Assessing the suitability of community-based management for the Nyungwe Forest Reserve, Rwanda

www.elsevier.com/locate/forpol

Forest Policy and Economic

Assessing the suitability of community-based management for the

Nyungwe Forest Reserve, Rwanda

Michel K. Masozeraa, Janaki R.R. Alavalapatib,*,

Susan K. Jacobsonc, Ram K. Shresthab

aWildlife Conservation Society, P.O. Box 1699, Kigali, RwandabSchool of Forest Resources and Conservation, Institute of Food and Agricultural Sciences, University of Florida,

P.O. Box 110410, Gainesville, FL 32611-0410, USAcDepartment of Wildlife Ecology and Conservation, Institute of Food and Agricultural Sciences, University of Florida,

P.O.Box 110430, Gainesville, FL 32611-0430, USA

Received 4 March 2004; received in revised form 2 August 2004; accepted 20 August 2004

Abstract

This study assesses the perceptions of representatives from three stakeholder groups—local communities, a government

agency, and an environmental organization—towards the suitability of community-based management (CBM) approach to the

Nyungwe Forest Reserve (NFR), Rwanda. A strengths, weaknesses, opportunities, and threats (SWOT) technique in

combination with an analytic hierarchy process (AHP) was used to achieve the task. Results show that representatives of local

communities perceive positive aspects of CBM outweigh its negative aspects. However, representatives of a government agency

and a nongovernmental organization anticipate that weaknesses associated with CBM approach outweigh its strengths. Our

analyses show that stakeholder groups view CBM differently, suggesting a need for better understanding about this approach.

Implementation of CBM in small scales first along with outreach activities might bring stakeholders together and will ensure

conservation and rural community stability.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Biodiversity conservation; Community-based management; Community development; Protected area; Rwanda; Nyungwe Forest;

SWOT-AHP

1389-9341/$ - see front matter D 2004 Elsevier B.V. All rights reserved

doi:10.1016/j.forpol.2004.08.001

* Corresponding author. Tel.: +1 352 846 0899; fax: +1 352 846

1277.

E-mail address: [email protected] (J.R.R. Alavalapati).

1. Introduction

The continuous loss of biodiversity in tropical

forests has led to the creation of protected areas in

many developing countries. However, conventional

management strategies such as dfences and fines

s 8 (2006) 206–216

.

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216 207

approachT that prohibit local access to protected areas

have escalated conflicts between local communities

and management authorities in the tropics (Wells et

al., 1992). These conflicts are more pronounced in

places where communities are heavily dependent on

protected areas for their subsistence needs. Commun-

ity-based management (CBM), which explicitly rec-

ognizes the basic needs of local people in and around

the protected areas, is thought to alleviate the conflicts

related to biodiversity conservation (Western and

Wright, 1994; Gibson and Marks, 1995).1 Following

Uphoff (1998), we consider CBM as a way of

engaging local people in resource management by

incorporating their ideas, experiences, values, and

capabilities and sharing the benefits of management.

This approach is expected to increase local access to

protected areas, sense of ownership among locals, and

income to local communities through benefit sharing

arrangement. Although factors such as the lack of

resources for law enforcement, growing support for

decentralized decision making, and increased recog-

nition to customary rights of local communities are

providing impetus for CBM (Lewis and Carter, 1993;

Gibson and Marks, 1995; Murombedzi, 1998; Salaf-

sky and Wollenberg, 2000), there is skepticism among

resource managers about its potential in achieving

conservation goals (Wells et al., 1992; Barrett and

Arcese, 1995; Gibson and Marks, 1995; Hackel,

1998; Kellert et al., 2000; Songorwa et al., 2000).

Involving stakeholders in planning and manage-

ment is a necessary condition for sustainable con-

servation of protected areas. However, factors such as

the nature of resource under consideration, socio-

economic and cultural milieu of the area, opportuni-

ties to generate employment and economic activities,

community capacity to undertake management

responsibilities, and policy and institutional uncer-

tainties would influence stakeholders’ perceptions

about CBM and their involvement. If the resource

under consideration is sensitive and likely to be

threatened and if local communities have limited

skills and experience to deal with resource conserva-

tion, for example, government agencies in-charge of

1 In the literature, CBM is also referred to community-based

natural resource management (CBNRM), community wildlife/range

management (CWM), and integrated conservation and developmen

programs (ICDP).

t

that protected area would be hesitant to engage in

CBM. Furthermore, environmental agencies may not

embrace CBM if they perceive that the resource under

consideration will become endangered or extinct due

to shortcomings associated with CBM implementa-

tion. Therefore, identification and assessment of

factors influencing stakeholders’ perceptions about

the suitability of CBM are critical before it is

implemented.

