A Probabilistic Shortage of Private Land Opened to Hunters in Northwest Minnesota

Outdoor recreation in Northwest Minnesota is popular year round, and many residents and visitors participate in activities such as hunting, fishing, snowmobiling, boating, and much more. Land available for hunting, however, is at a particular premium. Hunters overall do not appear to have enough land on which to hunt as they compete with both other hunters and state regulations. Some private land owners have land that they keep for their own hunting purposes, and some of that land is kept exclusively for hunting. Private landowners in NWMN have consistently demonstrated an unwillingness to open their land to outside consumptive recreational uses, such as hunting, even for a fee. This situation may leads to potential overuse of some land with respect to hunting, while other land is potentially underused, creating a potential “tragedy of the anticommons”. Meanwhile, hotels and resorts in the region are engaged in the ever-growing worldwide trend of ecotourism and agritourism, though they have relatively few arrangements with private land owners. In this study, a probabilistic demand approach is used to analyze strategic interaction between land owners and hunters based on the results of three surveys conducted for the State of Minnesota and the Economic Development Administration (EDA). Mechanisms to create an outcome that aligns the utility maximization strategies of land owners and hunters are suggested.


Introduction
Looking over the vast fields of Minnesota, one could be forgiven for forgetting How to cite this paper: Johnson, R.C. and Walker II, E. (2018) A Probabilistic Shortage of Private Land Opened to Hunters in Northwest Minnesota. Modern Economy, 9, 213-240. https://doi.org/10.4236/me.2018.91014 the hospitality operations would like to have. That suggests a definite market potential, but the interest in doing so appears to be rather one-sided. Were land owners to be induced to participate, however, such hospitality operations could potentially serve as an effective manager of the private land's use by outside parties, thereby address some of the concerns private land owners have expressed.
This study uses the results of three surveys conducted for the State of Minnesota and the Economic Development Administration (EDA). The first asked private land owners in NWMN about their current land use and their willingness to accept compensation for opening land to outside parties for recreational purposes, including hunting. The second survey asked hospitality operations in NWMN about their current agritourism and ecotourism operations and their interest in expanding such recreational opportunities for their guests. This third survey was administered to hospitality operations in the region and asked questions pertaining current levels of ecotourism and agritourism offerings to their guests and their interest in expanding, including through collaborations with local land owners. The results of the surveys together show a shortage of land made available for hunting to outside parties has resulted due in part to private ownership and the preferences of private owners. A potential opportunity exists to meet the demand of hunters for land by using hotels and resorts in the region that are engaged in agritourism and ecotourism. Such an outcome may be able to align the utility maximization strategies of land owners and hunters, thereby increasing economic efficiency.

Background
Private owners can potentially increase efficiency through opening land, either pro bono or for a fee, to outside hunters [3]. However, decision strategies of land owners may be biased against opening land to outside use. As owners of property, they have the right to exclude [4]. Their decision strategies may be influenced by factors beyond price, such as psychological factors and the interaction with information and other land owners [5]. When two parties to a potential contract, i.e., the supply side and the demand side, differ sufficiently in terms of decision strategy, it is possible that a sub-optimal allocation of resources will result due to a misalignment of incentives. Redistribution of use of a particular parcel of land, for example, may yield gains for some while also imposing costs asymmetrically [6]. Such a misalignment can also contribute to social costs [7]. However, if the costs imposed in the situation of denying land use to outside hunters are justified by the benefits otherwise realize by the private ownership of the land, then the incentive to improve the situation for hunters is reduced, for it comes into direct conflict with the real or perceived benefits to land owners [8].
One such cost that could be imposed on private land owners opening their land to outside parties is a loss of intangible value of the land as perceived by its owner. This is similar to the way in which agricultural land bought en masse by outside investors may damage society through damage to the family farm, which has intrinsic and indispensable value [9]. That is, private land owners may perceive use of their land by outside parties will change the nature of their land and its use in ways that may not be seen by outside observers. Although it is possible that a decision by a private land owner to open land or not to open land to outside parties is driven entirely by financial considerations, such decisions typically involve other factors that are not directly economic [3]. Thus, the decision strategies of private land owners and of hunters who wish to use private land may quite easily yield different levels of available acreage. Since hunters are left with less available land relative to their quantity of land demanded, a sub-optimal allocation of land use results.

