within the bounds of the
locality.
5.1
Linear Disamenity Costs
Assume that disamenity costs are linear, so that the cost function is c(d) = 1 − d. In this
case, the voter that suffers mean costs is the voter at the mean distance. Mean distance is
defined by the parameters of the Beta distribution so that d∗ = d¯ = α/(α + β). Of course
there are still many possibilities for the distance distribution. Consider the first subset of
parameters, β = 1, α ∈ [2, ∞]. As mentioned earlier, this subset describes a population that
is concentrated further and further away from the proposed site.
Within this parameter subset, [α, β] = [2, 1] simplifies to a positively-sloped straight
line density function for distance, f (d) = 2d. Mean distance is d∗ = 2/3 and evaluating the
cumulative distribution function for distance at this point, the efficient supermajority is equal
to 5/9. Therefore, if the locality requires a 5/9 supermajority to allow the facility to operate,
the host fee that satisfies the pivotal voter will be equal to the total costs generated by the
facility. As the population becomes more concentrated away from the proposed facility (i.e.
as α increases), the efficient supermajority (see Appendix C.1: increases to account for the
fact that a higher density of voters are located in places with relatively lower costs, driving
down the firm's host fee offer relative to total costs:
M=
5 e−1
,
9 e
f or α ∈ (2, ∞].
17
(12)
As α increases, the required supermajority approaches approximately 0.632. In both cases,
it is clear that a simple majority rule to determine whether the facility is established will
not be sufficient in generating enough host fees to cover disamenity costs.
In another specification, we consider the fact that populations tend to centralize around
particular areas for a variety of reasons, areas that are likely not the farthest points from
a polluting facility. For example, populations are often observed to be concentrated around
central business districts. Using the parameter combinations β = 3, α ∈ (3, ∞], we can again
derive efficient supermajorities. Note that Beta(3,3) is a symmetric distribution so a simply
majority of 0.5 will achieve efficiency. However, if such a distribution of distance to a facility
existed in a two-dimensional locality, it must be the case that population is concentrated in
close proximity to the facility. Then there will exist an alternative location that generates
lower median costs. A firm would choose this alternative location to minimize the cost of
paying host fees. We therefore are relatively unconcerned about this particular parameter
combination that generates a symmetric distribution of distance.
For cases in which β = 3, α ∈ (3, ∞], the efficient supermajority (see Appendix C.2:) is
M=
1 e3 − 8.5
,
2
e3
f or α ∈ (3, ∞].
(13)
The upper limit of approximately 0.577 is considerably smaller than earlier. As seen in
the previous scenario, the inefficiency in majority rule is amplified by increasing density
away from the facility. However, the increase in density around another location serves as a
countering force as measured against concentration at the farthest possible distances.
An alternative means of interpreting this is in the context of the required host fee. As
the population concentrates at an area relatively closer to the facility, the median falls and
a higher host fee is required to win a majority vote. While the mean decreases as well, it
decreases at a rate slower than that of the median (since the two converge as a symmetric
distribution is approached), so that median damages increase more rapidly. This implies an
18
increase in the host fee relative to mean damages, mitigating the magnitude of the inefficiency
in a simple majority decision.
5.2
Nonlinear Disamenity Costs
We now return to the general case of convex costs, but use only specific parameterizations
of the distance distribution. In particular, we consider the distance distributions defined
by Beta(2,1), Beta(3,1), and Beta(6,3). As a general rule, increasing convexity in the cost
function leads to a greater required supermajority to reach efficiency. This arises as a simple
majority vote is dominated by voters far away that have relatively lower costs as convexity
increases. As discussed earlier, an increase in the convexity of the cost function causes mean
costs to increase at a faster rate than median costs.
The lack of a closed form solution for the distance at which mean costs are incurred
requires that we numerically solve for the the efficient supermajority. Given the simple
solution for mean costs derived earlier, we use a bisection algorithm to find the efficient
supermajority. Tables 1-3 display supermajorities for our three specific parameterizations
of the distance distribution. Upon examination of similar parameter combinations across
tables, the pattern discussed in the previous section is clear. For any given disamenity cost
function, the necessary supermajority increases as the population distribution becomes more
concentrated at farther distances (i.e. as α increases). This is evident from a comparison
of Table 1 to Table 2. In addition, the necessary supermajority decreases as the population
distribution becomes more concentrated around some interior point in the locality, as is seen
in a comparison of Table 1 to Table 3.
Focusing on the impact of the shape of the disamenity function, these tables demonstrate
the earlier result that increasing convexity exacerbates the efficiency problem. Increasing
convexity can be modeled as either an increase in the δ parameter or a decrease in the γ
parameter. The top left corner of Tables 1-3 replicates the case of linear damages. As the
cost function becomes more convex the necessary supermajority quickly increases, requiring
19
a large portion of the population to support siting the facility. While a siting decision is
based on a simple yes/no decision related to some threshold value, efficiency is based on the
magnitude of costs. A convex cost function leads to costs being highly concentrated among
those individuals that disapprove of the facility, increasing aggregate costs, but without such
a large increase in costs at farther distances to increase the required host fee enough. An
extreme version of this scenario is one in which a single voter lives next to the facility and
the remainder of the population lives sufficiently far away to incur zero costs. In such a
situation, ensuring that the aggregate host fee covers aggregate damages requires that the
host fee covers the costs of that single individual, thereby creating a necessary supermajority
of 1.