This study assesses the potential of CBM approach

to the Nyungwe Forest Reserve (NFR), Rwanda as

perceived by representatives of three stakeholder

groups—local communities, a government agency,

and an environmental organization. We apply

strengths, weaknesses, opportunities, and threats

(SWOT) in combination with analytic hierarchy

process (AHP) to achieve this task. While SWOT

analysis uses a diagnostic approach to identify key

factors determining the success or failure of an

approach or a plan (Weihrich, 1982; Kotler, 1994;

Smith, 1999), AHP measures the relative importance

of factors from stakeholders’ view (Saaty, 1977, 1982,

1993; Zahedi, 1986; Wind, 1987). These approaches

have been widely used to assess factors influencing

forest management planning (Mendoza and Sprouse,

1989; Kuusipalo and Kangas, 1994; Kurttila et al.

(2000) and Ananda and Herath, 2003), biodiversity

protection (Kangas and Kuusipalo, 1993), manage-

ment of national parks (Peterson et al., 1994;

Schmoldt et al., 1994), and buffer zone management

of a nature reserve (Li et al., 1999).

2. SWOT-AHP method

SWOT is a convenient way of conducting a

situation analysis or a diagnostic analysis of factors

influencing a particular decision. In conventional

SWOT analysis, the magnitude of factors is not

quantified to determine the effect of each factor on

the proposed plan or strategy. One can overcome this

problem by using the AHP method, which assigns

relative priority to each factor through pair-wise

comparison (Zahedi, 1986; Wind, 1987; Saaty,

1993). Furthermore, this analysis can be conducted

even with a small sample of individuals or groups

who are knowledgeable with the issue under inves-

tigation (see Kurttila et al., 2000; Ananda and Herath,

able 1

WOT factors relating to CBC approach

trengths

1: Additional source of income

– Income generation

– Employment opportunities

2: Management benefits

– Reduction of management cost

3: Favorable institutional setup

– Existing decentralization process helps succeed CBNRM

– Existing government policies and CBNRM are similar

eaknesses

1: Limited income generation

– Lack of uniformity in forestry activities

– Insufficient income from forest products

– Widespread poverty in communities

– Limited access to markets

2: Limited awareness about conservation and development

activities

– Low-level perception about conservation

– Limited skills in conservation and development

3: Unfavorable traditions pose challenges

4: Limited control by governmental control of on community

actions

– Weak control from government agencies

pportunities

1: Better community–agency relationship

– Relations between communities and agencies would improve

– Profit sharing

2: Reduction of poverty

– Socioeconomic improvement of communities

– Promotes equality in distribution of income

3: Improved community awareness

– Increasing understanding of the importance of forest

4: Additional future benefits

– Rural–urban exodus might drop

– CBNRM may lead to overall buffer zone management by

communities

– Leads to sustainable forests

– Improvement in forest protection

hreats

1: Biodiversity loss

– Wildlife and habitats may suffer

– Potential negative impacts of tourism

2: Potential collapse of CBNRM

– Potential conflicts within and between communities

– Communities may go out of control

3: Uncertainty associated with high-level decisions

– Limited influence of communities/agencies in high-level

decision-making

– Limited influence of field staff over high-level decisions

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216208

T

S

S

S

S

S

W

W

W

W

W

O

O

O

O

O

T

T

T

T

2003). As such, it is a decision analysis method that is

different from statistical analyses, wherein large

samples are required to derive confidence intervals

around the means.

Following Kurttila et al. (2000), we explain

SWOT-AHP analysis in three steps. The first step is

to identify possible SWOT factors relating to the

proposed strategy or decision (see Table 1 for the list

of factors relating to CBM). It is often suggested to

include less than 10 factors within each SWOT group

so that the number of pair-wise comparisons is

manageable. Human cognitive limitations are taken

into account in constructing the AHP model, con-

ducting pair-wise comparisons, and including the

number of factors (Saaty, 1977). Pair-wise comparison

of factors within each SWOT group is the second step

(Fig. 1 indicates a portion of the questionnaire used

for pair-wise comparison). Pair-wise comparisons will

be conducted separately for all factors and a priority

value for each factor is computed using the eigenvalue

method (see Appendix A for details). The factor with

the highest priority value under each SWOT group

will be brought forward for further comparisons. The

third step involves pair-wise comparison of four

factors that are brought forward and computation of

a scaling factor for each factor. Scaling factors and

priority values are used to calculate the overall priority

of each factor as shown below:

Overall priority of factorij

¼ priority value of ij

�scaling factor of groupj

���

where j =4 (strength, weakness, opportunity, and

threat). The overall priority scores of all factors across

groups sum to one and each score indicates the

relative importance of each factor in decision.

