22
33The metrics that have been implemented so far are the following:
44
5- 1 . ** Nakamoto coefficient** : The Nakamoto coefficient represents the minimum number of entities that
6- collectively produce more than 50% of the total blocks within a given timeframe. The output of the metric is an
7- integer.
8- 2 . ** Gini coefficient** : The Gini coefficient represents the degree of inequality in block production. The
5+ 1 . ** Nakamoto coefficient** : The Nakamoto coefficient represents the minimum number of entities that collectively control
6+ more than 50% of all tokens in circulation at a given point in time. The output of the metric is an integer.
7+ 2 . ** Gini coefficient** : The Gini coefficient represents the degree of inequality in token ownership. The
98 output of the metric is a decimal number in [ 0,1] . Values close to 0 indicate equality (all entities in
10- the system produce the same number of blocks ) and values close to 1 indicate inequality (one entity
11- produces most or all blocks ).
12- 3 . ** Entropy** : Shannon entropy represents the expected amount of information in the distribution of blocks across entities.
9+ the system control the same amount of assets ) and values close to 1 indicate inequality (one entity
10+ holds most or all tokens ).
11+ 3 . ** Entropy** : Shannon entropy represents the expected amount of information in the distribution of tokens across entities.
1312 The output of the metric is a real number. Typically, a higher value of entropy indicates higher decentralization
1413 (lower predictability).
15144 . ** HHI** : The Herfindahl-Hirschman Index (HHI) is a measure of market concentration. It is defined as the sum of the
1615 squares of the market shares (as whole numbers, e.g. 40 for 40%) of the entities in the system. The output of the
17- metric is a real number in (0, 10000] . Values close to 0 indicate low concentration (many entities produce a similar
18- number of blocks ) and values close to 1 indicate high concentration (one entity produces most or all blocks ).
16+ metric is a real number in (0, 10000] . Values close to 0 indicate low concentration (many entities hold a similar
17+ number of tokens ) and values close to 10000 indicate high concentration (one entity controls most or all tokens ).
1918 The U.S. Department of Justice has set the following thresholds for interpreting HHI values (in traditional markets):
2019 - (0, 1500): Competitive market
2120 - [ 1500, 2500] : Moderately concentrated market
@@ -24,9 +23,9 @@ The metrics that have been implemented so far are the following:
2423 or the redundancy, in a population. In practice, it is calculated as the maximum possible entropy minus the observed
2524 entropy. The output is a real number. Values close to 0 indicate equality and values towards infinity indicate
2625 inequality. Therefore, a high Theil Index suggests a population that is highly centralized.
27- 6 . ** Max power ratio** : The max power ratio represents the share of blocks that are produced by the most "powerful"
28- entity, i.e. the entity that produces the most blocks . The output of the metric is a decimal number in [ 0,1] .
26+ 6 . ** Max power ratio** : The max power ratio represents the share of tokens that are owned by the most "powerful"
27+ entity, i.e. the wealthiest entity . The output of the metric is a decimal number in [ 0,1] .
29287 . ** Tau-decentralization index** : The tau-decentralization index is a generalization of the Nakamoto coefficient.
30- It is defined as the minimum number of entities that collectively produce more than a given threshold of the total
31- blocks within a given timeframe . The threshold parameter is a decimal in [ 0, 1] (0.66 by default) and the output of
29+ It is defined as the minimum number of entities that collectively control more than a given threshold of the total
30+ tokens in circulation . The threshold parameter is a decimal in [ 0, 1] (0.66 by default) and the output of
3231 the metric is an integer.
0 commit comments