# Representative Group Decision-Making in Forest Management: A Compromise Approach

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Pairwise Comparison Matrices (PCMs)

- Reciprocity: ${w}_{ij}\hspace{0.33em}x\hspace{0.33em}{w}_{ji}=1\hspace{1em}\hspace{1em}\forall \hspace{0.17em}i,j$
- Consistency: ${w}_{ij}\hspace{0.33em}x\hspace{0.33em}{w}_{jk}={w}_{ik}\hspace{1em}\hspace{0.33em}\forall \hspace{0.33em}i,j,k$

#### 2.2. Voting Power (VP)

_{1}, n

_{2}, …, n

_{m}) are known. In this model, the 3 rules previously described are combined, integrating them as objectives: “1 person, 1 vote” (4), with all the individuals acquiring the same importance of opinion; “1 social group, 1 vote” (5), in which all the social groups have the same importance regardless of the number of stakeholders forming each group; and the third rule (6), which is associated with the minimisation of the maximum deviation (D) or discrepancy between the two previous rules in which the interests of the groups and of the individuals are confronted.

## 3. Case Study

#### 3.1. Survey

#### 3.2. Group Formation

Group 1 | Group 2 | |||||||
---|---|---|---|---|---|---|---|---|

Land | Asso | Firm | Ecol | Land | Asso | Firm | Ecol | |

Public authority/technicians | 5 | 4 | 1 | |||||

Hunters | 2 | 1 | 1 | |||||

Ecologists/NGOs | 3 | 3 | ||||||

Forestry work firms | 1 | 1 | ||||||

Cattle farmers | 1 | 1 | 2 | |||||

Industry | 2 | 1 | 1 | 2 | ||||

Mycologists | 1 | 1 | 2 | |||||

Small forest firms | 1 | 1 | ||||||

Professional/university professor | 3 | 5 | 1 | 6 | ||||

Landowner | 1 | 2 | ||||||

Total stakeholders | 13 | 8 | 4 | 3 | 10 | 11 | 4 | 3 |

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

LAND | ECOL | FIRM | ASSO | LAND | ECOL | FIRM | ASSO | LAND | ECOL | FIRM | ASSO | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

