user19880: In the Magnus Carlsen Invitational 2020, Magnus Carlsen invited 7 of the world’s best players to compete with him in the first professional online chess tournament. However, I wasn’t able to find an explanation of why Magnus selected these particular players.
My initial thought was that he would more-or-less invite players from the 2020 Candidates Tournment. However, Wang Hao and Alexander Grischuk, who qualified for the Candidates Tournament, did not participate in the Magnus Carlsen Invitational. Alireza Firouzja, who was invited to the Magnus Carlsen Invitational, did not play in the Candidates Tournament.
My second thought was that Magnus would choose the top-rated players. This turned out not to be true, since, in April 2020, Alexander Grischuk, who was not invited, was #6 while Anish Giri, who was invited, was #10.
My final thought was that perhaps Carlsen just invited his friends. But this doesn’t seem to be the case, since, e.g., there seems to have been some friction between Carlsen and Giri.
On what basis did Carlsen invite players to this tournament?

user11749: Tania Sachdev asked Carlsen about his exact involvement in his eponymous tournament here around 4:41:40. Carlsen responded that he was involved 

in the format, and especially the 4 games format, and 
in the choice of the players. He added with a big smile "otherwise Anish [Giri] would have not been part of the tournament"! 

Chess24 and PlayMagnus were also in charge.

user8472: Magnus Carlsen had the major saying in the selection. There was no "objective" qualification of any kind, besides the hope to create an interesting line-up.
Firouzja was included because he beat Carlsen in the Banter Blitz Cup, so a "rematch" would attract many viewers.
Disclosure: I work for chess24. I wasn't involved in the decision process, and I can't publish everything I know about this.

19880: <p>In the <a href="https://www.magnuscarlsen.com/en/invitational" rel="nofollow noreferrer">Magnus Carlsen Invitational 2020</a>, Magnus Carlsen invited 7 of the world’s best players to compete with him in the first professional online chess tournament. However, I wasn’t able to find an explanation of why Magnus selected these particular players.</p>
<p>My initial thought was that he would more-or-less invite players from the <a href="https://en.wikipedia.org/wiki/Candidates_Tournament_2020" rel="nofollow noreferrer">2020 Candidates Tournment</a>. However, Wang Hao and Alexander Grischuk, who qualified for the Candidates Tournament, did not participate in the Magnus Carlsen Invitational. Alireza Firouzja, who was invited to the Magnus Carlsen Invitational, did not play in the Candidates Tournament.</p>
<p>My second thought was that Magnus would choose the top-rated players. This turned out not to be true, since, in April 2020, Alexander Grischuk, who was not invited, was #6 while Anish Giri, who was invited, was #10.</p>
<p>My final thought was that perhaps Carlsen just invited his friends. But this doesn’t seem to be the case, since, e.g., there seems to have been <a href="https://en.chessbase.com/post/the-twitter-war-between-magnus-carlsen-and-anish-giri" rel="nofollow noreferrer">some friction between Carlsen and Giri</a>.</p>
<p>On what basis did Carlsen invite players to this tournament?</p>
 11749: <p>Tania Sachdev asked Carlsen about his exact involvement in his eponymous tournament <a href="https://www.youtube.com/watch?v=a0A1XRRJNy0" rel="nofollow noreferrer">here</a> around 4:41:40. Carlsen responded that he was involved </p>

<ul>
<li>in the format, and especially the 4 games format, and </li>
<li>in the <strong>choice of the players</strong>. He added with a big smile "otherwise Anish [Giri] would have not been part of the tournament"! </li>
</ul>

<p>Chess24 and PlayMagnus were also in charge.</p>
 8472: <p>Magnus Carlsen had the major saying in the selection. There was no "objective" qualification of any kind, besides the hope to create an interesting line-up.</p>

<p>Firouzja was included because he <a href="https://chess24.com/en/read/news/firouzja-beats-carlsen-to-win-the-banter-blitz-cup" rel="noreferrer">beat Carlsen in the Banter Blitz Cup</a>, so a "rematch" would attract many viewers.</p>

<p>Disclosure: I work for chess24. I wasn't involved in the decision process, and I can't publish everything I know about this.</p>