3. Description of the study site

The Nyungwe Forest Reserve (NFR), located in

the Southwest part of Rwanda (Fig. 2), covers 970

km2 of mountainous terrain. It is one of the largest

tracts of forest remaining in the Albertine Rift

Highlands of east-central Africa. The NFR contains

more than 275 bird species, of which 25 are endemic

to the Albertine Rift Highlands. Thirteen primate

Fig. 1. An example of a pair-wise comparison between strength factors. Note: Respondent will be asked to compared the important of the two

strength factors (Strength A and Strength B) and base his/her preferences of the particular factor s/he will be asked to assign a weight from 1–9

for the relatively important factor to reflect the magnitude of the importance. This process will be repeated until all pair-wise comparisons are

exhausted.

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216 209

species, constituting one-fifth of Africa’s primate

species, have been documented in the NFR. These

include the highly endangered owl-faced monkey

(Cercopithecus hamlyni), Angolan colobus monkey

(Colobus angolensis), golden monkey (Cercopithecus

mitis kandti), and one of the largest remaining

populations of the eastern chimpanzee (Pan troglo-

dytes shweinfurthii). The NFR is densely populated

with an average of 300 inhabitants per square

kilometer. Over 90% of the population has been

engaged in subsistence farming, with family farms

averaging less than 1 ha in size. Although the NFR

has little agricultural value due to its steep slopes and

poor soils, population pressure and lack of alternative

Fig. 2. Nyungwe Forest and other protected areas

employment opportunities have resulted in substantial

loss of its forest cover during the past 40 years.

The NFR has a long conservation history. Since the

early 1900s, colonial authorities started to emphasize

the protection of natural forests. At the end of the

German colonial period in 1911, large parts of natural

forests along the Congo–Nile divide were set-aside as

forest reserves. Recognizing the importance of the

Nyungwe Forest as a watershed, the Belgian colonial

government declared it a national reserve in 1933.

However, local people were granted rights for gather-

ing dead wood for domestic consumption. While

prohibiting further clearing of forest for agriculture,

the forest conservation legislation during the colonial

of Rwanda. Source: Plumptre et al. (2001).

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216210

period authorized other forms of exploitation such as

mining and timber harvesting under a system of

government-controlled permits (MINAGRI, 1984).

Following the biosphere reserve model (Sayer,

1991), the Rwandan Department of Forestry devel-

oped an action plan for the conservation and manage-

ment of Rwanda’s montane forests in 1984. The plan

envisaged three management regimes for the

Nyungwe Forest: (1) a core area where only tourism

and research is permitted; (2) multiple use zone where

controlled harvesting of forest products is allowed;

and (3) a buffer zone (a belt of exotic tree plantations

surrounding the natural forest) with the dual intent of

demarcating the forest boundary and generating a

steady flow of forest products and revenue (Weber,

1989). Four management units were established for

implementation of the action plan supported by Swiss

and French bilateral aid agencies, the World Bank,

and the European Development Fund.

In 1988, the Office Rwandais du Tourisme et Parcs

Nationaux (ORTPN) known as Rwandan Tourism and

National Parks Services was given the responsibility of

enforcing conservation regulations such as controlling

illegal mining, hunting, and forest clearing in the NFR.

The Wildlife Conservation Society (WCS), whose

mission is to promote scientific research, tourism

development, public awareness, and training of park

staff, had started to extend its support to the ORTPN. At

present, both the WCS and ORTPN are actively

engaged in law enforcement, conservation education

to local communities, ecotourism, professional train-

ing, and scientific research relating to the NFR.

3.1. Survey design and data collection

We have selected 11 participants representing three

stakeholder groups—5 from local communities, 3

from the ORTPN, and 3 from the WCS for collecting

their perceptions about the suitability of CBM to the

NFR. Through field observations and formal/informal

enquiries, we made sure that the chosen participants

have adequate knowledge about the NFR and

represent opinion leaders of their groups (see Rogers

et al., 1988).2 The criteria for selecting community

3 Local Council is the village-level administrative unit. Members

f the council are responsible for the wellbeing of their communities

nd conservation of their natural resources.