LAND | $\left[\begin{array}{cccc}1& 1/3& 1/3& 1/3\\ 3& 1& 3& 3\\ 3& 1/3& 1& 3\\ 3& 1/3& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 7& 3& 3\\ 1/7& 1& 1/7& 1/9\\ 1/3& 7& 1& 1/3\\ 1/3& 9& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 7& 5& 5\\ 1/7& 1& 1/3& 1/3\\ 1/5& 3& 1& 3\\ 1/5& 3& 1/3& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 5& 3& 3\\ 1/5& 1& 1/3& 1\\ 1/3& 3& 1& 3\\ 1/3& 1& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 5& 3\\ 1/3& 1& 3& 1/3\\ 1/5& 1/3& 1& 1/3\\ 1/3& 3& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 3& 5\\ 1/3& 1& 3& 5\\ 1/3& 1/3& 1& 3\\ 1/5& 1/5& 1/3& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 1& 3& 3\\ 1& 1& 3& 5\\ 1/3& 1/3& 1& 3\\ 1/3& 1/5& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 5& 7& 5\\ 1/5& 1& 1/3& 1\\ 1/7& 3& 1& 3\\ 1/5& 1& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 1/7& 1/3& 1/5\\ 7& 1& 5& 5\\ 3& 1/5& 1& 1\\ 5& 1/5& 1& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 5& 9& 7\\ 1/5& 1& 1/3& 1/3\\ 1/9& 3& 1& 1/3\\ 1/7& 3& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 3& 3\\ 1/3& 1& 3& 3\\ 1/3& 1/3& 1& 1/3\\ 1/3& 1/3& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 1/3& 1/3& 1/3\\ 3& 1& 1/3& 1/3\\ 3& 3& 1& 3\\ 3& 3& 1/3& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 3& 1& 5\\ 1/3& 1& 1/3& 3\\ 1& 3& 1& 7\\ 1/5& 1/3& 1/7& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 5& 5& 5\\ 1/5& 1& 1& 1\\ 1/5& 1& 1& 1/3\\ 1/5& 1& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 1& 3\\ 1/3& 1& 1/3& 1\\ 1& 3& 1& 1\\ 1/3& 1& 1& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 1& 3& 5\\ 1& 1& 3& 5\\ 1/3& 1/3& 1& 3\\ 1/5& 1/5& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 5& 3& 5\\ 1/5& 1& 1/5& 1/3\\ 1/3& 5& 1& 3\\ 1/5& 3& 1/3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 1/3& 1/7\\ 1/3& 1& 1/5& 1/7\\ 3& 5& 1& 1/5\\ 7& 7& 5& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 7& 5& 3\\ 1/7& 1& 1/5& 1/7\\ 1/5& 5& 1& 1/5\\ 1/3& 7& 5& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 1/3& 3& 1/5\\ 3& 1& 3& 1/3\\ 1/3& 1/3& 1& 1/3\\ 5& 3& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 7& 1& 1/5\\ 1/7& 1& 1/5& 1/9\\ 1& 5& 1& 1\\ 5& 9& 1& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 7& 7& 7\\ 1/7& 1& 1/3& 1/3\\ 1/7& 3& 1& 1\\ 1/7& 3& 1& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 1/9& 9& 3\\ 9& 1& 9& 9\\ 1/9& 1/9& 1& 1/3\\ 1/3& 1/9& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 5& 1& 3\\ 1/5& 1& 1/5& 1/5\\ 1& 5& 1& 5\\ 1/3& 5& 1/5& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 1/3& 1& 1/3\\ 3& 1& 7& 3\\ 1& 1/7& 1& 1/3\\ 3& 1/3& 3& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 3& 3& 5\\ 1/3& 1& 3& 1\\ 1/3& 1/3& 1& 1\\ 1/5& 1& 1& 1\end{array}\right]$ | $\left[\begin{array}{cccc}1& 9& 7& 7\\ 1/9& 1& 1/5& 1/7\\ 1/7& 5& 1& 1\\ 1/7& 7& 1& 1\end{array}\right]$ | |||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO | ||||||||||||

LAND | $\left[\begin{array}{cccc}1& 3& 3& 1\\ 1/3& 1& 1& 1/3\\ 1/3& 1& 1& 1\\ 1& 3& 1& 1\end{array}\right]$ | |||||||||||

