Risk preferences in strategic wildfire decision making: A ...

Risk Analysis, Vol. 33, No. 6, 2013 DOI: 10.1111/j.1539-6924.2012.01894.x

Risk Preferences in Strategic Wildfire Decision Making: AChoice Experiment with U.S. Wildfire Managers

Matthew J. Wibbenmeyer,1,† Michael S. Hand,2,∗ David E. Calkin,2 Tyron J. Venn,3

and Matthew P. Thompson2

Federal policy has embraced risk management as an appropriate paradigm for wildfire man-agement. Economic theory suggests that over repeated wildfire events, potential economiccosts and risks of ecological damage are optimally balanced when management decisions arefree from biases, risk aversion, and risk seeking. Of primary concern in this article is howmanagers respond to wildfire risk, including the potential effect of wildfires (on ecologicalvalues, structures, and safety) and the likelihood of different fire outcomes. We use responsesto a choice experiment questionnaire of U.S. federal wildfire managers to measure attitudestoward several components of wildfire risk and to test whether observed risk attitudes areconsistent with the efficient allocation of wildfire suppression resources. Our results indicatethat fire managers’ decisions are consistent with nonexpected utility theories of decisions un-der risk. Managers may overallocate firefighting resources when the likelihood or potentialmagnitude of damage from fires is low, and sensitivity to changes in the probability of fireoutcomes depends on whether probabilities are close to one or zero and the magnitude of thepotential harm.

KEY WORDS: Fire management; nonexpected utility theory; risk preferences

1. INTRODUCTION

Public land and natural resource managers inthe United States are increasingly responsible foraddressing threats posed by environmental distur-bances and natural disasters. Wildland fire, floods,invasive species, and climate change impacts (amongothers) often require the involvement of public agen-

1Graduate student, Department of Economics, University of Cal-ifornia, Santa Barbara, CA, USA.

2USDA Forest Service, Rocky Mountain Research Station,Missoula, MT, USA.

3University of Montana, College of Forestry and Conservation,Missoula, MT, USA.

†The research was conducted as a contractor for Collins Consult-ing, Missoula, MT, USA.

*Address correspondence to Michael S. Hand, PO Box 7669, Mis-soula, MT 59807, USA; tel: +406 329-3375; fax: +406 329-3487;[email protected].

cies to manage the likelihood that a disturbance oc-curs and mitigate negative consequences when anincident does occur. Wildland fire managers (andsometimes managers of floods) may also be calledupon to enhance the beneficial effects while mini-mizing potential for large and destructive incidents.Inherent in these responsibilities is risk: outcomesof environmental disturbances and natural disas-ters, as well as the effectiveness of potential re-sponse strategies, are generally not known with cer-tainty before and during an incident.4 Managerialresponses to risk, and tradeoffs between the costsand potential benefits of protecting life, property,

4Although responses to natural disturbances, including wildlandfire, involve risk, where managers know the probability distri-bution for potential outcomes, and pure uncertainty, where theoutcome probabilities are unknown or ambiguous, this study isconfined only to manager responses to risk.

1021 0272-4332/13/0100-1021$22.00/1 C© 2012 Society for Risk Analysis

1022 Wibbenmeyer et al.

and natural resources, are important determinantsof the efficiency of government responses to naturaldisturbances.

In this article, we ask how public agency man-agers respond to risk during wildfire incidents, andwhether responses to risk are consistent with strate-gies that would minimize the expected loss from wild-land fire incidents. Although the majority of eco-nomic studies of risk preference rely on expectedutility models, it is well established that individualsoften make decisions that are inconsistent with ex-pected utility theory;(1)) ignoring this behavior mayresult in biased conclusions about preferences foroutcomes related to natural resources.(2) Yet little isknown about how managers acting on behalf of pub-lic agencies respond to risk, and to what degree ex-pected or nonexpected utility models describe theirdecision making under risk.

Wildland fire provides an interesting labora-tory for examining public managers’ risk prefer-ences. Unlike other types of incidents to whichpublic managers respond, wildland fire events andfire suppression efforts occur with great frequencyevery year. Also, wildfire managers often havegreater capacity to change the likelihood and phys-ical extent of the disturbance than do managersof other natural disturbances, such as hurricanes,earthquakes, etc., in which management responsesare generally limited to mitigating consequences.Wildfire management can consume significant re-sources and account for large portions of pub-lic land management agency budgets. In addi-tion, suppression costs have been rising for severaldecades,(3,4) threatening the ability of the U.S. For-est Service (USFS) to meet other objectives, suchas recreation, landscape restoration, and wildlifemanagement.(5)

Managerial responses to risk from wildland fireoccur within a complex decision-making environ-ment. Decisions in wildfire management are deter-mined in part by institutional rules, regulations, andmanagement directives,(6) and interactions betweenmanagers and the community can affect optionsavailable for responding to a fire.(7) Social and po-litical pressure can play a role in how intensivelymanagers respond to fires,(8) and managers have ex-pressed concern that political pressures and an in-creasing array of policies and rules may limit optionsfor responding to fire.(9) Further, the incentives facedby managers may encourage aggressive suppressionand discourage consideration of the beneficial effectsof wildland fire.(10−12)

Manager decisions also occur within a context ofbehavioral biases, heuristics, and risk attitudes. Re-cent research has demonstrated that loss aversion,discounting, and status quo bias are significant factorsin how wildfire managers make decisions.(13) Thisfinding supports a broader view that actions (and in-action) by public agency managers are subject to bi-ases that can result in suboptimal outcomes whenviewed from a social welfare perspective.(14−15)

This study uses responses to a choice experi-ment (CE) survey of fire managers to estimate riskpreferences when suppression strategies involve risksto structures, watersheds, and firefighting personnel.Results indicate whether more cost-effective sup-pression efforts can be achieved through more effi-cient responses to risk, and have implications for awide range of government responses to natural andman-made disasters and disturbances.(16) We antici-pate that this line of research will help improve riskmanagement efforts for natural disturbance incidentsand policies designed to align manager decisions withefficient outcomes.