Survey Data
The primary survey instrument was designed to collect data from private land owners on their willingness to accept compensation (  to opening their land to outside use [10].

A Land Use Model of Parallel Rationality
Additionally, in terms of strategic interaction between the land owners and outside parties, the "power distribution" is inherently unequal. The land owners, being the owners, have all the power over the use of their land, within the law, and have the sole right to decide whether to open that land to outside parties [11]. In the presence of such an asymmetrical power distribution, the payoff matrix for each side may be such that compromise between land owners and outside parties over land use is not a stable equilibrium (Carrillo and Palfrey, 2009).
Put another way, land owners do not have to open their land. They have the right to exclude. Their decision is based on their own strategy and does not typically internalize costs and/or penalties borne by the hunters. That friction contributes to the potential sub-optimal allocation of private land opened for recreational use relative to the demand for such land by outside parties and therefore should be kept in mind when considering programmes or incentives to induce land owners to open their land. However, the asymmetry in power distribution may have a positive impact in that, should incentives cause the paradigm shift in favour of opening land to outside use, peer-induced fairness may induce some land owners to be fair in distribution of land access among outside users rather than instituting price discrimination or similar policies (Ho and Su, 2009). The surveys support anecdotal evidence attained before the said surveys were given and suggests that land owners and hunters have different decision strategies such that the optimal outcome for one is statistically different from the optimal outcome of the other. Drawing from probabilistic demand, a Choice Wave, then, may be used to model both groups as two separate consumer types. Choice Waves are mathematically orthogonal in an n-dimensional Hilbert space and represent non-interacting decision strategies yielding statistically different outcomes in expectation value [12] [13]. Each Choice Wave represents its own noninteracting, parallel economic "world," each with its own decision strategy and its own rationality distinct from those in other "worlds." In that framework of economic parallel rationality, the classical economic man still exists, yet there is an infinite number of different versions in an infinite number of parallel economic worlds in hyperspace.
In the land use scenario of the present study, there are two worlds: land owners and hunters. There is "Economic Man-Land Owner" and "Economic Man-Hunter." However, since in this case that division does not represent two different groups of consumers, but rather two sides to a potential transaction, the Choice Waves do not represent different segmentations of a market, but two distinct stakeholders in the land use decision. That is, the stakeholders in the land use decision exist within two parallel rational economic worlds. If the decision strategy of each parallel state of rationality results in a utility maximizing land use allocation significantly different from the utility maximizing choice other stakeholders, then there is a misalignment of incentives, and an inefficient allocation of land and sub-optimal outcomes may quite likely result. That is, if land owners and hunters have significantly different utility maximizing levels of use of private land for hunting by outside parties, then the incentives of land owners and hunters are misaligned, and a sub-optimal allocation of private land for outside use may result. However, even in such a case of sub-optimal allocation of land for hunting, the distribution of burden is borne asymmetrically due to the asymmetrical power distribution, i.e., the private land owners have all the power relative to the hunters regarding how they use their land. Land owners can easily choose their utility maximizing level of land allocation for hunting by outside parties, and the optimal level of land desired by the hunters need not be achieved in order for the land owners to maximize utility. That utility maximizing choice by the land owners may impose an externality in the form of overuse of other available land by hunters; crowding of hunters, creating potentially dangerous situations; and wildlife management issues.
Under the assumption that there exists a goal of inducing more private land owners to open their land to outside parties for hunting, then it is necessary to establish a "bridge" that can span the two economic worlds and align their incentives, creating a more efficient allocation of resources and a more optimal allocation of land use. Certain mechanisms and/or institutions may be able to serve as a bridge between two different groups, better align incentives, and promote a more efficient allocation of resources [14].
In the absence of strong institutions or mechanism that facilitate land use transactions between private land owners and outside parties, there is likely to be a lack of commitment by both sides [15]. The public may see little incentive to use a particular parcel of land, other things being equal, instead continuing to use land that may be overused or overcrowded. Hunters seek land on which to hunt, and the ownership of specific piece of equivalent land is irrelevant unless said ownership imposes costs on the hunter. Land owners similarly feel little commitment to the public in terms of providing land for hunting, which may simply indicate preferences. It also may be a form of response to the lack of commitment by the public, i.e., the hunters simply want suitable land for hunting, so land owners may assume that if they do not open their land to outside hunters, the hunters will simply find other land.
Again, the land owners are the stronger party in the transaction, and so they are more likely to prefer slowing the release of land usage and negotiation due to a real or perceived mismatch in incentive compatibility [15]. Other things being equal, the land owners and the public, i.e., the hunters in this case, can be modeled as being in states of parallel rationality. They each seek to maximize utility rationally according to their decision strategy. So, utility maximization by one party is reasonably expected to yield a land use level different from that determined by utility maximization by the other party. If that is the case, then they cannot achieve a total market efficient outcome without a bridge.
Bridges can be artificial or natural. Artificial bridges comprise certain types of mechanisms that help to align incentives and improve outcomes, such as an institution established for such a purpose. However, recalling that, in this frame-