2 Opinion leadership is earned and maintained by technical

ompetence, social accessibility, and conformity to a system’s

orms (Rogers et al., 1988, p. 311).

c

n

representatives were based on the ability of an

individual to understand and express community’s

views, experience in collective action process, knowl-

edge of Nyungwe Forest conservation issues, and

formal leadership at local community level. Consis-

tent with a representative democracy principle (see

Van Den Doel and Velthoven, 1993), we selected one

democratically elected member from each of five

different Local Councils.3 The community represen-

tatives were contacted 2 weeks before the actual

meeting; the purpose of our research was explained

and they were provided adequate details about CBM.

Among three ORTPN representatives, one was from

the national headquarters (Kigali), one was the

Warden of the Nyungwe Forest, and the other was a

field staff. Among three WCS representatives, one

was the project director and the other two were the

conservation education officer and a field staff,

respectively. Selecting survey participants based on

the principles of opinion leadership and representative

democracy, which were applied in this study, is not

uncommon in the literature (see Kangas and Kuusi-

palo, 1993; Ananda and Herath, 2003).

In June 2001, a 3-day meeting was organized in

Gisakura, a semiurban center near the Nyungwe Forest,

Rwanda, to generate required data for SWOT-AHP

analysis. We conducted a brainstorming session with

participants and generated an exhaustive list of SWOT

factors relating to the CBM approach to the NFR. The

factors listed were further reviewed, deliberated, and

organized into meaningful groups. For example,

factors such as income generation and employment

opportunity associated with CBM were grouped as

additional source of income and considered a

bstrengthQ factor (Table 1). This process yielded 3

strengths, 4 weaknesses, 4 opportunities, and 4 threats.

The SWOT factors listed in Table 1 were used to

develop a survey questionnaire for pair-wise compar-

ison. The survey questionnaire included a rating scale

of one to nine to weigh each factor relative to the

other (Fig. 1). The questionnaire was administered to

each group separately. Members in each group were

asked to deliberate and evaluate SWOT factors in

pairs and indicate if both factors are equally important

o

a

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216 211

or one is more important than the other. In Fig. 1, if

the response was b3Q on the right side, it implies that

badditional source of incomeQ factor is three times

more important than bmanagement benefitQ factor.

Members within groups were asked to deliberate and

come to a consensus in assigning relative weights.

Because it is not uncommon for members of an

agency or organization to have a unified position or

statement on a policy issue, we followed this bgroupconsensusQ approach. Following pair-wise compari-

sons, as explained earlier, overall priority scores were

calculated for each factor within each SWOT group.

Throughout our analysis, consistency ratios are

maintained below 0.1 and we used Expert Choice

computer software to analyze the pair-wise compar-

ison data (Expert Choice, 2001).

4. Results and discussion

The overall priority scores of factors for three

stakeholder groups are given in columns 5–7 of

Table 2. Because the overall priority scores add up to

one, each priority score can be interpreted as the

Table 2

SWOT factors and their priority and overall priority scores

SWOT groups Factors priority scores

Community ORTPN

Strengths

S1: Additional source of income 0.627 0.674

S2: Management benefits 0.094 0.226

S3: Favorable institutional setup 0.28 0.101

Weaknesses

W1: Limited income generation 0.096 0.096

W2: Limited awareness. . . 0.55 0.55

W3: Unfavorable traditions. . . 0.053 0.053

W4: Limited control by govt. . . . 0.301 0.301

Opportunities

O1: Better community relations 0.054 0.301

O2: Reduction of poverty 0.558 0.539

O3: Improved comm. awareness 0.289 0.104

O4: Additional future benefits 0.102 0.057

Threats

T1: Biodiversity loss 0.627 0.234

T2: Potential collapse of CBNRM 0.094 0.081

T3: Uncertainty associated. . . 0.28 0.685

Figures in bold are factors of each SWOT group.

weight of each factor on the proposed CBM. The

scores of strength and opportunity factors can be

interpreted as positives of CBM, while the scores of

weakness and threat factors as negatives. For

example, overall priority scores of 0.572 and 0.127

(column 5 of Table 2) suggest that strengths and

opportunities of CBM would account, respectively,

for about 57% and 13%. This result indicates that

representatives of communities perceive CBM as a

suitable strategy for the NFR. The overall priority

scores of other stakeholder groups can be interpreted

in the same way. The relative importance of each

factor within each SWOT group provides valuable

insights for decision-making. For example, a priority

value of 0.627 reported in the second column of

Table 2 indicates that community representatives

perceive that additional source of income (S1) alone

accounts for about 63% of the total strength of CBM.