2. WILDLAND FIRE DECISION MAKINGUNDER RISK

The current policy guidance for U.S. federalwildfire managers states: “Notwithstanding protec-tion of life, the cost of suppression, emergency sta-bilization and rehabilitation must be commensuratewith values to be protected.”(17) One interpretationof this statement is that resources should be investedin wildfire management until the marginal benefitsequal marginal costs.(11) This interpretation is con-sistent with models of efficient wildland fire man-agement in which the objective is to minimize thesum of suppression costs and net value change dueto fire.(18−20)

Efficient strategies for wildland fire managementthat incorporate risk have also been characterizedin the literature.(21−24) These strategies seek to min-imize the sum of expected suppression costs and netvalue change, and require that managers are risk neu-tral in their decision making. That is, efficiency inwildland fire management supposes that managersare coolly analytical decisionmakers, recalculatingexpected impacts of a fire when conditions change,and making proportional changes in strategy thatare free from biases, risk aversion, and risk seek-ing. This assumption is akin to disengaging the expe-riential and affective mode of information process-ing described by Epstein(25) and Slovic et al.(26) in

Risk Preferences in Strategic Wildfire Decision Making 1023

complete favor of rational and analytic processing ofrisk information.

2.1. Nonexpected Utility Model of WildlandFire Management

In practice, we know that most decisions willinvolve a role for both analytical and affective in-formation processing. Thus, in this study we inves-tigate the degree to which wildfire managers are re-sponsive to various factors affecting risk. Further, weask whether responses to these factors are consistentwith the behavior that would minimize the expectedeconomic losses due to wildfire, or whether they arebetter described by expected or nonexpected utilitymodels. In this context, expected economic loss is ex-pressed as the probability-weighted sum of potentialdamage to homes and degradation of watersheds re-sulting from wildfire.

The majority of economic studies of risk pref-erences rely on an expected utility model, in whichpreferences over outcomes are nonlinear but pref-erences over probabilities are linear;(22−24) however,behavior that is inconsistent with expected utilitytheory is well documented. Prospect theory(1) andits allied theories rank-dependent utility theory(27)

and cumulative prospect theory,(28) referred to col-lectively as nonexpected utility theories, allow pref-erences for risky decisions to be nonlinear in bothoutcomes and probabilities. These theories help ex-plain the observed “fourfold” pattern of risk atti-tudes, wherein individuals are risk averse over low-probability losses and high-probability gains, andrisk seeking over high-probability losses and low-probability gains.

Shaw and Woodward(2) argue that many deci-sion problems in natural resource economics can bedescribed by nonexpected utility models of choice,where the assumption of preferences that are linearover probabilities is violated due to the common im-portance of ambiguity and low probabilities. In thefire management context, managers face consider-able ambiguity with respect to social preferences, fireprobabilities, and potential fire outcomes to a vari-ety of resources, and they must frequently considerlow-probability high-consequence events. We knowof only a handful of CE studies that have evalu-ated preferences over risky attributes using modelsthat allow for nonlinear preferences over probabili-ties.(29−31) Although previous studies have examinedthe role of decision heuristics in wildfire manage-

ment,(13,14) no study has yet provided a detailed ac-count of wildfire manager risk preferences.

We model manager risk preferences by com-bining a random utility model of choices of multi-attribute goods(32−34) and a nonexpected utilityframework where the probability of an outcome maybe weighted by individuals. A similar treatment ofthis type of model was developed by Hensher et al.(31)

The basic choice that managers must make is be-tween strategies that yield utility based on poten-tial outcomes. Respondents were asked to choose thestrategy expected of them in their professional ca-pacity; thus, utility represents a form of professionalutility.

Each strategy n can result in several potentialoutcomes (i) that occur with probability p. A man-ager receives utility vi (xi |β) when outcome i occurs,where xi is a vector of outcome characteristics andβ is a vector of utility function parameters that de-scribe preferences over xi . Thus, the utility derivedfrom strategy n is a function of the utility associatedwith each outcome and the probability that each out-come occurs, or Vn = f (π(pi ), v(xi |β)), where π(pi )is a probability weighting function that describes howmanagers weight each potential outcome.

Managers choose among the menu of strategiesthe one where Vn is highest. In a random utilitymodel, given an unobserved random component tochoices (ε), the probability of observing a choice ofstrategy m is,

Pr (m = 1) = Pr (Vm + ε > Vn + ε) ∀m �= n. (1)

To summarize, Equation (1) describes how man-agers evaluate the utility associated with differentoutcomes by making tradeoffs between different at-tributes (based on the β parameter vector), how man-agers weight the likelihood of potential outcomes as-sociated with each strategy (the function π(pi )), anda decision rule for choosing among strategies.

3. ECONOMETRIC METHODS

To explore decision making under risk in thecontext of wildfire management, we analyze twoeconometric choice models. By specifying functionalforms for the arguments in Equation (1), these mod-els use observations of strategies chosen by man-agers (in a hypothetical wildfire incident) to relatethe characteristics of each strategy to the proba-bility of choosing a strategy. Econometric analy-sis is useful in this context where the model andexperimental design necessitate that choices are a


function of multiple attributes, and when we seekparametric estimates of utility function and probabil-ity weighting parameters. We estimate a categoricalmodel and a probability weighting model, which pro-vide descriptive accounts of fire manager risk pref-erences. The estimated models allow fire managerpreferences over risky outcomes to be nonlinear overoutcomes and probabilities, as in nonexpected utilitytheories such as prospect theory. We estimate bothmodels using the conditional logit model of proba-bilistic choice, which follows directly from the ran-dom utility model of choice.(32−34)

We specify a functional form for the strategyutility function, adapted from Kahneman and Tver-sky,(1) as the weighted sum of the utility of eachoutcome:

Vn =∑

i

π (pi ) ν(xi ). (2)

Here, ν(xi) is the value a manager would re-ceive from each potential outcome i of strategy n,and π(pi ) represents the decision weight appliedto the probability of outcome i. This function canaccommodate the special case where ν(xi) is lin-ear and π(pi ) = pi ; testing these conditions indicateswhether nonexpected utility is an appropriate wayof modeling wildfire manager decision making underrisk.