ECOL | ||||||||||||

FIRM | ||||||||||||

ASSO |

## References

- Diaz-Balteiro, L.; Romero, C. Making forestry decisions with multiple criteria: A review and an assessment. For. Ecol. Manag.
**2008**, 255, 3222–3241. [Google Scholar] [CrossRef] - Diaz-Balteiro, L.; Gonzalez-Pachon, J.; Romero, C. Forest management with multiple criteria and multiple stakeholders: An application to two public forests in Spain. Scand. J. For. Res.
**2009**, 24, 87–93. [Google Scholar] [CrossRef] - Segura, M.; Ray, D.; Maroto, C. Decision support systems for forest management: A comparative analysis and assessment. Comput. Electron. Agric.
**2014**, 101, 55–67. [Google Scholar] [CrossRef] - Xu, Z. A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci.
**2004**, 166, 19–30. [Google Scholar] [CrossRef] - Uhde, B.; Andreas Hahn, W.; Griess, V.C.; Knoke, T. Hybrid MCDA Methods to Integrate Multiple Ecosystem Services in Forest Management Planning: A Critical Review. Environ. Manag.
**2015**, 56, 373–388. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ezquerro, M.; Pardos, M.; Diaz-Balteiro, L. Operational Research Techniques Used for Addressing Biodiversity Objectives into Forest Management: An Overview. Forests
**2016**, 7, 229. [Google Scholar] [CrossRef][Green Version] - Ortiz-Urbina, E.; González-Pachón, J.; Diaz-Balteiro, L. Decision-making in forestry: A review of the hybridisation of multiple criteria and group decision-making methods. Forests
**2019**, 10, 375. [Google Scholar] [CrossRef][Green Version] - Diaz-Balteiro, L.; Iglesias-Merchan, C.; Romero, C.; de Jalón, S.G. The sustainable management of land and fisheries resources using multicriteria techniques: A meta-analysis. Land
**2020**, 9, 380. [Google Scholar] [CrossRef] - Kangas, A.; Laukkanen, S.; Kangas, J. Social choice theory and its applications in sustainable forest management-a review. For. Policy Econ.
**2006**, 9, 77–92. [Google Scholar] [CrossRef] - Nordström, E.M.; Romero, C.; Eriksson, L.O.; Öhman, K. Aggregation of preferences in participatory forest planning with multiple criteria: An application to the urban forest in Lycksele, Sweden. Can. J. For. Res.
**2009**, 39, 1979–1992. [Google Scholar] [CrossRef] - Koksalmis, E.; Kabak, Ö. Deriving decision makers’ weights in group decision making: An overview of objective methods. Ink. Fusion
**2019**, 49, 146–160. [Google Scholar] [CrossRef] - Kabak, Ö.; Ervural, B. Multiple attribute group decision making: A generic conceptual framework and a classification scheme. Knowl. -Based Syst.
**2017**, 123, 13–30. [Google Scholar] [CrossRef] - Nordström, E.-M.; Eriksson, L.O.; Öhman, K. Integrating multiple criteria decision analysis in participatory forest planning: Experience from a case study in northern Sweden. For. Policy Econ.
**2010**, 12, 562–574. [Google Scholar] [CrossRef][Green Version] - Vuillot, C.; Mathevet, R.; Sirami, C. Comparing social representations of the landscape: A methodology. Ecol. Soc.
**2020**, 25, 1–36. [Google Scholar] [CrossRef] - Saaty, T.L. The Analytic Hierarchy Process; McGraw-Hill: New York, NY, USA, 1980; ISBN 0070543712. [Google Scholar]
- González-Pachón, J.; Diaz-Balteiro, L.; Romero, C. A multi-criteria approach for assigning weights in voting systems. Soft Comput.
**2019**, 23, 8181–8186. [Google Scholar] [CrossRef] - Thurstone, L.L. A law of comparative judgment. Psychol. Rev.
**1927**, 34, 273–286. [Google Scholar] [CrossRef] - Ramík, J. Pairwise Comparisons Method; Lectures Notes in Economic and Mathematical Systems; Springer: Berlin/Heidelberg, Germany, 2020; Volume 690, ISBN 978-3-030-39890-3. [Google Scholar]
- Saaty, T.L. A scaling method for priorities in hierarchical structures. J. Math. Psychol.
