HELP: aggregating insert rule for multirow inserts.

I'm having a problem with the use of the NEW rowset,
in a rule intended to aggregate across inserts.

I've never really grokked how NEW and OLD really work,
syntactically, other than that they seem to be implicit
in every top-level FROM clause, and any mention elsewhere
gets an error: '42P01: relation "*NEW*" does not exist'.

I've tried different flavours of the UPDATE command,
in the following rule, and they either produce syntax errors
or the wrong results.

Any suggestions much appreciated ...

====================== CODE
"How many critters are in the zoo, of the 4,5,6...-legged varieties?"

create table critter(name text, legs int);
create table zoostats(legs int, headcount int default 0,
primary key(legs));

create or replace rule critter_counter as
on INSERT to critter do (

insert into zoostats
select distinct new.legs
where new.legs not in (select legs from zoostats);

update zoostats
set headcount = headcount + (select count(*)) -- "from new"
where new.legs = zoostats.legs
);

insert into critter values('cat',4);
insert into critter values('starfish',5);
insert into critter values('ant',6);
insert into critter values('dog',4);

insert into critter select * from critter; -- double everything.

select * from zoostats;

drop table zoostats cascade;
drop table critter;
====================== EXPECTED OUTPUT
legs headcount
---- ---------
4 4
5 2
6 2
====================== ACTUAL OUTPUT
legs headcount
---- ---------
4 3 -- !?
5 2
6 2
====================== OTHER ATTEMPT:
This version of the update looks syntactically right to me,
but makes CREATE RULE fail on a syntax error:

...

update zoostats
set headcount = headcount + tally
from (select new.legs, count(new.legs) as tally -- from new !?
group by new.legs) as poll
where poll.legs = zoostats.legs;

ERROR: 'Subquery in FROM may not refer to other relations
of same query level'.
--
Engineers think equations approximate reality.
Physicists think reality approximates the equations.
Mathematicians never make the connection.