5.3
Disamenity Costs Decay to Zero
Finally, one may be interested in the particular cost function in which the disamenity cost
becomes zero at some finite point. Such a situation arises when the facility has no negative
impact on some households within the locality that are sufficiently far away. However, we
consider only cost functions that approach zero continuously. These properties are captured
by the disamenity cost function
c(d) = dγ (` − d)δ ,
(14)
where ` denotes the distance at which the disamenity becomes 0.11 Similar to above, we
calculate mean damages among households and find the efficient supermajority by finding
the pivotal voter that suffers these mean damages. To illustrate the impact of a cost function
in which the disamenity becomes zero at some finite point within the locality, we examine
the simplest case of a population distribution defined by Beta(2,1) and a linear cost function
(γ = 0, δ = 1). In this situation, the efficient supermajority becomes
2 4 1 6
M =1− ` − ` + ` .
3
9
11
2
Since maximum distance has been normalized to 1, ` ≤ 1.
20
(15)
If ` = 1, Equation (15) simply reduces to the results of the above section detailing linear
disamenity costs. Taking the first derivative of Equation (15), it is clear that a decrease in `
will increase the required supermajority towards the extreme case of M = 1.12 In general, the
modified cost function increases the concentration of the disamenity around the hypothetical
facility, thus requiring a larger majority of voters to correct the inefficiency. In Figure 2,
we plot the relationship between ` and M for several different scenarios, reflecting linear
or convex disamenity costs as well as populations concentrated increasingly farther away or
around a specific point. In addition to the increasing inefficiency that results from a larger
portion of the population suffering zero costs, Figure 2 illustrates two other properties. First,
it is clear that the impact of the shape of the cost function remains unchanged, as convex
costs imply a higher supermajority than linear costs, regardless of the value of `. Second,
we see that when population is concentrated further away, relative to being concentrated
around a specific interior point, a higher supermajority is required only for larger values
for `. If the disamenity costs decay to zero at some distance, a larger supermajority is no
longer required for population distributions that are concentrated increasingly farther away.
Whether a larger supermajority is necessary under a population distribution concentrated
increasingly farther away or a population concentrated at an interior point depends on a
both the relative skew of the population distributions and the value of `.
This case presents an interesting point related to fiscal federalism. A cost function that
becomes 0 within the locality can be replicated by extending the political boundaries of
the voting population beyond the point at which the distance-related costs cease to matter.
Extending the core fiscal decentralization arguments, the preceding discussion indicates that
a decision-making jurisdiction that includes a significant population of unaffected individuals
will inefficiently site noxious facilities. Combined with spatial spillovers that could result if
too small of a jurisdiction is considered, these results suggest the importance of properly
aligning the decision-making jurisdiction with those individuals that are impacted by the
12
The first derivative is equal to 0 at ` = 0 and ` = 1 and is convex for 0 ≤ ` ≤ 1, so it is therefore negative
over this range.
21
decision.
6
Empirical Estimates of the Beta Distribution
The previous sections considered hypothetical shapes of the Beta distribution that are built
from general expectations of population patterns and are useful for analyzing the role that
population distribution has in majority-rule inefficiencies. We now examine observed population distributions to determine the degree to which such inefficiencies may be potential
problems. We continue to rely on the Beta distribution due to its flexibility in fitting a
variety of spatial patterns and estimate the parameters α and β.
We use 116 counties from New York and Pennsylvania as the basis for our empirical analysis. Summary statistics are presented in Table 4. For each county, we create a hypothetical
location for a facility. This location is chosen as the point in the county that maximizes the
median distance between the facility and individuals, which is analogous to the point that
minimizes the cost of getting the facility approved. Using publicly available U.S. Census
data, an individual’s location within the county is approximated by the geographic center
of the census block in which she resides. While such an assumption is logically unrealistic,
blocks are geographically small and contain small populations relative to the county. Our
method therefore should be close to observing actual housing locations.
Due to the variety in geographic shape and spatial population distribution across counties, we use a brute force technique to find a hypothetical location for a facility in each
county. First, we create a grid of geographic points evenly spaced throughout the county at
distances of approximately 100 meters in both east-west and north-south directions.13 For
each point, we calculate distance to each block centroid and choose the point with the largest
median distance, where distance is weighted by block population. Given a location for the
hypothetical facility, we use maximum likelihood estimation separately for each county to
13
The distance between points in the generated grid varies across county since we defined the grid as a
fixed number of points (250,000) within the county’s borders. The 10th and 90th percentiles for grid distance
are 37.38 and 139.61 meters, respectively, with a maximum of 364.77 meters in the largest county.
22
find 116 sets of Beta distribution parameters, {α, β}, that characterize the population distribution in each county. Results suggest a considerably smaller degree of skewness than
parts of the previous analytical discussion. Table 5 summarizes the 116 sets of estimated
parameters and the skewness of each population distribution. In general, populations in
these counties are concentrated in locations away from hypothetical facilities, but centered
away from the farthest possible distance within the county. Thus all counties have a slightly
skewed distribution of distance to a facility, evidenced by α > β. Such skewness requires a
supermajority greater than 0.5.
