Measuring Consensus: Concepts, Comparisons, and Properties

Alcalde–Unzu, Jorge; Vorsatz, Marc

doi:10.1007/978-3-642-20533-0_12

Cited by 13 publications

(15 citation statements)

References 12 publications

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“…multiplying the inputs by a scalar λ > 0 increases/decreases the output by the same factor, OWA(λ · x) = λ · OWA(x). It is also shift-invariant meaning that adding the same value λ to each input increases the output by λ, OWA(x (1)…”

Section: Special Cases Of the Owa Operator Depending On The Weightinmentioning

confidence: 99%

“…If δ is positive then the equation will be satisfied, so we need not be concerned with g being infinite at g (1). On the other hand, if g(q i ) is below the mean of the remaining transformed values then δ will be negative and we hence require,…”

Section: Penalties Based On Generalized Owa Operatorsmentioning

confidence: 99%

“…Gagolewski has recently proposed the concept of spread measures 25 , which incorporates traditional measures of variation as special cases. Parallels have also been drawn between spread and the notion of disagreement (or lack of consensus) in decision making 1,5,6,14,28,31,32 and with evenness indices used in ecology 8,9 . In turn, we can observe that, historically, many traditional evenness measures were derived from inequality indices 43,44 , since the desireable property that evenness is increased with transfers of abundance from rare to more common species is one that is satisfied by the Pigou-Dalton principle proposed by Dalton 19 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Penalty-Based and Other Representations of Economic Inequality

Beliakov

Gągolewski

Liu

2016

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Economic inequality measures are employed as a key component in various sociodemographic indices to capture the disparity between the wealthy and poor. Since their inception, they have also been used as a basis for modelling spread and disparity in other contexts. While recent research has identified that a number of classical inequality and welfare functions can be considered in the framework of OWA operators, here we propose a framework of penalty-based aggregation functions and their associated penalties as measures of inequality. Please cite this paper as:

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Section: Special Cases Of the Owa Operator Depending On The Weightinmentioning

confidence: 99%

Section: Penalties Based On Generalized Owa Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Penalty-Based and Other Representations of Economic Inequality

Beliakov

Gągolewski

Liu

2016

Int. J. Unc. Fuzz. Knowl. Based Syst.

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show abstract

“…This measure determines, for any pair of alternatives, the absolute value of the difference between the ratio of persons who choose one alternative and the proportion of individuals who choose the other option and then takes the average of these numbers over all possible pairs of alternatives [18]. The concepts, comparisons, and properties of these two measures are well introduced in [19].…”

Section: Introductionmentioning

confidence: 99%

Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n

Rahem

Darrah

2018

International Journal of Mathematics and Mathematical Sciences

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There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in -dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs.

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“…In the related literature, Kendall and Gibbons [10] considered measuring concordance among only two linear orders. Then, Hays [11] and Alcalde-Unzu and Vorsatz [12] generalized the idea to any number of linear orders. Similarly, Bosch [13] proposed a measure of consensus for any given profile of linear orders by a mapping which assigns a number between 0 and 1 according to the degree of homogeneity in that profile.…”

Section: Introductionmentioning

confidence: 99%

Measuring consensus in a preference-approval context

et al. 2014

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We consider measuring the degree of homogeneity for preference-approval profiles which include the approval information for the alternatives as well as the rankings of them. A distance-based approach is followed to measure the disagreement for any given two preference-approvals. Under the condition that a proper metric is used, we propose a measure of consensus which is robust to some extensions of the ordinal framework. This paper also shows that there exists a limit for increasing the homogeneity level in a group of individuals by simply replicating their preferenceapprovals.

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Measuring Consensus: Concepts, Comparisons, and Properties

Cited by 13 publications

References 12 publications

Penalty-Based and Other Representations of Economic Inequality

Penalty-Based and Other Representations of Economic Inequality

Using a Computational Approach for Generalizing a Consensus Measure to Likert Scales of Any Size n

Measuring consensus in a preference-approval context

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