Wildfire managers’ choices among potentialmanagement strategies may vary based on the at-tributes of those strategies and the characteristics ofthe wildfires to which those strategies will be applied.For example, a wildfire manager may be less will-ing to select a strategy offering a lower probability ofsuccess when faced with a very threatening wildfire.Let qk equal the probability that wildfire k reachesa single resource-at-risk (in absence of suppressionefforts), and let sn equal the probability that a givenstrategy will be successful in protecting that resource.The nonexpected utility provided by strategy n inscenario k can be expressed as:

Vnk = (1 − π(qk))vn0 + πq(qk)πs(sn)vn0

+πq(qk)(1 − πs(Sn))vn1.(3)

where vn0 is the value of reduced-form utility underthe status quo (i.e., when the endowed level of theresource-at-risk is preserved), and vn1 is utility whenthe fire event occurs (i.e., when the suppression strat-egy fails and the fire burns the resource-at risk). No-tice that the resource can preserve its status quo valuein two ways: the fire may fail to reach it, or the fire

may reach it and the suppression strategy may be suc-cessful in protecting it.

In the context of the CE design presented in thenext section, vn0 and vn1 each contain a vector ofdeterministic attributes of strategy k that occur withcertainty (Xn, which is identical for outcomes vn0 andvn1). In addition, vn1 accounts for the impact on util-ity of the probabilistic loss to the resource-at-risk (zk,the value lost when the strategy fails and the fire dam-ages the resource). Specifying utility as a linear func-tion of outcome factors and utility parameters givesforms of the utility function when the event does anddoes not occur:

νn0 = X′nβ, and

νn1 = X′nβ + zkδ,

(4)

where δ is a typically negative parameter represent-ing the change in utility when resource zk is lost. Af-ter collecting terms, the random utility problem forwildland fire strategy choices becomes:

Vik = X′nβ + πq(qk)(1 − πs(sn))zkδ. (5)

In this study we are interested in whether man-agers’ choices among strategies are consistent withthe nonexpected utility presented in Equation (1),and the specific formulation of this model presentedin Equation (4). Under the special case of expectedutility theory (where π(pi ) = pi in Equation (1)),strategy choices would be consistent with the min-imization of expected economic losses from wild-fire. We follow the example of van Houtven et al.(29)

and investigate these questions by estimating cate-gorical and parametric probability weighting func-tion econometric models that examine preferencesover different probabilities and values-at-risk.

3.1. The Categorical Model

The categorical model describes fire managerdecisions over risky outcomes through the inclu-sion of separate dummy variables for each combina-tion of resource-at-risk (zk), probability fire reachesthe resource-at-risk (qk), and probability of strat-egy success (sn). Comparing the parameter estimatesacross different combinations of factors affecting riskcan indicate whether changes in these factors resultin choices consistent with minimization of expectedeconomic loss.

Incorporating the categorical variables, the util-ity function estimated in the categorical model is


expressed as follows:

Vn = Xnβ′ + Rn,kδ

′, (6)

where Xn is a vector of deterministic attributes of thefire management strategy and Rn,k is a vector of cat-egorical variables representing all possible combina-tions of (1 − sn), qk, and zk, excepting combinationsomitted as reference cases.5 Values of qk and zk arescenario-specific and therefore do not vary amongstrategies offered to address a particular wildfire sce-nario. The base case for the categorical model is cre-ated by omitting all combinations of (1 − sn) × qk ×zk where sn takes its maximum value.

Estimates of the δ parameter vector form the ba-sis of tests of three hypotheses about sensitivity todifferences in the level of value-at-risk, probability ofstrategy success, and probability that the fire reachesthe value-at-risk.

H1: Respondents are not sensitive to changesin factors affecting risk (value-at-risk, burnprobability, and probability of success).

Tests of H1 are constructed by comparing theterms in δ across different levels of (1 − sn), qk, and zk

while holding the other two factors constant. Define δ

as the parameter associated with the categorical vari-able in Rn,k with given levels of (1 − sn), qk, and zk.Respondent sensitivity to differences in value-at-riskacross scenarios k and k + 1 is tested by evaluatingwhether:

δsn,qk,zk − δsn,qk,zk+1 = 0. (7)

If the test statistic in the left-hand side of Equa-tion (7) equals zero, then we cannot reject thehypothesis H1 that respondents are sensitive to dif-ferences in value-at-risk. Because values of δ are typ-ically negative, given that they represent the utilityof an increase in expected loss, positive values ofthe test statistic indicate greater aversion to select-ing strategies with reduced probability of success inscenarios with greater value-at-risk. Similar statisticscan be constructed across varying levels of qk and sn.

If managers are sensitive to value-at-risk, burnprobability, and probability of success, a stronger hy-pothesis is that they react to changes in these vari-ables in a manner consistent with minimization of ex-pected economic loss.5For simplicity, we present the econometric framework with one

resource-at-risk; however, the choice experiment application de-scribed in the following section includes two resources-at-risk:homes and a highly valued watershed. In our results, categori-cal variables relevant to homes and watershed are representedby Hs,q,z and Ws,q,z, respectively.

H2: As factors affecting risk (value-at-risk,burn probability, and probability of success)increase, estimated declines in the utility of astrategy are proportional to changes in calcu-lated expected economic losses.

Define additional expected economic loss rela-tive to the reference case as (0.90 − sn) × qk × zk,because reference categories in this application arecombinations of (1 − sn), qk, and zk where sn equalsits maximum value, 0.90. This quantity is calculatedfor each value of (0.90 − sn) × (qk) × zk. Then therelevant test for H2, again using sensitivity to value-at-risk as an example, is:(

(0.90 − sn) × qk × zk

(0.90 − sn)× qk × zk+1)

)×δsn,qk,zk+1 − δsn,qk,zk = 0. (8)

If the left-hand side of Equation (8) is greater(less) than zero, then the estimated utility changeis smaller (larger) than the change in expected loss.This indicates that managers are less (more) sensi-tive to changes in value-at-risk than would be consis-tent with minimization of expected economic losses.Similar test statistics can be constructed for compar-isons over changes in sn or qk, holding other factorsconstant.

For probability of success, which is measured inthis application across more than two attribute levels,we are also interested in whether respondents valuedecreases in probability of success proportionally tothe increases in expected loss those changes in prob-ability of success imply. That is, we are interested inwhether respondents weight changes in probabilityof success nonlinearly depending upon where in theprobability spectrum those changes occur, consistentwith nonexpected utility theory.

H3: Changes in utility relative to expected eco-nomic loss are constant across adjacent inter-vals of probability of success.

