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Extended Gini Index

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 Added by Ram Sewak Dubey
 Publication date 2020
  fields Economy
and research's language is English




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We propose an extended version of Gini index defined on the set of infinite utility streams, $X=Y^mathbb{N}$ where $Ysubset mathbb{R}$. For $Y$ containing at most finitely many elements, the index satisfies the generalized Pigou-Dalton transfer principles in addition to the anonymity axiom.



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As a fundraising method, Initial Coin Offering (ICO) has raised billions of dollars for thousands of startups in the past two years. Existing ICO mechanisms place more emphasis on the short-term benefits of maximal fundraising while ignoring the problem of unbalanced token allocation, which negatively impacts subsequent fundraising and has bad effects on introducing new investors and resources. We propose a new ICO mechanism which uses the concept of Gini index for the very first time as a mechanism design constraint to control allocation inequality. Our mechanism maintains an elegant and straightforward structure. It allows the agents to modify their bids as a price discovery process, while limiting the bids of whales. We analyze the agents equilibrium behaviors under our mechanism. Under natural technical assumptions, we show that most agents have simple dominant strategies and the equilibrium revenue approaches the optimal revenue asymptotically in the number of agents. We verify our mechanism using real ICO dataset we collected, and confirm that our mechanism performs well in terms of both allocation fairness and revenue.
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A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation matrix, that relies on city-block distances, is robust to outliers. Monte Carlo simulations and an application on cars data (with outliers) show the robustness of the Gini PCA and provide different interpretations of the results compared with the variance PCA.
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