Parameters of the population spatial distribution can be used to calculate efficient supermajorities necessary to ensure a solution in which the total host fee is equal to total
costs imposed on the county in the case of linear damages. Results are presented in Figure
3. Point estimates for the optimal supermajority range from 50.15 to 58.93 across the 116
counties, with an interquartile range of 51.96 to 53.71. While a proposed increase from 50 to
51.96 appears small, such an increase in that particular county (population of 31,582) corresponds to 619 voters, while the largest proposed increase to 58.93 (county with population
of 111,931) corresponds to 9,995 voters.
In addition to calculating supermajorities using point estimates, we use bootstrapping
methods to calculate confidence intervals for efficient supermajorities in each county, following Krinsky and Robb (1986).14 Using parameter estimates and the corresponding covariance
matrix to describe the distributions of α and β, we take 10,000 random draws of {α, β} for
each county. For every draw, we calculate the efficient supermajority. We then use the
sample of 10,000 supermajorities to determine a confidence interval for each county. All 95%
confidence intervals have a range of less than 0.0063, generating very similar results to the
point estimates.
Finally, we examine the impact of convex disamenity costs using empirical estimates of
the beta distribution for the 116 counties in our sample. Since the hypothetical site loca14
We calculate standard errors using an alternative bootstrapping technique described in Runkle (1987).
Results are nearly identical and therefore not reported here.
23
tion is based on the median voter, the monotonic transformation of moving to a convex
cost function has no impact on the proposed location. As discussed earlier, however, the
degree of convexity determines mean costs and thus the efficient supermajority. For each
combination of county population distribution parameters and possible parameters in the
previously discussed convex cost function, we can calculate mean damages to find the supermajority that will ensure efficiency. In Figure 4, we illustrate the impact of convexity in the
cost function by plotting the efficient supermajority for each county and different degrees
of convexity. The degree of convexity simply refers to various combinations of the α and β
parameters that exacerbate the majority rule inefficiency. For disamenities that are highly
convex in distance, it is clear that the necessary supermajority is a substantial portion of
the population.
It is also evident that convex costs and population distributions have a complicated relationship in generating siting inefficiencies, as there is not a consistent ranking (in terms
of required supermajority) of counties across different cost functions. While the efficient
supermajority increases with independent increases in convexity and skewed population distance distributions, the impact of convexity is not independent of the cost function, and vice
versa. For example, the smallest required supermajority for each of the function parameter
combinations reported in Tables 1-3 appears in one of three different counties in our sample.
These three counties have distance distributions with with parameters (α = 11.67, β = 4.07),
(α = 6.21, β = 5.50), and (α = 12.95, β = 3.74), respectively. The inefficiency of majority rule is relatively smaller in these counties due to the concentration of the population
at less than extreme distances from the hypothetical site, evidenced by a relatively large β
parameter. This type of population distribution reduces the concentration of site supporters
at extreme distances that suffer very low costs. Similarly, the largest required supermajority for each of the reported cost function parameter combinations appear across three
counties with distribution parameters (α = 1.25, β = 0.96), (α = 15.01, β = 1.61), and
(α = 2.12, β = 1.00), respectively. Here, we see counties with population distributions that
24
have a larger portion of the population at the farther distances.
7
Conclusion
This paper has investigated the ability of community decision-making in the efficiency of
siting noxious facilities. We have shown that a supermajority rule is required to overcome
the inherent inefficiency in simple majority rule decisions. The exact value of this supermajority varies with the spatial distribution of the population and with the relationship
between damages and proximity to the facility. In general, the necessary supermajority
increases as populations concentrate farther away from the facility, as well as when the damage function becomes (more) convex in distance. Both of the effects relate directly to the
fundamental driver of the inefficiency: an individual decision based entirely on whether the
outcome is positive or negative, combined with an evaluation of efficiency that depends on
the magnitude of the outcome. We have also provided empirical evidence to show that while
potential inefficiencies in a small sample of counties are modest, they do exist. Thus welfare
improvements are possible through the use of supermajority voting rules.
Empirical population distributions suggest that the distribution of distance to an optimally sited facility has a negative skew, but there exists some concentration of the population
around some other location, likely a city center or central business district. Such a concentration works to mitigate siting inefficiencies. It is important to recognize that the required
supermajority, given observed population distributions, is highly dependent on the degree of
convexity in the cost function.
We end with a discussion of a few limitations that exist in our analysis. First, our
definition of efficiency pertains only to aggregate benefits (host fees) and aggregate damages
in the potential host locality, but ignores any surrounding localities. As the damages from
a facility are of a spatial nature, it is likely that damages will impact neighboring localities.
The existence of these spillover damages will generate greater aggregate damages when the
25
perspective is that of a group of localities. Furthermore, such a situation may also lead to
competitive behavior on the part of localities to host the facility.15 Still, our results illustrate
the inefficiency that is inherent in the decision facing all localities, a decision that will exist
whether or not a competitive environment exists.
Another potential limitation pertains to our choice of a parametric function to model
the distribution of individuals distances to a potential facility. However, the beta function is
very flexible and is capable of representing a wide array of spatial patterns. We are therefore
confident that it is adequate in characterizing observed population distributions. While we
model specific distribution patterns, our results depend only on the asymmetric distribution
of damages throughout the population. It is unlikely that other parametric or nonparametric
distributions that capture the same distributional features will have a considerable impact
on our findings.