The relevant test over two adjacent intervals ofprobability of success, (sn−1, sn) and (sn, sn+1), is:[

((0.90 − sn−1) × qk × zk) − ((0.90 − sn) × qk × zk)((0.90 − sn) × qk × zk) − ((0.90 − sn+1) × qk × zk)

]

×(δsn,qk,zk − δsn+1,qk,zk) − (δsn−1,qk,zk − δsn,qk,zk) = 0. (9)

Equation (9) tests whether respondents weightchanges across adjacent probability of success inter-vals equally, after accounting for the size of those in-tervals. With value-at-risk and burn probability heldconstant, the term in brackets is the ratio of the dif-ference in probability of success over two intervals,


or (sn − sn−1)/(sn+1 − sn). If the test statistic is greaterthan zero, then the change in probability from sn tosn+1 is overweighted relative to the change from sn−1

to sn; if the second term is greater (i.e., the test statis-tic is less than zero), then the sn to sn+1 interval isunderweighted relative to the first interval.

3.2. Probability Weighting Function Model

The probability weighting model integrates con-cepts from nonexpected utility theory and provides amore concise description of risk preferences amongfire managers. As explained earlier, risk preferencesunder nonexpected utility theory comprise two func-tions, a value function and a probability weight-ing function. Accordingly, we allow preferences overprobabilities to follow one of the nonlinear func-tional forms proposed in the experimental literature.To gain insights regarding the value function we usea simple approach that includes categorical variablesto indicate the different levels of each resource-at-risk.6 This specification can be expressed as follows:

Vn = Xnβ′ + wδ1 + wδ2 Dz, (10)

where Dz is a categorical variable indicating thedifferent levels of resource-at-risk (Dz = 0 if z =zk, Dz = 1 if z = zk+1), and:

w = (1 − πs (s)) πq (q) . (11)

The probability weighting function w estimatesseparate weighting parameters for the probability ofstrategy success and the probability the fire reachesthe resource, within the functions πs(p) and πq(q),respectively.7 Also, two resources are at risk withinthe application presented in the following section.Therefore, we estimate four probability weightingfunctions: two probability of success weighting func-tions, and two burn probability weighting functions.

The probability weighting functions we esti-mate here are based on the single-parameter form8

6The resources-at-risk in this study each have only two levels, soestimating a parametric value function would not provide any ad-ditional information over estimating utility parameters for eachcategory of the resource-at-risk variables.

7In the application presented in the following section two re-sources are at risk: homes and a highly valued watershed. There-fore, we estimate separate weighting functions w for homes andthe watershed, and we estimate parameters δ1 and δ2 separatelyfor homes and the watershed.

8Several other parametric forms for probability weighting func-tions have been described in the literature, including a two-parameter form from Prelec,(35) a one-parameter form from

described by Prelec:(35)

π (p) = exp (−(− ln p)γ ). (12)

The parameter γ in this equation controls thecurvature of the probability weighting function.When γ = 1, π(p) = p. This shape implies per-fect discriminability, where individuals respond toall equivalent changes in probability equally. Al-ternatively, as γ approaches 0, the function beginsto approximate a step function, where probabilitiesof 0 and 1 are perceived, but all other probabili-ties are indistinguishable from one another. Exper-iments have generally found γ values between 0 and1, which is consistent with overweighting low prob-abilities and underweighting high probabilities. Thisproperty, coupled with the certainty effect, results inthe inverse-S shaped probability weighting functiontypically observed in experimental studies.

In addition to providing estimates of probabil-ity weighting parameters, the probability weightingmodel provides insight into respondents’ value func-tions. For example, (δ1 + δ2)/.δ1

indicates the relativevalue of protecting the two different levels of theresource-at-risk (z). Comparing this ratio to the ratioof two levels of z (i.e., z2/.z1

) provides a measure ofthe degree of curvature of respondents’ value func-tions; risk-averse behavior is associated with concavevalue functions.

4. SURVEY DESIGN AND DATACOLLECTION

This study uses data from a web-based CE ques-tionnaire of federal fire managers regarding theirmanagerial preferences toward hypothetical wildfiremanagement strategies. CE is frequently used toelicit stated preference data within environmentalvaluation studies; in the context of this study, CE fa-cilitates efficient collection of manager preferenceswithin a controlled environment designed to reflectcontemporary spatial risk assessment tools familiarto fire managers.

In a decision support system such as theWildland Fire Decision Support System (WFDSS)used for fire management in the United States,(36)

Tversky and Kahneman,(28) and a two-parameter form fromGonzalez and Wu.(51) The discrete choice experiment data usedhere do not provide sufficient variation in probability values toestimate two-parameter forms. Of the single-parameter forms,the one-parameter form provided by Prelec appeared to fit ourdata better; therefore, it is the only form presented here.


Fig. 1. Example wildfire scenario and choice set provided to respondents. Photographs within the scenario supplemented text above thescenario to indicate potential fire severity within the watershed; in this case, there is potential for moderate-severity fire. Each scenarioprovided to respondents was accompanied by four choice sets.

simulated fire probability contours, calculated using apredictive model of fire spread, are overlaid with spa-tial identification of values-at-risk. Fire managers arethen asked to consider suppression strategies and theprobabilities they will be successful in containing thefire. Correspondingly, we elicited managerial pref-erences toward wildfire suppression strategies usinga two-tiered experimental design consisting of fire

scenarios and strategies. Questionnaires asked man-agers to respond to a series of choice sets, which pre-sented potential strategies that could be used to man-age the fire described in the associated hypotheticalwildfire scenario. An example wildfire scenario andchoice set are provided in Fig. 1. Each questionnaireconsisted of three wildfire scenarios describing vary-ing levels of risk to a valued watershed, and asked


Table I. Definitions and Levels of Scenario- and Strategy-Specific Attributes

Attribute Definition Levels

Scenario attributesh30 30 homes (value of $200,000 on average)

are at risk.= 1 if yes; = 0 if no. If no, then 5 homes

are at risk.qh Probability fire will reach homes in

absence of suppression efforts.0.25; 0.75

mod The highly valued watershed has mediumtree density, although the riparianzone along the river illustrated hashigh tree density. Mixed severity innonriparian areas and high-severityfire in the riparian area is projected.

= 1 if yes; = 0 if no. When the watershedis at risk for high severity fire, it is notat risk for moderate severity fire.

high The highly valued watershed has hightree density throughout, including inthe riparian zone. High-severitywildfire in nonriparian areas and in theriparian area is projected.

= 1 if yes; = 0 if no. When the watershedis at risk for moderate severity fire, it isnot at risk for high severity fire.

qws Probability fire will reach the watershedin absence of suppression efforts.