Choice Wave Models
Equation (1) gives a Choice Wave model of the probabilistic decision strategy of land owners, where k is a probability function of some form, l is the principal decision variable, i.e., amount of land willing to open to outside hunters, x is a bundle of all other decisions that might impact choice regarding opening land, Y is the standard income constraint, and B is an artificial bridge, such as an institution designed to bring land owners and hunters together. Interaction between land owners and hunters, as well as interaction between each side and outside parties, may result in influence that impacts decision strategy and hence expectation value of outcome. That is included in Equation (1) as net F n from a multipoint gravitational model [5]. The term F net is the net influence of others on the land owner, and n is the strength of the land owner's own influence over others.
In Equation (1), the Choice Wave for land owners is expressed as variable over time except at the decision point, at which time the Choice Wave collapses to a probability of 1 for the selected level of l. The expectation value, then, is expressed as some function of the Choice Wave and is given in Equation (2).
The functional form of z must be such that the expectation value in Equation (2) equals that of the observational revealed preferences. Also, since the Choice Wave in Equation (1) contained the possibility of an artificial bridge, B, the expectation value in Equation (2) necessarily changes based on the value of B.
The amount of land demanded by hunters may be expressed by a Choice Wave as in Equation (3), which is identical in functional form to that of the land owners, with the addition of the subscript D to indicate different functional forms of the probability and constraint functions for the demand side. , In the absence of the bridge, the expectation values for the supply and demand sides are given in Equations (4) and (5) Given the orthogonality of the Choice Waves, the expectation values in Equations (4) and (5) clearly cannot be equal. Given that the supply side, i.e., the land owners, are more likely to want to open less land than the hunters want, it is reasonable to assume that D l l < .
If an artificial bridge were to exist, then 1 B > . Assuming it to be a "perfect" bridge that aligns choices absolutely, . That is, the probabilistic outcomes momentarily align. In those cases, the optimal allocation of resources occurs because the utility-maximizing choices of each side align. However, it is only for that specific interaction, as the exact allocation of resources is never known until the decision point. Given its likely rarity, since the expectation values of each side of the transaction are statistically different, the presence of natural bridges is unlikely to eliminate the inefficiencies in the market overall. Indeed, natural bridges could only completely eliminate market inefficiency if they occurred at each and every decision point. Given the different in expectation values, such an occurrence would be expected to have an extremely low probability.
The probability of a natural bridge ought not to be ignored, however. If they occur, they at least create a momentary increase in welfare. If they occur frequently, then the Choice Waves of the two sides, though orthogonal, must be such that they generate expectation values that are statistically different, but not very much so. Also, if a natural bridge occurs, it shows what potential there might be for market improvement and might aid in the development of institutions or mechanisms that could serve as artificial bridges. The probability of a natural bridge occurring is given in Equation (6).
In Equation (6), a i and a j represent all ranges over which there is probabilistic overlap, i.e., the areas where natural alignment of choices may occur. For example there may be low-probability ranges of land use out in the tails of the probability function of both the land owners and the hunters that overlap, even though their expectation values are quite different. The closer the expectation values of the two groups are, the higher P Bridge is, implying more areas of overlap.
With too much overlap, on the other hand, orthogonality disappears, and t he the Choice Wave permits each choice that may maximize utility and no choice that will not maximize utility. Each utility-maximizing choice has a probability contained within the Choice Wave, and therefore each such choice is possible at the decision point, however likely or unlikely each may be. It is quite theoretically possible that both land owners and hunters may have land use choices that are unlikely for each group, but still could not only occur, but occur simultaneously. That is a natural bridge.
Since an artificial bridge is part of the constraint (see Equation (1)

