[Paper Review] Generalized Linear Weights for Sharing Credits Among Multiple Authors

Ash Mohammad Abbas|arXiv (Cornell University)|Dec 25, 2010

scientometrics and bibliometrics research5 references6 citations

TL;DR

This paper proposes a generalized linear weight assignment scheme, called Arithmetic: Type-2, for distributing credit among multiple authors of a research paper. The scheme assigns weights in a linearly decreasing or increasing fashion based on author position and a tunable decrement/increment parameter α, with equal weighting and the prior Arithmetic: Type-1 scheme as special cases. The key contribution is a flexible, mathematically grounded framework that allows for controlled, position-based credit sharing across diverse academic fields.

ABSTRACT

Assignment of weights to multiple authors of a paper is a challenging task due to its dependence on the conventions that may be different among different fields of research and research groups. In this paper, we describe a scheme for assignment of weights to multiple authors of a paper. In our scheme, weights are assigned in a linearly decreasing/increasing fashion depending upon the weight decrement/increment parameter. We call our scheme Arithmetic: Type-2 scheme as the weights follow an arithmetic series. We analyze the proposed weight assignment scheme and compare it with the existing schemes such as equal, arithmetic, geometric, and harmonic. We argue that the a positional weight assignment scheme, called arithmetic scheme, which we refer to Arithmetic: Type-1 in this paper, and the equal weight assignment scheme can be treated as special cases of the proposed Arithmetic: Type-2 scheme.

Motivation & Objective

• To address the challenge of fairly distributing credit among multiple authors in multi-authored research papers.
• To develop a generalized weight assignment scheme that accommodates varying conventions across academic fields and research teams.
• To provide a mathematically sound and tunable method for assigning weights based on author position and contribution order.
• To demonstrate that existing schemes like equal, arithmetic (Type-1), geometric, and harmonic weighting can be seen as special cases of the proposed framework.
• To enable more accurate researcher evaluation by integrating weighted citations into academic indices.

Proposed method

• Proposes a linear weight assignment model where the weight of the jth author is defined as wj = w1 − (j−1)α, forming an arithmetic sequence.
• Derives closed-form expressions for the first and last author weights: w1 = 1/k + α(k−1)/2 and wk = 1/k − α(k−1)/2, ensuring total weight sums to 1.
• Introduces α as a tunable weight decrement/increment parameter (0 ≤ α ≤ 1) to control the rate of weight decay or growth across author positions.
• Establishes that the equal weight scheme (1/k for all) and the Arithmetic: Type-1 scheme (from prior work) are special cases of the proposed Type-2 scheme.
• Compares the proposed scheme with geometric and harmonic weighting schemes using analytical derivations and asymptotic approximations.
• Proposes integration into academic indices by multiplying paper citations by individual author weights before index computation.

Experimental results

Research questions

• RQ1 How can credit be fairly distributed among multiple authors when contributions vary by position?
• RQ2 Can a unified, generalized framework be developed that subsumes existing weighting schemes like equal, arithmetic, geometric, and harmonic?
• RQ3 What mathematical constraints ensure that the sum of assigned weights equals one while maintaining linear progression?
• RQ4 How does the proposed scheme’s flexibility—controlled by α—compare to non-tunable schemes like geometric or harmonic weighting?
• RQ5 To what extent can the proposed scheme be integrated into existing researcher evaluation indices without altering core indexing logic?

Key findings

• The proposed Arithmetic: Type-2 scheme generalizes both the equal weight assignment and the Arithmetic: Type-1 scheme as special cases, with α = 0 yielding equal weights and specific α values matching Type-1.
• The first author’s weight is w1 = 1/k + α(k−1)/2 and the last author’s weight is wk = 1/k − α(k−1)/2, derived from the constraint that the sum of all weights equals 1.
• The weight decrement parameter α allows fine-grained control over the rate of credit decay or increase across author positions, enabling gradual or steep shifts.
• Unlike geometric and harmonic schemes, the proposed linear scheme offers direct control over weight distribution via α, which is not available in nonlinear schemes.
• The harmonic weighting scheme assigns the first author’s weight as k times that of the last author, a ratio that is fixed and not adjustable, unlike the proposed scheme.
• The proposed scheme can be seamlessly integrated into existing citation-based indices by multiplying citations with author-specific weights before index computation.