0.25; 0.75

Strategy attributeshprotect Strategy protects homes. = 1 if yes; = 0 if no.wsprotect Strategy protects the watershed. = 1 if yes; = 0 if no.probsucc Probability of success if a strategy that

protects homes or the watershed ischosen.

0.50; 0.75; 0.90

aviation Aviation person-hours. 50; 100; 1,000ground days Direct line person-days. 0; 100; 3,000duration Wildfire duration. <14 days; >30 dayscost Wildfire management cost. $0.2 million; $0.5 million; $2 million;

$4 million; $8 million; $15 million

respondents to select a strategy from each of fourchoice sets associated with each scenario. Attributesused in the CE questionnaire are defined as eitherscenario-specific or strategy-specific, and definitionsand levels used for each attribute are provided inTable I.

Scenarios described the current perimeter ofa hypothetical wildfire and its 0.75 and 0.25 burnprobability contours (likelihood of a fire reaching agiven extent projected over the next 14 days, pro-vided the fire is not suppressed). Located within theburn probability contours (which were drawn con-sistently across scenarios), each scenario containedtwo values-at-risk: a highly valued watershed and agroup of homes. We varied levels of risk to these at-tributes by varying the number of homes at risk (5 or30 homes) and the potential wildfire severity withinthe watershed (moderate or high severity), and byvarying the locations of homes and the watershed rel-ative to the reported fire probability contours. Us-ing an experimental design, we selected 12 wildfirescenarios, which described different levels of risk to

homes and the highly valued watershed, to present torespondents.

The choice sets accompanying scenarios askedrespondents to select from three alternative fire man-agement strategies the “strategy that you believe bestmeets community, agency leadership and politicalexpectations, and conforms to federal fire and landmanagement policies.”9 Strategy attributes included

9Respondents were asked to indicate the management strategythey expected they would pursue in the field. In addition, respon-dents were separately asked to indicate a “preferred” strategy, or“the strategy you believe would result in the best long term firemanagement outcomes, ignoring community, agency leadershipand political expectations.” In this study, we only report modelsusing expected strategy as the dependent variable. (A compari-son of expected and preferred responses with these survey datacan be found in Calkin et al.(52)) Expected management strategyselections are more likely to reflect the actual choices managerswould make, and thus are more relevant to fire managementoutcomes. The models of expected strategy choices also had sub-stantially better goodness of fit than models of preferred strategychoices, and tests of responses to risk with preferred responsesyielded highly inconsistent results. For the probability weighting


suppression cost, expected fire duration, personnelexposure to hazard, and risk to homes and the highlyvalued watershed. Definitions and levels for “Wild-fire cost” (cost), “Wildfire duration” (duration), and“Personnel exposure” (aviation and ground days),which were described as deterministic attributes offire management strategies (components of Xn), aregiven in Table I.

Risk to the homes and watershed was describedprobabilistically based on the chosen strategy’s prob-ability of success and the base level of risk de-scribed by the resources’ locations relative to thefire probability contours. Each management strat-egy was described as providing protection to homes,the watershed, both, or neither; resources protectedby each strategy were indicated by the variables“Protect homes” (hprotect) and “Protect watershed”(wsprotect). Second, management strategies were de-scribed as succeeding with a probability given bythe attribute “Probability of success” (probsucc).For example, if the management strategy protectedthe watershed, but not homes, and had a proba-bility of success of 0.75, the strategy would havea 0.75 probability of protecting the watershed, butzero probability of protecting homes. Therefore,we define probabilities of success with respect tohomes (sh) and the watershed (sws), respectively,as:

sh = probsucc × hprotect, and (13)

sws = probsucc × wsprotect. (14)

In addition, on the basis of the location of re-sources relative to fire probability contours, therewould be either 0.25 or 0.75 probability (qk) thatthe fire never reached the homes (or the watershed),even without protection. This two-tiered design, inwhich risk enters in both tiers, adds a level of com-plexity absent in other studies of risk preferences;therefore, analyses of managerial risk preferencesare somewhat more involved. Due to the complex-ity, however, we are able to test reactions to variouscomponents and levels of risk that are salient to theactual sources of risk fire managers must consider inevaluating various management strategies.

We designed and administered the survey in aweb-based questionnaire following best-practice pro-cedures described in the environmental choice mod-eling literature.(37,38) We held a focus group in Mis-

function model, the preferred strategy model estimates generallyfailed to converge.

soula, MT to allow fire managers to provide inputinto the survey design. Later, at a national fire con-ference, we pretested the questionnaire with a groupof fire managers to suggest areas where it mightbe improved. Beginning in March 2009, the surveywas administered to agency administrators within theU.S. Forest Service (district rangers and forest su-pervisors, all of whom have fire management au-thority) and fire and fuels management professionals(including U.S. Forest Service Fire Management Of-ficers, Assistant Fire Management Officers, and fed-eral land management agency personnel who hadcompleted higher level courses in fire managementdecision making administered by the National Wild-fire Coordination Group). In total, we sent 2,054 fed-eral fire managers e-mails asking them to completethe web-based questionnaire.

5. RESULTS

We received a total of 583 completed surveys,resulting in an overall response rate of 28.4%.10

Table II summarizes several characteristics of thesample. The sample primarily consists of Forest Ser-vice managers with significant experience and/orsome level of seniority within the federal land man-agement agencies. We specifically targeted fire man-agers who have decision-making authority, eitherin the formulation or execution of fire manage-ment plans. Agency administrators (generally districtrangers or forest supervisors who are responsible fordeveloping suppression strategies and objectives con-sistent with existing fire and land management plans)comprise 37.7% of the sample, whereas 37.9% of thesample was made up of fire or fuels managementprofessionals (those specifically engaged in fire

10Our response rate is within the range, although on the low end,of typical response rates found in other studies of similar surveymethods, for example, between 22% and 79% for general pop-ulation surveys;(53) between 20% and 60% for contingent valu-ation surveys;(54) and between 28% and 86% in a meta-analysisof survey nonresponses.(55) Wilson et al.(13) obtained a responserate of 34% with a similar target population. Despite a reason-able response rate, the possibility remains that respondents arenot representative of the target population, and that nonrespon-dents have different risk attitudes and preferences. Due to thenarrow time frame for conducting the survey (when managersare preparing for the fire season, but before they are in the field),a nonresponse survey was not conducted. Thus, conclusions maynot be representative of all fire managers. Ongoing research us-ing a more recent survey of fire managers specifically designeda nonresponse survey into the sample contact plan to more fullyaccount for potential nonresponse bias and representativeness.


