Serializable Isolation Level Confusion - Write Skew (Postgres) - database

Question

I'm running Postgres12 and confused about the behavior of the serializable transaction level.
Tables:
Events
id
difficulty
Managers
id
level
Intended behavior (within serialized transaction):
check if there are 7 or more events of difficulty=2
if so, insert a manager with level=2
I'm running the following transactions in serializable but not seeing the behavior I am expected (expected the serializable transaction to detect write skew between 2 sessions)
-- session 1:
BEGIN TRANSACTION ISOLATION LEVEL SERIALIZABLE
SELECT count(*) from events WHERE difficulty=2
-- RETURNS 7
-- now start session 2
-- session 2:
BEGIN TRANSACTION ISOLATION LEVEL SERIALIZABLE
SELECT id FROM events WHERE difficulty=2 LIMIT 1;
/*
id
----
4
*/
UPDATE events SET difficulty=1 WHERE id=4;
COMMIT;
now there are only 6 events of difficulty=2
-- back in session 1
-- since we have counted 7 events of difficulty=2 in this session, create a manager
INSERT INTO manager (level) VALUES (2);
COMMIT;
-- Expected write skew to be detected here bc the read event rows have seen updates (only 6 actually)
Unfortunately, our final state is now 6 events of difficulty=2 and a manager of level 2.
Why didn't serializable isolation prevent this write skew?
What am I misunderstanding about serializable isolation use case? Why are events with difficulty=2 not locked or watched by predicate locking or some isolation mechanism?
Picture for clarity

Answer 1

SERIALIZABLE means that there is a way to execute the transactions serially (one after the other) so that the effect is the same. In your case, this equivalent serial execution would run session 1 first, then session 2, with the same effect.
You could say that session 1 executes "logically" before session 2.

Answer 2

Answering my own question after some thinking!
The serialization check is not preventing the two sessions from committing because it is possible to serialize the two transactions and still end up with a level 2 manager and 6 events of difficulty=2.
E.g.
Run session 1 (check if 7 events with difficulty=2, create manager level=2) COMMIT;
Run session 2 (remove one event, now 6 events with difficulty=2) COMMIT;
^Output = 6 events, 1 manager
This is the same result as running concurrently so this is deemed an "acceptable" state for these two serializable transactions.
if you want to prevent this behaviour, session 2 can be updated to the following
begin transaction isolation level serializable;
select count(*) from manager where level=2;
--if no managers
update events set difficulty=1 where id=4;
Now there is no logical way to end up with the state 6 events 1 manager with a serialized ordering. The two possible outcomes from a sequential ordering are
session 1 runs
session 2 runs
^output = 7 events 1 managers
session 2 runs
session 1 runs
^output = 6 events 0 managers
So in this case (with the updated session 2), one of your transactions would be blocked because the transactions are no longer serializable.

Answer 3

Write skew doesn't occur in SERIALIZABLE in PostgreSQL:
Isolation Level
Write Skew
READ UNCOMMITTED
Yes
READ COMMITTED
Yes
REPEATABLE READ
Yes
SERIALIZABLE
No
I experimented if write skew occurs in SERIALIZABLE in PostgreSQL. There is event table with name and user as shown below.
event table:
name
user
Make Sushi
John
Make Sushi
Tom
Then, I took these steps below for the experiment of write skew. *Only 3 users can join the event "Make Sushi":
Flow
Transaction (T1)
Transaction (T2)
Explanation
Step 1
BEGIN;
T1 starts.
Step 2
BEGIN;
T2 starts.
Step 3
SELECT count(*) FROM event WHERE name = 'Make Sushi';2
T1 reads 2 so only one user can join it.
Step 4
SELECT count(*) FROM event WHERE name = 'Make Sushi';2
T2 reads 2 so only one user can join it.
Step 5
INSERT INTO event values ('Make Sushi', 'Lisa');
T1 inserts Lisa to event table.
Step 6
COMMIT;
T1 commits.
Step 7
INSERT INTO event values ('Make Sushi', 'Kai');ERROR: could not serialize access due to read/write dependencies among transactions
T2 cannot insert Kai to event table and gets error.
Step 8
COMMIT;
T2 rollbacks with COMMIT query.*Write skew doesn't occur.