Mathematicians are developing a new decision-making algorithm

A research team from RUDN University has developed an algorithm that will help large groups make optimal decisions as soon as possible. They confirmed the effectiveness of their models using the market model in which COVID-19 was launched. The model helped management and retailers agree to close the market and agree on the amount of compensation in just three steps. Credit: RUDN University

A research team from RUDN University has developed an algorithm that will help large groups make optimal decisions as soon as possible. The effectiveness of the model was confirmed using the market example in which the start-up took place COVID-19 started. The model helped management and retailers agree to close the market and agree on the amount of compensation in just three steps. An article about the algorithm Information sciences Journal.

Decision theory is a field of mathematics that studies the laws of decision making and strategy selection. Mathematical decision-making is a multi-criteria optimization task. Expert opinions, judgments, and possible risks are considered variable, and the relationships between participants and the search for optimal solutions are expressed as mathematical operations. LSGDM is a model in decision theory that describes decision-making situations with participants at more than 20 expert levels. Their opinions are influenced by personal relationships: for example, friends support each other’s opinions. This increases the level of uncertainty as it becomes more difficult to convince participants and reach an agreement. A research team of mathematicians from RUDN University proposed a method to overcome this uncertainty.

“Thanks to today’s technological advances, more and more people are participating in decision-making processes. Therefore, LSGDM has become a topical issue for researchers. At LSGDM, participants represent different areas of interest and therefore take longer to come to an agreement. The process requires a moderator who is able to convince all parties to settle their views, ”he said. Prof. Leader of the research team at RUDN University. Enrique Herrera-Viedma.

The solution proposed by a group of mathematicians is based on the so-called robust optimization technique. Applies to optimization tasks that are sensitive to changes in initial data (in this case in personal relationships between participants). Mathematicians have proposed a new way to divide experts into groups according to the strength of the relationship and the level of trust between them. The algorithm consisted of several steps. First, experts were grouped; then the team identified a group with the most different opinions by collective decision; and after that such an idea was corrected. The repetitions were repeated until all participants agreed on a solution. Opinion correction methods were mathematically insignificant. The only factor that was important was the single negotiation costs: the resources (time, money, etc.) that had to be spent to achieve the desired result.

The research team applied the model to a real-life example. After the spread of COVID-19, a seafood market in Wuhan had to be closed. Management was looking for an optimal solution: it had to compensate the sellers for losses while within the market budget. The mathematicians selected 20 vendors who demanded different compensation to close their countertops: between 200 and 900 yuan. Participants shared similar ideas, the proximity of the stalls to each other, and so on. They were divided into four groups based on such factors. The algorithm proposed by the team allowed sellers and managers to come to an agreement in just three steps. The final compensation was only 880 yuan, and the cost of negotiations for market management was the lowest compared to other existing models.

Reference: “Large-scale group decision-making consensus on social media: a minimum cost model based on strong optimization” Yanling Lu, Yejun Hu, Enrique Herrera-Viedma and Yefan Han, 29 August 2020, Information sciences.
DOI: 10.1016 / j.ins.2020.08.022

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