76 lines
2.5 KiB
Python
76 lines
2.5 KiB
Python
# Copyright (c) 2020, salesforce.com, inc.
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# All rights reserved.
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# SPDX-License-Identifier: BSD-3-Clause
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# For full license text, see the LICENSE file in the repo root
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# or https://opensource.org/licenses/BSD-3-Clause
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import numpy as np
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def get_gini(endowments):
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"""Returns the normalized Gini index describing the distribution of endowments.
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https://en.wikipedia.org/wiki/Gini_coefficient
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Args:
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endowments (ndarray): The array of endowments for each of the agents in the
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simulated economy.
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Returns:
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Normalized Gini index for the distribution of endowments (float). A value of 1
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indicates everything belongs to 1 agent (perfect inequality), whereas a
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value of 0 indicates all agents have equal endowments (perfect equality).
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Note:
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Uses a slightly different method depending on the number of agents. For fewer
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agents (<30), uses an exact but slow method. Switches to using a much faster
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method for more agents, where both methods produce approximately equivalent
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results.
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"""
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n_agents = len(endowments)
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if n_agents < 30: # Slower. Accurate for all n.
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diff_ij = np.abs(
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endowments.reshape((n_agents, 1)) - endowments.reshape((1, n_agents))
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)
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diff = np.sum(diff_ij)
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norm = 2 * n_agents * endowments.sum(axis=0)
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unscaled_gini = diff / (norm + 1e-10)
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gini = unscaled_gini / ((n_agents - 1) / n_agents)
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return gini
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# Much faster. Slightly overestimated for low n.
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s_endows = np.sort(endowments)
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return 1 - (2 / (n_agents + 1)) * np.sum(
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np.cumsum(s_endows) / (np.sum(s_endows) + 1e-10)
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)
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def get_equality(endowments):
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"""Returns the complement of the normalized Gini index (equality = 1 - Gini).
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Args:
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endowments (ndarray): The array of endowments for each of the agents in the
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simulated economy.
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Returns:
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Normalized equality index for the distribution of endowments (float). A value
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of 0 indicates everything belongs to 1 agent (perfect inequality),
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whereas a value of 1 indicates all agents have equal endowments (perfect
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equality).
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"""
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return 1 - get_gini(endowments)
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def get_productivity(coin_endowments):
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"""Returns the total coin inside the simulated economy.
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Args:
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coin_endowments (ndarray): The array of coin endowments for each of the
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agents in the simulated economy.
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Returns:
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Total coin endowment (float).
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"""
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return np.sum(coin_endowments)
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