Summary of Land Use Survey Results
Forty-eight landowners in the NWMN region responded to the land use survey.
With a 95% confidence level, and assuming a total number of land owners of hunting land in all of Minnesota of approximately 4500 5 , and a response distribution of 50%, the margin of error is 14.07%. However, it was expected a priori that results would be skewed in the direction of not being willing to open land to outside use. If a response distribution of 88.24% is assumed, which is the actual distribution in the results, then the margin of error is 9.07%. Neither a margin of error of 9.07% nor one of 14.07% is enough to change the interpretation of the results.
Few of the land-owner survey respondents were interested in opening land to outside hunters (or other recreational uses) for a variety of reasons (vide infra). Table 1 provides a summary of respondent answers regarding use of their land for recreational purposes.
As Table 1 indicates, a number of the respondents make quite regular use of their land for themselves across a wide variety of outdoor activities and sports common in the region. There is much less interest in letting outside parties use the land. There is even less interest in opening land to outside parties for profit or pay as opposed to not for profit or pay. Table 2 gives the acreage dedicated to hunting, though not necessarily 5 Based on the 2017 list of Deer Landowners in Minnesota provided by the Minnesota Department of Natural Resources. The number of such landowners in northwest Minnesota is clearly much lower. However, assuming a higher number provides a larger margin of error for the calculation, so the margin of error based solely on northwest Minnesota likely is lower.

Discussion
The  follow separate decision strategies that lead to non-matching group-optimal land use outcomes. Land use is, therefore, sub-optimal.
The results, then, suggest that a pair of Choice Waves of the form indicated in Equation (1) would be logical. Following that, therefore, the values for Equations (4) and (5)  are necessary to span the economic worlds of land owners and hunters, which could potentially be in the form of an institution aimed at aligning incentives. In addition, given that many hospitality operations in the region are looking to make arrangements with private land owners for agri-ecotourism, the hospitality industry may be a useful intermediary between the land owner and the guests.

Conclusions
This study applied a Choice Wave probabilistic model to analyze the potential misalignment in decision strategies regarding land use for hunting between pri- The following is the original transcript of the three surveys from which the data were gathered. The transcript was then programmed into the Qualtrics system with appropriate modifications for the system and administered via the internet. Northwest Minnesota Land Use Survey Administered to Land Owners in the Northwest Minnesota area.
There should be three mutually-exclusive selection buttons next to each choice as follows:  Note that this section is omitted if the respondent in Category 3 indicated "No" to all questions, i.e., is not interested in opening land to outside use in any circumstance whatsoever.
The Questions display in the order provided. (Subject to results of the pre-survey and any necessary modifications determined therefrom.) Q1: "For each of the following land use choices, please indicate whether or not you would accept $X per person for a single use." ($X is determined from the results of the pre-survey. There may be more than one value of $X, and if so, the bid shown for a given respondent will be chosen by the computer randomly from the set of options." [Display list of all land use options the respondent selected in Category 3. Next to each is a pair of mutually-exclusive radio buttons, one named "Accept," the other "Decline."] Q2: "For each of the following land use choices for which you accepted the offer, is there a lower amount you would be willing to accept? If so, please type it in the blank space next to the specific land use." [Display list of all land use options for which the respondent accepted the offer in Q1. Next to each is an entry box into which an amount may be typed.] Q3: "For each of the following land use choices for which you did not accept the offer, what is the amount that you would be willing to accept? If so, please type it in the blank space next to the specific land use." [Display list of all land use options for which the respondent did not accept the offer in Q1. Next to each is an entry box into which an amount may be typed.]   : 18-22, 23-27, 28-32, 33-37, 38-42, 43-47, 48-52, 53-57, 58-62, 63-67, 68-72, 73-77  HOUSEHOLD AGE: For those who indicated household size of more than 1: "Please give the age range of any children living in your household."(Provide a free-response space and a radio button that says "There are no children living in my household.") Category 2: Past Use of NW Minnesota Recreational Facilities by Non-

Residents
This category is only for those whose ZIP codes place them outside NW Minnesota.
The following questions are presented in the order given. This category is only for those whose ZIP codes place them outside NW Minnesota.
The following questions are presented in the order given. The open-ended (free response) bids received in the pre-survey will be used to establish one or more starting-point bids for the final survey.