Finally, we acknowledge that our model deals with a stationary population that accepts
the damages generated by its proximity to a noxious facility. In reality, one might expect
to see a significant amount of migration within or out of a locality in response to siting,
as supported by an expansive literature on residential sorting in response to environmental
attributes. Such migration, absent transaction costs, will serve to alleviate some of the damages imposed by a facility. The degree to which an individual’s ability to change household
location weighs in on her voting decision raises another interesting question.
15
See, for example, Ingberman (1995) for a further discussion of localities competing to host.
26
Appendix A:
Derivation of Mean Costs
Normalizing the maximum distance in a locality to 1, mean costs are found by integrating
costs (as a function of distance) over the density function of distance,
Z
c̄ =
1
xγ (1 − x)δ xα−1 (1 − x)β−1
0
1
dx,
B(α, β)
(A.1)
which can be simplified as
1
c̄ =
B(α, β)
Z
1
xΘ−1 (1 − x)Φ−1 dx,
(A.2)
0
where Θ = α + γ and Φ = β + δ. The above integral is simply the definition of the beta
function, B(Θ, Φ), so that
c̄ =
Appendix B:
B(Θ, Φ)
.
B(α, β)
(A.3)
Convex Costs
In the case of a linear damage function, mean costs (damages) that are greater than median
costs result from a mean distance that is smaller than the median distance. To demonstrate
that the difference in costs holds and, in fact, increases, we look at the change in costs when
the cost function becomes (more) convex through a decrease in γ or an increase in δ. We
hold the distribution of the population constant so that we need to show only that the cost
function increases more at the point of mean costs than it does at the point of median costs,
exacerbating the inefficiency problem.
27
B.1:
Decrease in γ
We take the derivative of the cost function with respect to γ and evaluate it at mean and
median costs, respectively, to get
∂c(d)
¯γ
= c(d)
∂γ
d¯
∂c(d)
γ
Median:
= c(dm ) .
∂γ
dm
Mean:
(B.1)
(B.2)
Recall that γ ≤ 0 and we are interested in a decrease in its value. Therefore, mean costs will
increase by a greater amount relative to median costs if
¯
c(d)
c(dm )
.
>
¯
dm
d
(B.3)
Since d¯ < dm and c(d) is decreasing in d, it is clear that this inequality holds.
B.2:
Increase in δ
Similar to the previous section, we take the derivative of the cost function with respect to δ
and evaluate it at mean and median costs, respectively, to get
∂c(d)
¯ γ
= c(d)
∂γ
1 − d¯
γ
∂c(d)
Median:
= c(dm )
.
∂γ
1 − dm
Mean:
(B.4)
(B.5)
Since δ ≥ 1 and we are interested in an increase in its value, mean costs will increase by a
greater amount than median costs if
¯
c(d)
c(dm )
>
.
¯
1 − dm
1−d
28
(B.6)
Define ε = dm − d¯ > 0 and substitute in for dm in Equation (B.6). Cross-multiplying terms,
Equation (B.6) can be written as
1−
ε
c(dm )
>
¯ .
1 − d¯
c(d)
(B.7)
¯ (decreasing function), the right-hand side of Equation (B.7) is less than
Since c(dm ) < c(d)
1. Since ε > 0 and d¯ < 1, the left-hand side of Equation (B.7) is greater than one, and
Equation (B.6) is satisfied.
Appendix C:
Efficient Supermajority With Linear Damages
Average distance from the Beta distribution is d¯ =
α
.
α+β
To find the efficient supermajority
for the specified parameter values, we evaluate the cumulative distribution function at this
average distance,
R d¯ α−1
¯ α, β)
t (1 − t)β−1 dt
B(
d;
¯ α, β) =
= xα ,
F (d;
= R01
α−1
β−1
B(α, β)
t (1 − t)
dt
0
(C.1)
¯ α, β).
and calculate an efficient supermajority M = 1 − F (d;
C.1:
α ∈ [2, ∞], β = 1
For β = 1, Equation (C.1) reduces to d¯α and the solution for the efficient supermajority is
α
α
M = 1 − α+β
. It is then obvious that for α = 2, M = 95 . To calculate M for cases of
populations concentrated away from the facility, we take the limit of M as α goes to infinity
and β = 1. Algebraic manipulation shows that
lim
α→∞
α
1+α
α
1
α.
α→∞ (1 + 1/α)
= lim
29
(C.2)
To find this limit, define the denominator as L16 so that
ln L = lim α ln(1 +
α→∞
1
)
α
(C.3)
Using L’Hopital’s rule,
ln L =
1
−1
1+1/α α2
lim
−1
α→∞
α2
α
= 1.
α→∞ 1 + α
(C.4)
= lim
which means that L = e. Plugging this result back into equation (C.2), we have
lim
α→∞
α
1+α
α
=
1
e
(C.5)
so that
M =1−
C.2:
1
e−1
=
≈ 0.6321.
e
e
(C.6)
α ∈ (3, ∞], β = 3
For β = 3, Equation (C.1) can be evaluated at mean damages d¯ =
1
M =1−
2
α
α+3
α 18 + 39α + 17α2
(α + 3)2
α
α+3
to find
.