The overall priority scores of each stakeholder

group are presented in Figs. 3–5 to provide more

intuitive explanation. The lines in the top two

quadrants indicate the weights of positive factors

(strengths and opportunities), while those in the

bottom two quadrants reflect the weights of negative

Overall priority scores

WCS Community ORTPN WCS

0.572 0.289 0.056

0.627 0.387 0.195 0.035

0.094 0.049 0.065 0.005

0.28 0.154 0.029 0.016

0.24 0.061 0.529

0.093 0.025 0.006 0.049

0.242 0.16 0.034 0.128

0.052 0.011 0.003 0.028

0.613 0.064 0.019 0.324

0.127 0.113 0.153

0.104 0.007 0.034 0.016

0.061 0.071 0.061 0.009

0.23 0.036 0.012 0.035

0.605 0.013 0.006 0.093

0.062 0.536 0.262

0.682 0.039 0.125 0.179

0.082 0.006 0.043 0.021

0.236 0.017 0.367 0.062

Fig. 3. Overall priority scores of SWOT factors for community members (units in the axis represent ratio scale sum to one).

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216212

factors (weakness and threats) relating to CBM.

Furthermore, the line in each quadrant indicates the

total weight of factors of each SWOT group and

points on each line show the weight of each factor

within the group.

4.1. Community representatives’ perceptions

The overall priority scores reported in column 5

of Table 2 provide the perspectives of community

Fig. 4. ORTPN preferences for CBNRM (units in

representatives toward CBM. The scores reveal that

additional source of income (S1) is the dominant

strength of CBM and reduction of poverty (O2) is

the key factor among opportunities. In the face of

widespread poverty within communities around the

Nyungwe Forest, community representatives expect

that CBM provides additional income and improves

the wellbeing of communities. This group, how-

ever, perceives that limited awareness about con-

servation and development activities (W2) will be a

the axis represent ratio scale sum to one).

4 Frequent changes of government structures create uncertainty in

any conservation outcome. The local government agencies and

communities in Rwanda have limited influence in decision-making

processes because of the existing top-down power structure, where

local politics have dominant influence in decision-making. The

ORTPN members strongly feel that if future institutional changes

impact the shared governance of the NFR, the filed staff will have

tough time to face local communities. Limited trust and tainted

relationships between communities and the implementing agency

would hinder the success of the CBC. The ORTPN members’

perceptions are consistent with observations of Fiallo and Jacobson

(1995) that poor relations between community members and the

park staffs in Ecuador were largely due to the top-down manage-

ment structure.

Fig. 5. WCS preferences for CBNRM (units in the axis represent ratio scale sum to one).

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216 213

major weakness in adopting CBM. This suggests

that community representatives recognize the com-

plexities involved in resources conservation and

limited capacities of community institutions to

undertake new challenges. Among threats, com-

munity representatives perceive that biodiversity

loss (T1) that may happen due to ineffective or

improper implementation CBM can be a serious

factor (Fig. 3).

The results suggest that, from the community

members’ perspective, positive factors with a weight

of approximately 0.7 would outweigh the negative

factors. This result is consistent with other findings

that community members generally perceive CBM

as an effective means of wildlife conservation and

providing economic incentives for locals (Western

and Wright (1994) as reported in Songorwa et al.

(2000)). Kellert et al. (2000) also found similar

results from case studies in Nepal and Kenya.

4.2. Government agency (ORTPN) members’

perceptions

The members of ORTPN perceive that negative

factors associated with the CBM approach would

outweigh its positive factors (Fig. 4). The overall

priority score of threats (0.536) reported in column

6 of Table 2 indicates that this group has significant

concerns about the applicability of CBM to the

NFR. In particular, this group believes that the

uncertainty associated with high-level decision-mak-

ing (T3) might pose challenges to the implementa-

tion of CBM.4 Future changes in the management, a

reduction in the share of the benefit to local

communities for example, might result in serious

conflicts between local communities and the imple-

menting agency. This is a legitimate concern for the

ORTPN because changes in government institutions

and their policies are frequent in Rwanda. Despite this

concern, the members of ORTPN perceive that CBM

has potential positive features such as providing

additional income (S1) and reducing poverty in local

communities (O2).