Table II. Respondent Characteristics

Count Percent Count Percent

Gender ExperienceMale 451 77.40% 0–4 years 7 1.2%Female 132 22.60% 5–9 years 30 5.1%Total 583 100.00% 10–14 years 45 7.7%

15–19 years 77 13.2%Current federal grade level 20–29 years 239 41.0%

5–6 13 2.20% 30+ years 185 31.7%7–8 45 7.70% Total 583 100.0%9–10 50 8.60%11–12 202 34.60% Agency13–15 270 46.30% Forest Service 495 84.9%SESa 1 0.20% Bureau of Indian Affairs 5 0.9%Other 2 0.30% Bureau of Land Management 13 2.2%Total 583 100.00% National Park Service 69 11.8%

Interagency 1 0.2%Total 583 100.0%

aSenior Executive Service, a pay schedule series including most managerial, supervisory, and policy positions above General Schedulegrade 15.

management). The remainder of the sample con-sisted of individuals who are not currently in a firemanagement position, but have completed advancedfire management training and likely maintain somerole within fire and fuels management.

5.1. Categorical Model Results and Tests

Table III provides parameter estimates fromthe categorical model. Coefficients on each of thecategorical variables provide estimates of losses tomanagerial utility when probability of success withrespect to homes or the highly valued watershed isreduced from 0.90 (the reference case) to the spec-ified amount, given the base level of risk describedin the associated wildfire scenario. Tests applied tothese estimates can be used to investigate whethermanagers are sensitive to various components of risk(hypothesis 1), and whether the degree of sensitivityto various components of risk corresponds with min-imization of expected economic loss (hypotheses 2and 3).

Tests of hypotheses 1 and 2 are presented inFigs. 2 and 3, respectively. In both figures, panel Apresents tests of sensitivity to burn probability andvalues-at-risk, whereas panel B presents tests of sen-sitivity to probability of success. In each figure, mark-ers for tests with respect to homes are unfilled andmarkers for tests with the respect to the watershedare filled.

Fig. 2 presents tests of hypothesis 1, which sup-poses that managers are sensitive to the various com-ponents of risk. Test statistics with respect to homesin Fig. 2(A) (tests of H1 with respect to burn prob-ability and values-at-risk) are generally significantlydifferent from zero and positive, indicating that man-agers are more averse to the prospect of diminishedprobability of success when more homes are at riskand when burn probability is greater. For watersheds,respondents were less inclined to select strategieswith lower probability of success when the watershedwas within a higher burn probability contour or wasat risk of high-severity fire. Respondents were gener-ally averse to strategies with reduced probability ofsuccess for both homes and watershed, as indicatedby Fig. 2(B); however, they displayed a peculiar pref-erence for strategies with 0.50 probability of successfor watersheds. These tests reject hypothesis 1 andprovide evidence that managers were attentive to dif-ferences in risk factors across scenarios.

Hypothesis 2, tests of which are presented inFig. 3, examines the stronger hypothesis that choicebehavior was consistent with choices that would min-imize expected economic losses. That is, did man-agers respond to a change in a factor affectingrisk proportionally to the change in expected eco-nomic loss? With a few exceptions, these tests rejecthypothesis 2.

Fig. 3(A) indicates that managers did not re-spond to increases in burn probability or the numberof homes at risk as strongly as would be predicted


Table III. Categorical Model Results: Conditional Logit

Variable Coeff. SE

aviation 1.10E-05 1.23E-04ground days 5.58E-05*** 1.92E-05duration −0.0226*** 0.0032cost −0.0256** 0.0106Hs = 0.75,q = 0.25,z = 5 0.1167 0.0974Hs = 0.50,q = 0.25,z = 5 −0.7045*** 0.1050Hs = 0,q = 0.25,z = 5 −1.5990*** 0.1168Hs = 0.75,q = 0.75,z = 5 −0.0347 0.0896Hs = 0.50,q = 0.75,z = 5 −0.9117*** 0.0907Hs = 0,q = 0.75,z = 5 −2.1840*** 0.1258Hs = 0.75,q = 0.25,z = 30 −0.1295 0.0999Hs = 0.50,q = 0.25,z = 30 −1.0140*** 0.1065Hs = 0,q = 0.25,z = 30 −2.0410*** 0.1244Hs = 0.75,q = 0.75,z = 30 −0.1805 0.1186Hs = 0.50,q = 0.75,z = 30 −1.4690*** 0.1254Hs = 0,q = 0.75,z = 30 −2.7910*** 0.1875Ws = 0.75,q = 0.25,z = mod −0.5331*** 0.1991Ws = 0.50,q = 0.25,z = mod 0.1559 0.1749Ws = 0,q = 0.25,z = mod −0.6681*** 0.1245Ws = 0.75,q = 0.75,z = mod −0.4317*** 0.1674Ws = 0.50,q = 0.75,z = mod 0.0575 0.1519Ws = 0,q = 0.75,z = mod −0.9784*** 0.1072Ws = 0.75,q = 0.25,z = high −0.6219*** 0.1812Ws = 0.50,q = 0.25,z = high 0.1141 0.1615Ws = 0,q = 0.25,z = high −0.9756*** 0.1155Ws = 0.75,q = 0.75,z = high −0.7837*** 0.1797Ws = 0.50,q = 0.75,z = high −0.2243 0.1590Ws = 0,q = 0.75,z = high −1.3540*** 0.1148No. of obs. 19575No. of pars. 28Log-Likelihood −5782.7Pseudo R2 0.1930

Note: *** and ** indicate p values of 0.01 and 0.05, respectively.

under expected loss minimization. For instance,holding burn probability constant, the loss in utilityresulting from a decrease in probability of successfrom 0.90 (the reference case) to 0.50 was less thansix times greater when 30 homes were at risk thanwhen 5 homes were at risk. Similarly, responses toburn probability for watersheds are not as strong aswould be predicted under expected loss minimizationwhen probability of success is held constant at 0.75or 0. (Because watershed fire severity is a qualita-tive measure, calculations of expected loss with re-spect to changes in severity cannot be calculatednumerically.)

