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One of the major concepts of voting is alternative. There are numerous examples of alternatives e.g. several version of an immigration reform bill, electing the political party etc. In this paper, we are considering the survey result, which shows the preferences over different mobile service provider’s alternatives. Statistical data referred from TelecomLead choosing mobile service provider’s customer share playing a major role in Indian Telecommunication scenario.
Currently the Indian market is facing tough competition as per the Cellular Data Communication is concerned.
Earlier voice Communication also played a key role but with new spectrum allocation, voice communication has become insignificant and it is the data and value added services, which is playing a key role in the revenue generation of MSP’s. Rather than to focus on the statistical inference and penetrating to the parameters which leads to the statistical inference result we develop this problem into a social choice problem and apply voting rule to these data set which helps us to conclude some facts.
One of the major concept of voting is the alternative.
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Voting may take place in the following scenario as mentioned in [2].The scenarios may be (a) different amounts to spend on building and (b) several version of an immigration reform bill. While dealing with voting at first the paper come across May’s rule, which states, “only reasonable voting method is the majority rule”. However, it is not true always specially the case where multicandidate voting is to be taken into account.
Voting theory defines SCF (Social Computing Function) as “Each voter submits a linear ordering of the alternatives specifying first, second, third choice so there may be a winner or groups of winner as outcome”. However while dealing with voting rule, researchers often come across majority cycle proposed by Condorcet in 1785 which says that collective preference violates what might be expected from an individual.
Arrow’s theorem plays a crucial role in voting theory, which states that, the “relative merits should not be influenced by individual voter opinion about an irreverent third alternative”. According to him having three or more alternatives is a dictatorship. Gibbard Satherwise Theoram states, “Every election will have an individual winner. According to him SCF (f) sometimes helps an individual voter ith to get an incentive and manipulate the voting result.” This paper does not consider the above two conditions as an influencing parameter.
Voting generally takes place whenever a group of voters cast ballots that are used as a basis for collective decision reached through the application of a voting rule. This paper has taken the statistical data from TelecomLead a portal that has given the current data set depicting mobile operator’s customer share as on April 2018.
A profile P= (≥1, ≥2,………….≥n ) specifies such a ballot for each voter i ∈ N, L (A)n denotes the set of all such profiles for a given n. ) L (A) < ∞ stands for Un∈ N L (A) n (where N denotes the set of all natural numbers).
In[1] there are different parameters e.g. billing performance, help services, network connectivity and coverage, call drop, customer satisfaction is covered and they get an average of 77% CSI (customer satisfaction index). In [2] researchers did addresse voting as a social choice approach where different approaches like plurality, pairwise majority, Copeland, Borda rules are mentioned. Inspired from this the approach of preferences and alternatives implemented in this paper. In [3] we come to the idea that different mobile internet application can cause deterioration in mobile network performance. QoE is the concept proposed where QoE stands for Quality of Experience, and the paper proposes a framework describing the process of estimating or predicting perceived QoE based on datasets.
In[4] TRAI(Telecom Regulatory Authority of India) has released the latest report on mobile operators market share up to April 2018 which reveals Airtel has 27.44% share, Vodafone has 19.74% share and Reliance Jio has 17.44% share. In [5] authors mention that in the age of digital technology how Reliance is capturing the market through its bundled packages. With the aid of univariate and multivariate statistical analysis, the paper concludes that customers are satisfied with JIO service.
In [6] researchers did study an objective to understand the Indian consumer’s perception choice in selecting cellular mobile communication service provider. They carried out factor analysis based on the parameters like communication quality, call service, facilities, price, customer care and service provider’s alternatives. The conclusion is that product quality and availability has a significant impact on consumer’s perception choice in selecting cellular mobile service provider. In [7] we come to note that by 2020 mobile industry will have 82% contribution to India’s GDP. Total 810 million users will be using Smartphone by 2020. Net effective price will be less than $25 and data rate will be less than $1 per GB. All the above papers have influenced the current paper where voting rule indirectly signifies the customer satisfaction parameters.
As per the statistical data, this paper has taken into account the customer base of major three providers:
As per [4] 27.44 million users prefer Airtel to Vodafone & Reliance. 19.74 million prefer Vodafone over Bharti and Reliance. 17.44 million prefer Reliance Jio over Airtel and Vodafone. So from the definition mentioned in 1.2.1 (1) we have N= {27.44, 19.74, 17.44} and A= {Airtel, Vodafone, Reliance-Jio} which satisfies the condition m ≥ 2. So now, we can represent the tabular structure.
