# Back-to-Basics: Group Decision Making

Supporting collective decisions made by groups of experts or stakeholders with their own different opinions, and supporting recommendations for groups of users that satisfy them all, constitute some of the fundamental research interests in our team. But, what are the principles and basic ideas underlying Group Decision Making?

In this post, we attempt to answer this question by introducing a brief introduction to the topic. The following content extends my originally written overview in the AFRYCA website back in 2014, whose software suite I founded as part of my PhD thesis:

A Group Decision Making (GDM) problem is a decision situation where:

• There exists a group m of individuals or experts, E = {e1, … ,em}, who each have their own attitudes and knowledge. Consider for example E={Binyamin, Ercan, Hugo, Ivan, James} as a group of five experts. Intuitively, m should be equal or higher than 2, since a group should have at least two members 🙂
• There is a decision problem consisting of n alternatives or possible solutions to the problem, X = {x1, … ,xn} (again, at least two). Say, for instance, that our five friends in group E want to choose a destination for a research group away day, among four possible options in England: X = {Costwolds, Cambridge, Oxford, Cheddar*}.
##### (*Note: Cheddar is a beautiful place in southwest England, not necessarily the cheese!)
• The experts try to achieve a common solution, i.e. a final decision on selecting one of the four possible destinations.

Each expert ei , with i=1,…m, expresses his/her opinions or preferences over the alternatives in X, in other words, they provide judgment information indicating to what extent they support – or don’t support – each of the available options.  For this, each participant supplies a preference structure. Some examples of preference structures widely used in scientific literature related to GDM, are:

• Preference orderings: A ranking established by each individual, establishing their ordering of alternatives from the most to the least preferred one. For instance, Ivan may provide the following preference ordering according to which Oxford is his most preferred place and Cheddar is his least preferred one. (Please note, this is merely and example and Ivan absolutely likes all four destinations! 😉 ):

Oxford > Costwolds > Cambridge > Cheddar

• Utility vectors: Despite being the most intuitive preference format to be provided by humans, preference ordering are also the least informative ones: they allow to express that Cambridge is preferred over Cheddar, but they do not allow to indicate how strongly Cambridge is preferred over Cheddar (a lot more? just slightly?). A suitable structure to indicate degrees of preference or likeness on each alternative are preference vectors. The following example shows a preference vector over X = {Costwolds, Cambridge, Oxford, Cheddar} with assessments in the [0,1], such that the higher the value of the assessment, the more preferred the alternative is. In this case, the fourth alternative in X (Cheddar) is the most preferred one, whereas the second alternative (Cambridge) is the least preferred one:

[0.6   0.4   0.7    0.8]

• Fuzzy preference relations: Represented as an nxn square matrix, where each element located at the row and column k  – excluding those in the main diagonal of the matrix – is called assessment and represents the degree to which the lth alternative is preferred against the the kth alternative in X. Assessments therefore describe “pairwise” comparative judgments among alternatives. For instance, assuming we use the [0,1] interval to assess pairs of alternatives, an intermediate value of 0.5 indicates indifference between two alternatives (see 0.5 for indifference between Costwolds and Cheddar), a value higher than 0.5 indicates preference towards the first alternative in the pair (see 0.8 for strong preference on Cambridge with respect to Oxford) and, conversely, a value lower than 0.5 indicates that the first alternative in the pair is less preferred than the second one (see 0.4 for weak preference against Cheddar with respect to Cambridge).
 Cost. Camb. Oxf. Ched. Cost. – 0.4 0.6 0.5 Camb. 0.6 – 0.8 0.6 Oxf. 0.4 0.2 – 0.4 Ched. 0.5 0.4 0.6 –

• Decision matrices: In some GDM problems, each alternative needs to be assessed in terms of multiple criteria, C = {c1, … ,cq}. Consider for instance the following scenario in medical treatment decision-making:
##### A group of clinicians with expertise in making treatment decisions for patients with complex health needs, need to prioritise possible treatment options (alternatives) for patients with multiple diagnosis, symptoms and risk factors, by evaluating each treatment in terms of safety, cost and efficiency level (criteria). (Acknowledgements: Dr Rachel Denholm, Population Health Sciences, University of Bristol Medical School)

In these contexts, we would define the decision framework as a Multi-Criteria Group Decision Making problem, in which case decision matrices would be the best approach to express preferential of judgement information by participating experts. Each element in a decision matrix is an assessment on a specific alternative (row) in terms of a specific criterion (column). For instance, the following decision matrix indicating that Treatment 3 is the safest but least efficient one:

 Safety Cost Efficiency Treat1 0.7 0.4 0.5 Treat2 0.6 0.5 0.9 Treat3 0.9 0.4 0.2 Treat4 0.5 0.6 0.5

GDM problems are usually defined in environments of uncertainty, in which the information regarding the problem is vague and imprecise. These situations are also known as GDM problems under fuzzy contexts. Some information domains for expressing preferences, that have been frequently utilized by experts to deal with uncertainty, are: numerical, interval-valued or linguistic information. This post has shown examples of preference modelling with numerical information between 0 and 1, but other approaches exist to allow participants to assess decision information both quantitatively and qualitatively.

The solution for a GDM problem has been classically determined by applying an alternative selection process, which is composted of two phases:

1. Aggregation phase: Experts’ preferences are combined at assessment level, by using an aggregation operator. How to aggregate individual opinions into a representative opinion, constitutes a key and very widely investigated question across the decision making and information fusion research communities.
2. Exploitation phase: Once a group preference has been obtained, an alternative or subset of alternatives is obtained as the solution for the GDM problem, by applying a selection criterion (e.g. dominance or non-dominance degrees).

Interested in delving deeper into Group Decision Making and its extended lines of research (consensus building, large-group decision making)? Then we suggest you taking a look at the newly published book Large Group Decision Making: Creating Decision Support Approaches at Scale, which includes a detailed overview on Group Decision Making and Consensus Decision Making in Chapter 2!