Why miner does less incentive to include SegWit transactions?


I have read from several articles that miners seem not favour SegWit transaction because they earn less fee from it:

[https://bitcoinmagazine.com/articles/are-bitcoin-miners-making-more-money-small-blocks/](https://bitcoinmagazine.com/articles/are-bitcoin-miners-making-more-money-small-blocks/)

[https://bitcoinist.com/bitmains-policy-questioned-as-antpool-stops-mining-segwit-blocks/](https://bitcoinist.com/bitmains-policy-questioned-as-antpool-stops-mining-segwit-blocks/)

[https://www.coindesk.com/one-year-later-whats-holding-back-segwit-adoption-on-bitcoin](https://www.coindesk.com/one-year-later-whats-holding-back-segwit-adoption-on-bitcoin)

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But among these articles they do not explain what is the reason behind. If people are willing to pay the same level of satoshi/byte fee, isn’t that miner will earn the same fee with the 1MB (4MB weight) block no matter it is SegWit or not?

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Thanks

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