Page 97 - Kỷ yếu hội thảo khoa học lần thứ 12 - Công nghệ thông tin và Ứng dụng trong các lĩnh vực (CITA 2023)

Thanh Trung Nguyen, Hai Bang Truong 81

It is also represented as:

(5)

For any grouped data, GM can be written as

(6)

Definition 3. Let x1 n R be a sample of estimates. The collective decision
colD(x) is the aggregation of these estimates by an aggregation function, which is a
statistical estimator of the true value [7].

(7)

For estimating a continuous value, the cost function is defined as a function of the
difference of the collective decision colD(x) and the true value [7].

(8)

Definition 4. The phenomenon of crowd wisdom can be conceptualized by the diver-
sity prediction theorem as follows [7].

(9)

Where 2 is the collective error,

is the mean squared error

and is the variance.

4 Aggregation methods

In this section, we briefly provide an overview of the aggregation methods utilized in
previous studies on the wisdom of crowds. There are various methods used for
aggregating judgments from multiple individuals, which include the arithmetic
average, geometric average, weighted average, median and mode average.

4.1 Arithmetic average

The fundamental approach was initially introduced by Francis Galton [8], who was
the first to describe the Wisdom of the Crowd from a scientific perspective. If the
decision-maker has limited knowledge about the domain, utilizing this basic average
is a practical and reasonable approach. Implementing the arithmetic average assumes
that all members of the crowd are assigned equal importance. Therefore, it appears
that this average method has become a common aggregation method in various
research studies [9], [10], [11], [12]. In addition, several studies have used arithmetic
average as a standard for comparation with other methods of aggregation [13], [9],

ISBN: 978-604-80-8083-9 CITA 2023