Fig. 3(B) shows that, with respect to homes, re-spondents overweighted decreases in probability ofsuccess from 0.90 to 0.50 relative to decreases from0.90 to 0.75, and decreases from 0.90 to 0 relative todecreases from 0.90 to 0.50. For watersheds, respon-

dents underweighted decreases in probability of suc-cess from 0.90 to 0.50 relative to decreases from 0.90to 0.75, and they overweighted decreases from 0.90to 0 relative to decreases from 0.90 to 0.50.

Fig. 4 presents tests of hypothesis 3, which askswhether relative probability weighting across adja-cent probability intervals is constant. For homes, re-spondents underweighted changes in probability ofsuccess from 0.90 to 0.75 relative to changes from 0.75to 0.50, but they overweighted changes in probabil-ity of success from 0.75 to 0.50 relative to changesfrom 0.50 to 0. Similar results were exhibited forwatersheds, although the pattern of weighting wasreversed and more difficult to interpret given theanomalous response to watershed risk when theprobability of success was 0.50 (see Fig. 2A). Over-all these test statistics reject hypothesis 3, indicatingnonlinear responses to changes in risk factors.

5.2. Parametric Probability Weighting Results

To provide additional detail regarding fire man-agers’ risk preferences, we estimated a probabilityweighting model based on Equations (9) and (10),the results of which are provided in Table IV. Thismodel is derived from nonexpected utility theory;therefore, it provides estimates of parameters thatsummarize sensitivity to probability and the value (orutility) function. Coefficients on wh and wh × h30can be interpreted as indicative of respondents’ valuefunction with respect to homes. Under the null hy-pothesis that managers minimize expected economiclosses (i.e., a linear value and probability weightingfunctions), the coefficient on wh × h30 is expectedto be five times larger than the wh coefficient, cor-responding to the 25 additional homes-at-risk whenh30 is equal to 1; however, the wh × h30 coefficientis less than the coefficient on wh. Although there isno relevant quantitative measure of expected loss as-sociated with moderate- and high-severity fire withinthe highly valued watershed, the value function ap-pears to be similar to that observed for the attributehomes: any fire within the watershed causes utilityloss, and the added loss associated with high-severityfire is somewhat smaller.

Probability of success and burn probability areeach weighted separately for homes and watershed;therefore, Table IV contains four γ values, and theprobability weighting functions implied by these pa-rameter estimates are illustrated in Fig. 5. The γ val-ues representing probability weighting on burn prob-abilities for homes and watershed are similar and


Fig. 2. Tests of sensitivity to changes in factors affecting risk (hypothesis 1, Equation (7)).

Fig. 3. Tests of consistency with expected loss minimization (hypothesis 2, Equation (8)).

relatively low. Values around 0.20 indicate that re-spondents substantially underweight the significanceof differences across burn probabilities; in otherwords, they are insensitive to differences across burnprobabilities. The estimated γ value for probability

of success with respect to homes is greater than 1, in-dicative of an S-shaped probability weighting func-tion. The γ value estimated for probability of suc-cess with respect to the watershed is not significantlydifferent from zero, though this result is no doubt


Fig. 4. Tests of consistency with expected loss minimizationacross adjacent probability of success intervals (hypothesis 3,Equation (9)).

influenced by unexpected responses to strategieswith 50% probability of success with respect to thewatershed.

6. DISCUSSION

The effects of natural disturbances, includingwildfire, are often directly tied to the actions and at-titudes of government agencies tasked with assess-ing and responding to large-scale risks. Theory sug-gests that over a large portfolio of wildfire events(or other types of natural disturbances), efficient out-comes will be realized when managers minimize theexpected losses from each event, and federal wild-land fire management policy appears to support thisview. However, results from this study indicate thatthe risk preferences of wildfire managers when se-lecting suppression strategies are inconsistent withbehavior that would minimize expected economicloss. Results are broadly consistent with other find-ings related to fire manager decision making, partic-ularly research by Wilson et al.(13)

When choosing among strategies, managers ap-pear to weight the probability of damage based in

Table IV. Probability Weighting Model Results:Conditional Logit

Param. Estimate SE

Coeffs. Aviation 1.94E − 05 1.14E − 04Ground days 1.99E − 05 1.78E − 05Duration −0.0198∗∗∗ 0.0029Cost −0.0356∗∗∗ 0.0102wh −5.4135∗∗∗ 0.2597wh × h30 −1.4377∗∗∗ 0.2827wws −5.1343∗∗∗ 0.4738wws × high −1.3992∗∗∗ 0.3522

Probability weighting pars.γ s,h 1.4325∗∗∗ 0.2092γ q,h 0.2021∗∗∗ 0.0352γ s,ws 0.0273 0.0578γ q,ws 0.1970∗∗∗ 0.0484

No. of obs. 19620Log-likelihood −5806.4No. of pars. 12

Note: ∗∗∗ indicates p values of 0.01.

Fig. 5. Probability weighting functions implied by γ values esti-mated in probability weighting model.

part on the source of probability variation; with re-spect to homes, manager choices were more sensi-tive to differences in the probability of success thanto burn probability. One possible explanation forthis difference (summarized by the substantial differ-ence between estimates of the probability weightingparameters γ s,h and γ q,h) is the isolation effect, sug-gested by Tversky.(39) The isolation effect suggeststhat individuals discount characteristics shared by


alternatives within a choice set and inflate the impor-tance of characteristics that differentiate them. Thatis, managers may have felt they had no control overfire scenarios but could control the probability of suc-cess within their chosen strategy.

Managers were more sensitive to changes in theprobability of success over moderate probabilitiesthan to changes over relatively high probabilities.This pattern is characteristic of an S-shaped probabil-ity weighting function rather than the inverse S-shapetypically observed in experimental studies. Robertset al.(31) also observed S-shaped probability weight-ing in the natural resource context, and compared itto the decision whether to leave home with an um-brella when there is a chance of rain: one takes theumbrella when the probability of rain is beyond someprobability threshold. In the fire management con-text, this implies that managers are overly optimisticabout strategies with a relatively high probability ofsuccess, and that they may be overly pessimistic re-garding strategies with a low probability of success.Of note is that while burn probabilities can be mod-eled with a relatively high degree of accuracy,(40) like-lihood of fire management strategy success is notwell understood. Differences in probability weight-ing across sources of probability variation may alsobe partly driven by attitudes toward the accuracy ofinformation provided in the CE questionnaire.