(C.7)
We then take the limit of this expression as α approaches infinity. Note that for the final
term in Equation (C.7),
lim
α→∞
16
18 + 39α + 17α2
(α + 3)2
18
39
17
+ lim
+ lim
2
2
9+α
α→∞ (3 + α)
α→∞ (6 +
) α→∞ 1 + α92 +
α
17
=0+0+
= 17.
1
= lim
This is simply the definition of the mathematical constant e.
30
6
α
(C.8)
(C.9)
whose limit is 17 as α approaches infinity. Then, define the variable L such that
ln L = lim ln
α→∞
α
α+3
α
= lim α ln(α + 3) = lim
α→∞
3 ln(1 −
α→∞
3
α
3
)
α+3
.
(C.10)
Define the variable t = α3 , which means limα→∞ t = 0 and substitute into the above equation
so that we are now interested in
3 (− ln(1 + t))
.
t→0
t
lim
(C.11)
Next, define h = ln(1 + t) or t = eh − 1. The variable h approaches 0 with t. Equation (C.11)
then becomes
lim −3
h→0
h
h
e −1
= −3.
(C.12)
Since this value is the limit of ln L, the limit of L is e−3 = .0498. Finally, return to Equation
(C.9) to see that the final limit is
1
e−3 (17) = 0.5768.
lim M = 1 −
α→∞
2
31
(C.13)
References
Richard Benjamin and Jeffrey Wagner. Reconsidering the law and economics of low-level
radioactive waste management. Environmental Economics and Policy Studies, 8:33–53,
2006.
Andrea Bosco. Majority vote says ’no’ to drill ban referendum. Peters Patch [Peters, PA],
Nov. 8 2011.
Geoffrey Castle. Hazardous waste facility siting in manitoba. case study of a success. Air
and Waste, 43(7):963–969, 1993.
S. Farber. Undesirable facilities and property values: A summary of empirical studies.
Ecological Economics, 24(1):1–14, 1998.
W.E. Harris. Siting a hazardous waste facility: A success story in retrospect. April 11 1994.
URL http://www.nwtrb.gov/meetings/1994/april/harris.pdf.
Kieth R. Ihlanfeldt and Laura O. Taylor. Externality effects of small-scale hazardous waste
sites: evidence from urban commercial property markets. Journal of Environmental Economics and Management, 47:117–139, 2004.
Daniel E. Ingberman. Siting noxious facilities: Are markets efficient? Journal of Environmental Economics and Management, 29(3):S20–S33, 1995.
Robin R. Jenkins, Kelly B. Maguire, and Cynthia L. Morgan. Host community compensation
and municipal solid waste landfills. Land Economics, 80(4):513–528, 2004.
Michael E. Kraft. Democratic Dialogue and Acceptable Risks: The Politics of High-Level
Nuclear Waste Disposal in the United States, chapter 3. Georgetown University Press,
2007.
Itzhak Krinsky and A. Leslie Robb. On approximating the statistical properties of elasticities.
The Review of Economics and Statistics, 68(4):715–719, Nov. 1986.
32
Howard Kunreuther and Paul R. Kleindorfer. A sealed-bid auction mechanism for siting
noxious facilities. American Economic Review (Papers and Proceedings, 76(2):295–299,
1986.
Howard Kunreuther, Paul Kleindorfer, Peter J. Knez, and Rudy Yaksick. A compensation mechanism for siting noxious facilities: Theory and experimental design. Journal of
Environmental Economics and Management, 14:371–383, 1987.
Jill J. McCluskey and Gordon C. Rausser. Hazardous waste sites and housing appreciation
rates. Journal of Environmental Economics and Management, 45:166–176, 2003.
Deborah Minehart and Zvika Neeman. Effective siting of waste treatment facilities. Journal
of Environmental Economics and Management, 43(2):303–324, 2002.
Robert Cameron Mitchell and Richard T. Carson. Property rights, protest, and the siting
of hazardous waste facilities. The American Economic Review, 76(2):285–290, May 1986.
Wallace E. Oates. Fiscal Federalism. New York: Harcourt Brace Jovanovich, 1972.
Wallace E. Oates. An essay on fiscal federalism. Journal of Economic Literature, 37:1120–
1149, 1999.
Wallace E. Oates and Robert M. Schwab. Economic competition among jurisdictions: Efficiency enhancing or distortion inducing? Journal of Public Economics, 35:333–354, 1988.
M. O’Hare, L. Bacow, and D. Sanderson. Facility Siting and Public Opposition. Van Nostrand
Reinhold, 1983.
Arthur O’Sullivan. Voluntary auctions for noxious facilities: Incentives to participate and
the efficiency of siting decisions. Journal of Environmental Economics and Management,
25:s12 – s26, 1993.
David Perez-Castrillo and David Wettstein. Choosing wisely: A multibidding approach. The
American Economic Review, 92(5):1577–1587, 2002.
33
David E. Runkle. Vector autoregressions and reality. Journal of Business and Economic
Statistics, 5(4):437–442, October 1987.
Arthur M. Sullivan. Victim compensation revisited: Efficiency versus equity in the siting of
noxious facilities. Journal of Public Economics, 41(2):211 – 225, March 1990.
The Times Observer. Our opinion: Change of plans. The Times Observer [Warren, PA],
May 1 2012.
