Postgres 9.6

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create table meetings (id serial, subject varchar);
insert into meetings (subject) values ('Kickoff'),('Relaunch'),('Party');
-- select * from meetings;

create table persons (id serial, name varchar);
insert into persons (name) values ('John'),('Anna'),('Linda');
-- select * from persons;

create table hobbies (id serial, name varchar);
insert into hobbies (name) values ('Soccer'),('Tennis'),('Swimming');
-- select * from hobbies;

create table meeting_person (id serial, meeting_id int, person_id int);
insert into meeting_person (meeting_id, person_id) 
values (1,1),(1,2),(1,3),(2,1),(2,2),(3,1);
-- select * from meeting_person;

create table person_hobby (id serial, person_id int, hobby_id int);
insert into person_hobby (person_id, hobby_id) 
values (1,1),(1,2),(1,3),(2,1),(2,2),(3,1);
-- select * from person_hobby;

/*
    select p.id, p.name, array_agg(h.name) hobby
    from person_hobby ph
    join persons p on ph.person_id = p.id
    join hobbies h on h.id = ph.hobby_id
    group by p.id, p.name
    ;
*/

create or replace function array_intersect(anyarray, anyarray)
returns anyarray language sql
as $$
    select 
        case 
            when $1 is null then $2
            when $2 is null then $1
            else
                array(
                    select unnest($1)
                    intersect
                    select unnest($2))
        end;
$$;

create aggregate array_intersect_agg (anyarray)
(
    sfunc = array_intersect,
    stype = anyarray
);

select 
    meeting_id, 
    array_agg(ph.name) persons, 
    array_intersect_agg(hobby) common_hobbies
from meeting_person mp
join (
    select p.id, p.name, array_agg(h.name) hobby
    from person_hobby ph
    join persons p on ph.person_id = p.id
    join hobbies h on h.id = ph.hobby_id
    group by p.id, p.name
) ph on ph.id = mp.person_id
group by meeting_id;

3 rows affected

3 rows affected

3 rows affected

6 rows affected

6 rows affected

meeting_id	persons	common_hobbies
1	{John,Anna,Linda}	{Soccer}
3	{John}	{Soccer,Tennis,Swimming}
2	{John,Anna}	{Soccer,Tennis}