We found managerial responses to low levels ofrisk (due to low home or watershed burn probabil-ities, or fewer homes at risk) to be disproportion-ately large relative to their responses to high-riskscenarios. This observation is consistent with prob-ability neglect (an overreaction to low-probabilityevents because of high-affect outcomes) coupledwith insensitivity to numbers (a greater response tolow or initial levels of the value-at-risk, and lowermarginal sensitivity to additional units of the value-at-risk) described in Slovic and Peters.(42)

Another possibility is that managers’ choices ex-hibit an emotional response, or affect. The degreeand shape of probability weighting can be explainedby how affect-rich or affect-poor are the potentialoutcomes.(42)11 For example, damage to homes is of-ten perceived as a devastating outcome for those af-fected. On the other hand, damage to watersheds ismore difficult to comprehend and may not to carrythe same emotional weight as homes. Thus, we maynot observe the same responses to risk for both

11Thanks to an anonymous reviewer for pointing out thisconnection.

homes and watershed due to greater affective con-tent of homes.

Although the survey was not designed to specif-ically test for the role of affect, the results also raisethe question of how managers (and others) weightprobabilities when multiple attributes are at risk andhave different affective content. Our results suggest,for example, that managers make tradeoffs betweenpotential damage to homes and watershed, and man-agers weight the risk to these attributes differently.An open theoretical and empirical question, then, ishow affect and risk attitudes relate to preferences(i.e., utility functions) for multiple attributes, whichbuilds on multiattribute utility theory and multicrite-ria decision analysis with uncertainty.(43,44)

A practical implication of these findings is thatwe do not know if choices made by managers, evenwhen they deviate from strategies that would min-imize expected losses, reflect broader social prefer-ences. Experimental evidence has shown that risk at-titudes of managers may not deviate greatly from riskattitudes of the general public,(45) but it is not knownif this result would hold when multiple attributes areat risk or in a fire management context.

Our results imply significant potential for im-proved risk management in wildfire suppression de-cision making. In particular, it appears that more ef-ficient allocations can be realized if managers choosestrategies that use fewer resources for fires thatpresent relatively little risk. Restraining the commit-ment of suppression resources on low-risk incidentscould reduce personnel exposure to risk and suppres-sion expenditures, and allow for more flexibility in al-locating appropriate resources to fires during times ofhigh fire activity. Given the emerging consensus thatthe trend in USFS expenditures on wildfire manage-ment is unsustainable,(5) avoiding overallocations ofresources to low-risk incidents may help the USFSmore cost effectively meet its fire and nonfire man-agement goals.

Although the potential exists for improved riskmanagement of wildland fires, this is not a trivialtask. First, institutional constraints and incentives area barrier to improvement. For example, the deci-sion to use wildland fires to attain beneficial resourceimpacts, which is perceived to be riskier than thedecision to aggressively suppress a fire, has in thepast been shown to lack agency support.(9,36) Canton-Thompson et al.(9) found that fire managers feltthey would receive little agency support, and mightbe held personally liable, if the suppression strate-gies they chose were ineffective. Furthermore, fire


managers may not have an incentive to constraincosts because wildfire suppression activities are of-ten funded through emergency funds and a nationalfunding pool.(9,14,46)

Second, Calkin et al.(16) argued that the absenceof formal risk-management training within the USFSand interagency fire training programs may impederisk-based wildfire management practices. Maguireand Albright(14) were more cautious, arguing thattraining may not be fully effective in mitigating deci-sion biases because these biases have been observedeven in well-trained individuals.(47) In this study,managers at higher pay grades or who had managedmore fires in their career did not have significantlydifferent risk attitudes than less experienced man-agers; agency administrators (separate from otherfire managers) showed statistically different choicepatterns with respect to risk, but generally not statis-tically different over- or underweighting of risk fac-tors relative to loss-minimizing strategies.12

Finally, it may be necessary to consider strat-egy choices as allocation decisions among multiplefire events. This would require greater responsibilityamong higher level managers for deciding which firesreceive more or fewer suppression resources (e.g.,at the area or regional level) and less autonomy forincident-level managers. However, it is not knownwhether suppression resource allocations made byhigher level managers in response to risk would besubstantively different.

This study is subject to several limitations, someof which should spur further research. First, we mea-sured fire manager risk preferences using a statedpreference survey instrument; future research mightexplore fire manager attitudes toward risk usingobservational data. Also, the conclusions are lim-ited to the target population surveyed—wildland firemanagers—and we caution against extrapolating re-sults beyond this group of respondents. Some in-formation about incident-level decisions and riskmanagement is available in the web-based WFDSS,although significant investments in data collectionwould be necessary to use this information for

12Results are available from the authors upon request. Analysesof choices by individual characteristics were limited to the cate-gorical model (due to lack of convergence of the maximum like-lihood function in the probability weighting function model). Foragency administrators, responses to risk of damage to the water-shed exhibited statistically different over- or underweighting fora few probability categories. In general, these responses showedless bias but still differed significantly from choices that wouldminimize expected losses from fire.

research purposes. WFDSS data could allow for anapplied study of how the content of risk communica-tion is related to risk attitudes, similar to experimen-tal studies by Keller et al.(48)

Second, we measured preferences over a lim-ited range of probability values and levels of valuesat risk, and the probabilities did not encompass val-ues near zero or one.13 For this reason, we interpretprobability weighting results primarily as reflectionsof sensitivity to changes over moderate probabil-ities. A more comprehensive account of managerrisk preferences would include attitudes toward low-probability, high-consequence events, similar to ex-periments using hypothetical earthquake risk,(49) orextending lottery experiments by Holt and Laury(50)

to multiple attributes.Finally, risk preferences are a single component

within a large suite of decision biases and mentalheuristics that may contribute to less efficient firemanagement outcomes; additional research on fram-ing, discounting, status quo bias, and the role of in-centives in contributing to these decision biases haspotential to suggest possible opportunities for im-proving wildfire manager decision processes.

ACKNOWLEDGMENTS

The authors thank Patty Champ, Claire Mont-gomery, Tom Holmes, and two anonymous review-ers for helpful comments on previous drafts. Sem-inar participants at the W2133 meetings and theInternational Association of Wildland Fire 3rd Hu-man Dimensions Conference also provided valuablefeedback. The authors also acknowledge Jon Rieck,Derek O’Donnell, and the University of MontanaBureau of Business and Economic Research for as-sistance in developing and administering the survey.

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