34
35
0.556
0.558
0.575
0.594
0.613
0.632
0.652
0.671
0.691
0.710
0.730
0.750
0.608
0.610
0.623
0.639
0.655
0.672
0.688
0.705
0.722
0.739
0.756
0.774
1.5
0.650
0.651
0.663
0.677
0.691
0.706
0.720
0.735
0.750
0.765
0.780
0.796
2.0
0.684
0.685
0.696
0.709
0.721
0.734
0.747
0.760
0.773
0.787
0.801
0.815
2.5
0.713
0.714
0.724
0.735
0.746
0.758
0.770
0.782
0.794
0.806
0.819
0.832
3.0
0.00
-0.01
-0.10
-0.20
-0.30
-0.40
-0.50
-0.60
-0.70
-0.80
-0.90
-1.00
0.578
0.580
0.591
0.603
0.615
0.628
0.641
0.653
0.666
0.678
0.691
0.704
1.0
0.635
0.636
0.645
0.655
0.666
0.677
0.687
0.698
0.709
0.719
0.730
0.741
1.5
0.680
0.681
0.689
0.698
0.707
0.717
0.726
0.735
0.745
0.754
0.764
0.774
2.0
0.717
0.718
0.725
0.733
0.741
0.750
0.758
0.766
0.775
0.783
0.792
0.800
2.5
0.748
0.749
0.755
0.763
0.770
0.777
0.785
0.792
0.800
0.807
0.815
0.823
3.0
Table 2: Efficient Supermajority: α = 3, β = 1
0.00
-0.01
-0.10
-0.20
-0.30
-0.40
-0.50
-0.60
-0.70
-0.80
-0.90
-1.00
1.0
Table 1: Efficient Supermajority: α = 2, β = 1
0.774
0.774
0.781
0.787
0.794
0.800
0.807
0.814
0.821
0.828
0.835
0.842
3.5
0.737
0.738
0.747
0.758
0.768
0.779
0.789
0.800
0.811
0.823
0.834
0.846
3.5
0.796
0.796
0.802
0.808
0.814
0.820
0.826
0.833
0.839
0.845
0.851
0.858
4.0
0.758
0.759
0.767
0.777
0.787
0.796
0.806
0.816
0.826
0.837
0.847
0.858
4.0
0.815
0.815
0.820
0.826
0.831
0.837
0.843
0.849
0.854
0.860
0.866
0.871
4.5
0.776
0.777
0.785
0.794
0.802
0.811
0.821
0.830
0.839
0.849
0.859
0.869
4.5
0.831
0.831
0.836
0.841
0.846
0.852
0.857
0.862
0.867
0.873
0.878
0.883
5.0
0.792
0.793
0.800
0.808
0.817
0.825
0.833
0.842
0.851
0.860
0.869
0.878
5.0
0.845
0.846
0.850
0.855
0.859
0.864
0.869
0.874
0.879
0.884
0.888
0.894
5.5
0.806
0.807
0.814
0.821
0.829
0.837
0.845
0.853
0.861
0.869
0.878
0.886
5.5
0.858
0.858
0.862
0.866
0.871
0.875
0.880
0.884
0.889
0.893
0.898
0.902
6.0
0.818
0.819
0.825
0.833
0.840
0.847
0.855
0.862
0.870
0.878
0.885
0.893
6.0
0.869
0.869
0.873
0.877
0.881
0.885
0.889
0.894
0.898
0.902
0.906
0.910
6.5
0.829
0.830
0.836
0.843
0.850
0.857
0.864
0.871
0.878
0.885
0.892
0.900
6.5
0.878
0.879
0.882
0.886
0.890
0.894
0.898
0.902
0.906
0.909
0.913
0.917
7.0
0.839
0.840
0.846
0.852
0.859
0.865
0.872
0.878
0.885
0.892
0.899
0.906
7.0
0.887
0.887
0.891
0.894
0.898
0.902
0.905
0.909
0.912
0.916
0.920
0.923
7.5
0.848
0.849
0.854
0.860
0.867
0.873
0.879
0.885
0.891
0.898
0.904
0.911
7.5
0.895
0.895
0.898
0.902
0.905
0.909
0.912
0.915
0.919
0.922
0.925
0.929
8.0
0.857
0.857
0.862
0.868
0.874
0.880
0.885
0.891
0.897
0.903
0.910
0.916
8.0
36
0.00
-0.01
-0.10
-0.20
-0.30
-0.40
-0.50
-0.60
-0.70
-0.80
-0.90
-1.00
0.532
0.533
0.543
0.554
0.565
0.574
0.584
0.594
0.603
0.613
0.622
0.631
1.0
0.572
0.573
0.581
0.590
0.599
0.608
0.616
0.624
0.633
0.641
0.649
0.657
1.5
0.608
0.609
0.616
0.624
0.632
0.639
0.647
0.655
0.662
0.670
0.677
0.685
2.0
0.640
0.641
0.647
0.654
0.662
0.669
0.676
0.683
0.690
0.697
0.704
0.711
2.5
0.669
0.670
0.676
0.683
0.689
0.696
0.702
0.709
0.715
0.722
0.728
0.734
3.0
Table 3: Efficient Supermajority: α = 6, β = 3
0.696
0.696
0.702
0.708
0.714
0.720
0.726
0.732
0.738
0.744
0.750
0.756
3.5
0.719
0.720
0.725
0.731
0.737
0.742
0.748
0.754
0.759
0.765
0.770
0.776
4.0
0.741
0.742
0.746
0.752
0.757
0.762
0.768
0.773
0.778
0.783
0.789
0.794
4.5
0.761
0.761
0.766
0.771
0.776
0.781
0.786
0.791
0.796
0.800
0.805
0.810
5.0
0.778
0.779
0.783
0.788
0.793
0.797
0.802
0.807
0.811
0.816
0.820
0.825
5.5
0.795
0.795
0.799
0.803
0.808
0.812
0.816
0.821
0.825
0.830
0.834
0.838
6.0
0.809
0.810
0.813
0.818
0.822
0.826
0.830
0.834
0.838
0.842
0.846
0.850
6.5
0.823
0.823
0.827
0.831
0.835
0.838
0.842
0.846
0.850
0.854
0.858
0.861
7.0
0.835
0.835
0.839
0.842
0.846
0.850
0.853
0.857
0.861
0.864
0.868
0.871
7.5
0.846
0.846
0.850
0.853
0.857
0.860
0.863
0.867
0.870
0.874
0.877
0.880
8.0
Table 4: County summary statistics
County State
Pop.