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216214

4.3. WCS members’ perceptions

The perceptions of WCS members are similar to

those of ORTPN (Fig. 5). They perceive that

negative factors associated with the CBM approach

are even more serious. The overall priority scores

of weaknesses and threats (0.529 and 0.262)

reported in column 7 of Table 2 indicate that the

negative factors as perceived by this group would

account for about 80%. In particular, this group

believes that the limited control of government

agency (W4) associated with CBM could be a

major problem. Members of WCS think that

decentralization of power to local communities

may weaken the conservation capabilities of the

government agency. Furthermore, this group also

perceives that community access to the NFR and

tourism activities that are likely to be permitted

under CBM might pose serious threats to the

unique biodiversity of NFR.

5. Conclusions

Conservation of the NFR is complex due to

diverse preferences of stakeholder groups. Finding a

management strategy that integrates community’s

preferences with those of other stakeholders is of

paramount importance. There is a growing recog-

nition that CBM approach has such a potential.

However, ground truthing of the potential of CBM

from the perspectives of various stakeholders is

critical for better understanding of the scope of this

approach. Our SWOT-AHP analysis demonstrates

that there is little consensus among local commun-

ities, ORTPN, and WCS about the suitability of

CBM approach to the NFR. By placing a greater

weight on additional income opportunities associ-

ated with CBM, community members perceive that

CBM is an appropriate approach for the NFR.

Members of ORTPN and WCS, on the other hand,

perceive that uncertainty associated with high-level

decisions and that limited control by governmental

agency on community actions poses significant

challenges to the success of CBM. This suggests

that it is important to address major weaknesses and

threats perceived by the ORTPN and the WCS

before embracing CBM.

As a first step, key concerns expressed by

stakeholder groups must be investigated further and

efforts must be made to address them on a priority

basis. For example, the uncertainty associated with

the government policies must be dealt with. This

would not only help resource managers to devise

long-term plans but also ensure community support

for CBM. Furthermore, outreach and awareness

programs relating to CBM and establishment of

monitoring and control mechanisms of community

actions would reduce the concerns raised by the

ORTPN and the WCS. Because the biodiversity in

the NFR is sensitive, one cannot afford to make

mistakes even in the process of learning about a new

management such as CBM. Therefore, a cautious

approach is desirable in that, CBM or programs

based on CBM principles can be tried in a small area

first. Drawing on the experience from such an effort,

changes can be made and the approach can be tried

at a larger scale.

Acknowledgement

Partial funding support from the Compton Foun-

dation and the Wildlife Conservation Society for this

study is greatly appreciated. Authors would like to

acknowledge the participation of the respondents in

this research. Florida Agricultural Experiment Station

Journal Series S-10448.

Appendix A

Information derived from pair-wise comparisons

can be represented as a reciprocal matrix of weights,

where the assigned relative weight enters into the

matrix as an element aij and reciprocal of the entry

1/aji goes to the opposite side of the main diagonal.

A ¼ aij� �

¼

w1=w1 w1=w2: : : w1=wn

w2=w1 w2=w2: : :

v v : : : vwn=w1 wn=w2

: : : wn=wn

3775:

2664 ð1Þ

where rows indicate ratios of weights of each factor

with respect to all others. In the matrix, when i= j,

aij =1, i.e., the main diagonal elements of matrix is A.

M.K. Masozera et al. / Forest Policy and Economics 8 (2006) 206–216 215

When we multiply matrix A by the transpose of the

vector of weights, w, we get the resulting vector nw

(Eq. (2)).

Aw ¼ nw; where w ¼ w1;w2; : : :; wnð ÞT: ð2Þ

Eq. (2) can be rewritten as

A� nIÞw ¼ 0ð ð3Þ

where n is the largest eigenfactor, kmax, or trace of

matrix A. Saaty (1977) demonstrated that kmax = n is a

necessary and sufficient condition for consistency.

Inconsistency may arise when kmax deviates from n

due to inconsistent responses in pair-wise compar-

isons. Therefore, the matrix A should be tested for

consistency using the formula

CI ¼ kmax � nÞ= n� 1ð Þ;ð ð4Þ

CR ¼ CI=RI; ð5Þ

where CI is the consistency index, RI is random index

(RI) generated for a random matrix of order n, and CR

is the consistency ratio (Saaty, 1993; Mawapanga and

Debertin, 1996). The general rule is that CRV 0.1

should be maintained for the matrix to be consistent.

Homogeneity of factors within each group, smaller

number of factors within each group, and better

understanding of the decision problem can improve

the consistency index (Saaty, 1993).

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