  Decentralization has been widely acknowledged as a core virtue of
blockchains. However, in the past, there have been few measurement studies on
measuring and comparing the actual level of decentralization between existing
blockchains using multiple metrics and granularities. This paper presents a new
comparison study of the degree of decentralization in Bitcoin and Ethereum, the
two most prominent blockchains, with various decentralization metrics and
different granularities within the time dimension. Specifically, we measure the
degree of decentralization in the two blockchains during 2019 by computing the
distribution of mining power with three metrics (Gini coefficient, Shannon
entropy, and Nakamoto coefficient) as well as three granularities (days, weeks,
and months). Our measurement results with different metrics and granularities
reveal the same trend that, compared with each other, the degree of
decentralization in Bitcoin is higher, while the degree of decentralization in
Ethereum is more stable. To obtain the cross-interval information missed in the
fixed window based measurements, we propose the sliding window based
measurement approach. The corresponding results demonstrate that the use of
sliding windows could reveal additional cross-interval information overlooked
by the fixed window based measurements, thus enhancing the effectiveness of
measuring decentralization in terms of continuous trends and abnormal
situations. We believe that the methodologies and findings in this paper can
facilitate future studies of decentralization in blockchains.