Blocks
Mean Block
Total Area
Pop.
(km2 )
Mean Block Area (km2 )
36001
NY
294,565
5,584
52.75
1354
0.242
36003
NY
49,927
3,211
15.55
2666
0.830
36007
NY
200,536
4,795
41.82
1828
0.381
36009
NY
83,955
4,245
19.78
3389
0.798
36011
NY
81,963
3,555
23.06
1791
0.504
36013
NY
139,060
5,249
26.49
2742
0.522
36015
NY
91,070
2,831
32.17
1055
0.373
36017
NY
51,401
3,101
16.58
2314
0.746
36019
NY
79,894
2,843
28.10
2688
0.945
36021
NY
63,094
3,095
20.39
1644
0.531
36023
NY
48,599
1,988
24.45
1292
0.650
36025
NY
48,055
3,516
13.67
3737
1.063
36027
NY
280,150
4,615
60.70
2061
0.447
36029
NY
950,135
12,398
76.64
2700
0.218
36031
NY
38,851
2,638
14.73
4647
1.762
36033
NY
51,123
2,705
18.90
4219
1.560
36035
NY
55,073
2,121
25.97
1283
0.605
36037
NY
60,370
2,051
29.43
1277
0.622
36039
NY
48,195
2,041
23.61
1676
0.821
36041
NY
5,379
1,343
4.01
4448
3.312
36043
NY
64,427
3,726
17.29
3657
0.981
36045
NY
111,570
4,576
24.38
3258
0.712
36049
NY
26,944
2,676
10.07
3301
1.234
36051
NY
64,328
2,937
21.90
1636
0.557
36053
NY
69,441
2,922
23.76
1696
0.580
37
County State
Pop.
Blocks
Mean Block
Total Area
Pop.
(km2 )
Mean Block Area (km2 )
36055
NY
734,778
9,309
78.93
1702
0.183
36057
NY
49,708
2,452
20.27
1044
0.426
36063
NY
219,814
3,881
56.64
1353
0.349
36065
NY
235,469
7,434
31.67
3139
0.422
36067
NY
458,336
7,990
57.36
2016
0.252
36069
NY
100,224
3,359
29.84
1668
0.497
36071
NY
341,367
7,911
43.15
2102
0.266
36073
NY
44,119
1,343
32.85
1013
0.754
36075
NY
122,372
4,705
26.01
2465
0.524
36077
NY
61,676
4,006
15.40
2594
0.647
36079
NY
95,745
2,083
45.96
597
0.286
36083
NY
152,538
4,193
36.38
1690
0.403
36087
NY
286,753
3,740
76.67
449
0.120
36089
NY
111,931
5,479
20.43
6942
1.267
36091
NY
200,635
4,987
40.23
2098
0.421
36093
NY
146,555
2,992
48.98
529
0.177
36095
NY
31,582
2,363
13.37
1610
0.682
36097
NY
19,224
1,668
11.53
850
0.510
36099
NY
33,342
2,006
16.62
838
0.418
36101
NY
98,726
5,303
18.62
3602
0.679
36105
NY
73,966
4,198
17.62
2507
0.597
36107
NY
51,784
2,083
24.86
1343
0.645
36109
NY
96,501
3,193
30.22
1229
0.385
36111
NY
177,749
4,906
36.23
2912
0.594
36113
NY
63,303
2,399
26.39
2245
0.936
36115
NY
61,042
2,509
24.33
2153
0.858
36117
NY
93,740
3,254
28.81
1564
0.481
38
County State
Pop.
Blocks
Mean Block
Total Area
Pop.