**1977**, 15, 234–281. [Google Scholar] [CrossRef] - Kangas, J. An approach to public participation in strategic forest management planning. For. Ecol. Manag.
**1994**, 70, 75–88. [Google Scholar] [CrossRef] - Saaty, R.W. The analytic hierarchy process-what it is and how it is used. Math. Model.
**1987**, 9, 161–176. [Google Scholar] [CrossRef][Green Version] - Lakicevic, M.; Srdjevic, B.; Velichkov, I. Combining AHP and SMARTER in forestry decision making. Balt. For.
**2018**, 24, 124–131. [Google Scholar] - Grošelj, P.; Hodges, D.G.; Zadnik Stirn, L. Participatory and multi-criteria analysis for forest (ecosystem) management: A case study of Pohorje, Slovenia. For. Policy Econ.
**2015**, 71, 80–86. [Google Scholar] [CrossRef] - Segura, M.; Maroto, C.; Belton, V.; Ginestar, C. A New Collaborative Methodology for Assessment and Management of Ecosystem Services. Forests
**2015**, 6, 1696–1720. [Google Scholar] [CrossRef][Green Version] - Romero, C.; Tamiz, M.; Jones, D.F. Goal programming, compromise programming and reference point method formulations: Linkages and utility interpretations. J. Oper. Res. Soc.
**1998**, 49, 986–991. [Google Scholar] [CrossRef] - Pardos, M.; Pérez, S.; Calama, R.; Alonso, R.; Lexer, M.J. Ecosystem service provision, management systems and climate change in Valsaín forest, central Spain. Reg. Environ. Change
**2016**, 17, 17–32. [Google Scholar] [CrossRef] - Ezquerro, M.; Pardos, M.; Diaz-Balteiro, L. Integrating variable retention systems into strategic forest management to deal with conservation biodiversity objectives. For. Ecol. Manag.
**2019**, 433, 585–593. [Google Scholar] [CrossRef] - Diaz-Balteiro, L.; Alonso, R.; Martínez-Jaúregui, M.; Pardos, M. Selecting the best forest management alternative by aggregating ecosystem services indicators over time: A case study in central Spain. Ecol. Indic.
**2017**, 72, 322–329. [Google Scholar] [CrossRef] - López, I.; Pardo, M. Socioeconomic indicators for the evaluation and monitoring of climate change in national parks: An analysis of the sierra de guadarrama national park (Spain). Environments
**2018**, 5, 25. [Google Scholar] [CrossRef][Green Version] - Bugmann, H.; Cordonnier, T.; Truhetz, H.; Lexer, M.J. Impacts of business-as-usual management on ecosystem services in European mountain ranges under climate change. Reg. Environ. Chang.
**2017**, 17, 3–16. [Google Scholar] [CrossRef] - Langner, A.; Irauschek, F.; Perez, S.; Pardos, M.; Zlatanov, T.; Öhman, K.; Nordström, E.; Lexer, M.J. Value-based ecosystem service trade-offs in multi-objective management in European mountain forests. Ecosyst. Serv.
**2017**, 26, 245–257. [Google Scholar] [CrossRef] - Mendoza, G.A.; Prabhu, R. Evaluating multi-stakeholder perceptions of project impacts: A participatory value-based multi-criteria approach. Int. J. Sustain. Dev. World Ecol.
**2009**, 16, 177–190. [Google Scholar] [CrossRef] - Buchy, M.; Hoverman, S. Understanding public participation in forest planning: A review. For. Policy Econ.
**2000**, 1, 15–25. [Google Scholar] [CrossRef] - Sheppard, S.R.J.; Meitner, M. Using multi-criteria analysis and visualisation for sustainable forest management planning with stakeholder groups. For. Ecol. Manag.
**2005**, 207, 171–187. [Google Scholar] [CrossRef] - Ramanathan, R.; Ganesh, L.S. Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members’ weightages. Eur. J. Oper. Res.
**1994**, 79, 249–265. [Google Scholar] [CrossRef] - Marques, M.; Reynolds, K.M.; Marques, S.; Marto, M.; Paplanus, S.; Borges, J.G. A Participatory and Spatial Multicriteria Decision Approach to Prioritize the Allocation of Ecosystem Services to Management Units. Land
**2021**, 10, 747. [Google Scholar] [CrossRef] - Borges, G.; Marques, S.; Garcia-Gonzalo, J.; Rahman, A.U.; Bushenkov, V.; Sottomayor, M.; Carvalho, P.O.; Nordström, E.M. A Multiple Criteria Approach for Negotiating Ecosystem Services Supply Targets and Forest Owners’ Programs. For. Sci.
**2017**, 63, 49–61. [Google Scholar] [CrossRef] - Rönnqvist, M.; Amours, S.D.; Weintraub, A.; Jofre, A.; Gunn, E.; Haight, R.G.; Martell, D.; Murray, A.T.; Romero, C. Operations Research challenges in forestry: 33 open problems. Ann. Oper. Res.
**2015**, 232, 11–40. [Google Scholar] [CrossRef] - Vainikainen, N.; Kangas, A.; Kangas, J. Empirical study on voting power in participatory forest planning. J. Environ. Manag.
**2008**, 88, 173–180. [Google Scholar] [CrossRef]