Table 1: Depicting the Statistical Data
| Alternatives | Voters | Preference Order |
|---|---|---|
| Airtel | 27.44 | 1. Airtel |
| 2. Vodafone | ||
| 3. Reliance | ||
| Vodafone | 19.74 | 1. Vodafone |
| 2. Airtel | ||
| 3. Reliance | ||
| Reliance | 17.44 | 1. Reliance |
| 2. Airtel | ||
| 3. Vodafone |
Plurality rule states that once the alternatives are arrange in descending order no. of votes that put the first alternative in first position depicts the Plurality Value. So from the above definition we can write mathematically P(x) = {n: n ∈ N that puts x ∈ A in the 1st position} (1)
So directly from Table-I and from equation (1 ) we get the values of
P={27.44,19.74,17.44} which indicates the fact that P(Airtel)= 27.44,
P(Vodafone)=19.74 and P(Reliance)= 17.44 the time complexity is simple as just we have to search the number of columns and index the first element.
Therefore, we get an order of O (n) complexity.
The pairwise majority rule basically depicts the pairwise difference between number of votes received by a compared to b and number of votes received by b compared to.
Mathematically this can be denoted by
Netp (a > b) = | {j ∈ N | a >j b}| − | {j ∈ N | b>j a}| (2)
So we get γ(Airtel>Vodafone)=44.88 and γ (Vodafone> Airtel)=19.74.
So Netp (Airtel > Vodafone) =[ γ(Airtel >Vodafone) - γ (Vodafone > Airtel)]=25.14,
where γ is the intermediate Pairwise majority calculation constant. In this way we can get Netp (Vodafone > Reliance) =29.74 and Netp (Airtel > Reliance) = 29.74.
So Netp {A>V, V>R, A> R} = {25.14, 29.74, 29.74}
Thus, it is seen that pairwise majority can only compare between the two or three but individual discrete alternative value cannot be calculated. The order of complexity is O (n2).
Copeland score calculation deals with a rule that voting rule will score candidates according to their win loss record in the pairwise majority case. Defining from above, we get Copeland(x) = |{y ∈ A | x >μ y}| − |{y ∈ A | y >µ x}| (3)
Where μ is the intermediate Copeland constant. For example when we calculate
Copeland Vodafone (Airtel) = µ (Airtel > Vodafone) – μ (Vodafone > Airtel)
= 2 -1 or 1
Indicating that in the table 1 comparing the number of columns we get Airtel is greater than Vodafone 2 times where as Vodafone is greater than Airtel 1 time.
Similarly, we can calculate the value of
Copeland Reliance (Airtel) = µ (Airtel > Reliance) - μ (Reliance> Airtel)
= 2 -1
= 1
Thus Copeland (Airtel) = {Copeland Vodafone (Airtel) + Copeland Reliance(Airtel)} = {2 }
Similarly we get the values of Copeland (Vodafone) = {0} and Copeland (Reliance)={-2}. So by set theory notation Copeland {Airtel, Vodafone, reliance} ={2,0,-2} which is the union of all the three individual Copeland values. This algorithm also has approximately O(n2) complexity.
This is an interesting calculation. In mathematics Bordapsym (x) i.e. symmetric Borda operation is defined as Bordapsym (x) = y∈A Σ Netp (x > y) (4)
The equation depicted in (4) clearly indicates that calculation methodology is same as that of Copeland. But there is a relationship that exists between Bordapsym (x) i.e. symmetric Borda calculation and Bordapsym (x) i.e. Asymmetric Borda calculation.
The relationship is as follows:
Bordapsym (x) = n + ½ Bordapsym (x) (5) where n is the total number of voters.
So from equation (5) we see that if we calculate Bordapsym (x) we can very easily get the values of Bordapsym (x). So while calculating the asymmetric Borda value weightage value, given to the alternatives, which is set in the descending order as, mentioned in
So from here we calculate the following asymmetric values.
Bordapasym (Airtel) = [2×27.44 + 1×19.74 + 1× 17.44] = 92.06
Bordapasym (Vodafone) = [1×27.44 + 2×19.74 + 0×17.44 ] = 66.92
Bordapasym (Reliance) = [0× 27.44 + 0×19.74 + 2×17.44] = 34.88
So thus we see that Bordapasym {Airtel, Vodafone, Reliance} = {92.06, 66.92, 34.88}.
This algorithm also has O(n) complexity.
The application of voting rules yielded the following insights:
These results reflect Airtel’s market leadership but also highlight the significant market penetration achieved by Reliance Jio.
Voting Rule Applied to Mobile Service Provider’s Survey. (2024, Feb 17). Retrieved from https://studymoose.com/document/voting-rule-applied-to-mobile-service-provider-s-survey
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