(km2 )
Mean Block Area (km2 )
36121
NY
43,424
1,888
23.00
1535
0.813
36123
NY
24,621
1,747
14.09
876
0.501
42001
PA
91,292
3,378
27.03
1343
0.398
42003
PA
1,281,666 24,283
52.78
1891
0.078
42005
PA
72,392
3,451
20.98
1692
0.490
42007
PA
181,412
5,215
34.79
1126
0.216
42009
PA
49,984
2,913
17.16
2622
0.900
42011
PA
373,638
9,273
40.29
2218
0.239
42013
PA
129,144
4,100
31.50
1362
0.332
42015
PA
62,761
3,578
17.54
2971
0.830
42017
PA
597,635
9,506
62.87
1565
0.165
42019
PA
174,083
5,268
33.05
2043
0.388
42021
PA
152,598
6,188
24.66
1783
0.288
42023
PA
5,974
579
10.32
1026
1.772
42025
PA
58,802
2,499
23.53
989
0.396
42027
PA
135,758
3,476
39.06
2876
0.827
42031
PA
41,765
2,485
16.81
1556
0.626
42033
PA
83,382
5,328
15.65
2965
0.556
42035
PA
37,914
2,338
16.22
2298
0.983
42037
PA
64,151
2,977
21.55
1250
0.420
42039
PA
90,366
4,209
21.47
2622
0.623
42043
PA
251,798
7,363
34.20
1360
0.185
42047
PA
35,112
1,641
21.40
2143
1.306
42051
PA
148,644
4,978
29.86
2047
0.411
42053
PA
4,946
622
7.95
1107
1.779
42055
PA
129,313
3,841
33.67
2000
0.521
42057
PA
14,261
933
15.29
1133
1.215
39
County State
Pop.
Blocks
Mean Block
Total Area
Pop.
(km2 )
Mean Block Area (km2 )
42059
PA
40,672
2,226
18.27
1492
0.670
42061
PA
45,586
2,607
17.49
2265
0.869
42063
PA
89,605
3,723
24.07
2142
0.575
42065
PA
45,932
2,558
17.96
1690
0.661
42067
PA
22,821
1,313
17.38
1014
0.772
42069
PA
213,295
6,688
31.89
1188
0.178
42071
PA
470,658
9,501
49.54
2444
0.257
42073
PA
94,643
3,124
30.30
928
0.297
42075
PA
120,327
4,281
28.11
937
0.219
42077
PA
312,090
9,495
32.87
894
0.094
42081
PA
120,044
4,681
25.64
3182
0.680
42083
PA
45,936
2,572
17.86
2536
0.986
42085
PA
120,293
4,757
25.29
1742
0.366
42087
PA
46,486
1,615
28.78
1065
0.659
42089
PA
138,687
4,792
28.94
1575
0.329
42091
PA
750,097
11,620
64.55
1251
0.108
42093
PA
18,236
813
22.43
337
0.415
42095
PA
267,066
7,044
37.91
957
0.136
42097
PA
94,556
4,410
21.44
1188
0.269
42099
PA
43,602
2,075
21.01
1428
0.688
42101
PA
1,517,550 17,314
87.65
347
0.020
42103
PA
46,302
2,729
16.97
1412
0.517
42105
PA
18,080
1,527
11.84
2801
1.834
42107
PA
150,336
6,251
24.05
2017
0.323
42109
PA
37,546
1,747
21.49
852
0.487
42111
PA
80,023
4,169
19.19
2783
0.668
42113
PA
6,556
855
7.67
1166
1.363
40
County State
Pop.
Blocks
Mean Block
Total Area
Pop.
(km2 )
Mean Block Area (km2 )
42115
PA
42,238
2,927
14.43
2133
0.729
42117
PA
41,373
2,498
16.56
2937
1.176
42119
PA
41,624
1,504
27.68
818
0.544
42121
PA
57,565
2,446
23.53
1747
0.714
42123
PA
43,863
2,230
19.67
2290
1.027
42125
PA
202,897
6,798
29.85
2220
0.327
42127
PA
47,722
2,943
16.22
1879
0.639
42129
PA
369,993
9,745
37.97
2661
0.273
42131
PA
28,080
1,343
20.91
1029
0.766
42133
PA
381,751
9,061
42.13
2342
0.258
Table 5: Parameter estimates summary statistics
α
β
skew
min
max
mean
sd
median
25%
75%
1.25
0.96
-1.23
15.02
4.92
-0.02
3.19
1.99
-0.31
1.68
0.74
0.17
2.76
1.83
-0.28
2.28
1.46
-0.40
3.38
2.31
-0.22
41
. 2 [0,-1], / = 1
1
. = 0, / 2 [1,10]
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
c(d) 0.5
c(d) 0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.2
0.4
0.6
0.8
1
0
Distance to Facility: d
0.2
0.4
0.6
Distance to Facility: d
Figure 1: Disamenity Cost Function
42
0.8
1
1
0.95
0.9
Efficient Supermajority
0.85
0.8
0.75
0.7
0.65
0.6
Linear c(d), Beta(2,1)
Convex c(d), Beta(2,1)
Linear c(d), Beta(6,3)
Convex c(d), Beta(6,3)
0.55
0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Distance at which c(d)=0
Figure 2: Efficient Supermajorities: Costs Reach 0
43
1
0.6
Efficient Supermajority
0.58
0.56
0.54
0.52
0.5
0.48
0
20
40
60
80
100
County (ranked by efficient supermajority)
Figure 3: Efficient Supermajorities: Linear Costs
44
120
1
Efficient Supermajority
0.9
0.8
0.7
0.6
0.5
Convexity
County
Figure 4: Efficient Supermajorities: Convex Costs
45