**Figure 1.**Characteristics of the methodologies employed. Acronyms:

^{a}—PCMs: pairwise comparison matrices,

^{b}—VP: voting power.

**Table 1.**A summary of Saaty’s fundamental scale [19].

Value of Importance | Definition | Explanation |
---|---|---|

1 | Equal importance | Two activities contribute equally to the objective |

3 | Moderate importance | Experience and judgment slightly favour one activity over another |

5 | Strong importance | Experience and judgment strongly favour one activity over another |

7 | Demonstrated importance | An activity is favoured very strongly over another, and its dominance is demonstrated in practice |

9 | Extreme importance | The evidence favouring one activity over another is of the highest possible order of affirmation |

Land ^{1} | Asso ^{2} | Firm ^{3} | Ecol ^{4} | |
---|---|---|---|---|

PCM ^{5} | 0.409 | 0.211 | 0.207 | 0.173 |

^{1}landowner,

^{2}associations,

^{3}firms,

^{4}ecologists,

^{5}pairwise comparison matrix.

Group 1 | Group 2 | ||||||||
---|---|---|---|---|---|---|---|---|---|

VP ^{1} | Land | Asso | Firm | Ecol | Land | Asso | Firm | Ecol | |

n ^{2} | 13 | 8 | 4 | 3 | 10 | 11 | 4 | 3 | |

${\lambda}_{1}$ ^{3} | ${\lambda}_{2}$ ^{4} | ||||||||

0 | 1 | 0.464 | 0.286 | 0.143 | 0.107 | 0.357 | 0.393 | 0.143 | 0.107 |

1 | 0 | 0.388 | 0.209 | 0.204 | 0.199 | 0.242 | 0.279 | 0.242 | 0.237 |

0 | 0 | 0.25 | 0.255 | 0.25 | 0.245 | 0.25 | 0.255 | 0.25 | 0.245 |

0.6 | 0.2 | 0.464 | 0.286 | 0.143 | 0.107 | 0.357 | 0.393 | 0.143 | 0.107 |

^{1}voting power,

^{2}number of stakeholders in each group,

^{3,4}control parameters.

PCM | VP1 ^{1} | VP1 | VP1 | VP1 | VP2 ^{2} | VP2 | VP2 | VP2 | |||
---|---|---|---|---|---|---|---|---|---|---|---|

0–1 | 1–0 | 0–0 | 0.6–0.2 | 0–1 | 1–0 | 0–0 | 0.6–0.2 | ${\lambda}_{1}$ ^{3} | ${\lambda}_{2}$ ^{4} | ||

PCM | 0.000 | 0.131 | 0.034 | 0.185 | 0.131 | 0.210 | 0.195 | 0.185 | 0.210 | ||

VP1 | 0.000 | 0.155 | 0.278 | 0.000 | 0.151 | 0.276 | 0.278 | 0.151 | 0 | 1 | |

VP1 | 0.000 | 0.159 | 0.155 | 0.217 | 0.171 | 0.159 | 0.217 | 1 | 0 | ||

VP1 | 0.000 | 0.278 | 0.247 | 0.028 | 0.000 | 0.247 | 0 | 0 | |||

VP1 | 0.000 | 0.151 | 0.276 | 0.278 | 0.151 | 0.6 | 0.2 | ||||

VP2 | 0.000 | 0.230 | 0.247 | 0.000 | 0 | 1 | |||||

VP2 | 0.000 | 0.028 | 0.230 | 1 | 0 | ||||||

VP2 | 0.000 | 0.247 | 0 | 0 | |||||||

VP2 | 0.000 | 0.6 | 0.2 |

^{1}group 1,

^{2}group 2,

^{3,4}control parameters.

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**MDPI and ACS Style**

Ortiz-Urbina, E.; Diaz-Balteiro, L.; Pardos, M.; González-Pachón, J. Representative Group Decision-Making in Forest Management: A Compromise Approach. *Forests* **2022**, *13*, 606.
https://doi.org/10.3390/f13040606

**AMA Style**

Ortiz-Urbina E, Diaz-Balteiro L, Pardos M, González-Pachón J. Representative Group Decision-Making in Forest Management: A Compromise Approach. *Forests*. 2022; 13(4):606.
https://doi.org/10.3390/f13040606

**Chicago/Turabian Style**

Ortiz-Urbina, Esther, Luis Diaz-Balteiro, Marta Pardos, and Jacinto González-Pachón. 2022. "Representative Group Decision-Making in Forest Management: A Compromise Approach" *Forests* 13, no. 4: 606.
https://doi.org/10.3390/f13040606