emacs - elegant way to count items

Question

I have a list shaped like this:

  '(("Alpha" .  1538)
    ("Beta"  .  8036)
    ("Gamma" .  8990)
    ("Beta"  .  10052)
    ("Alpha" .  12837)
    ("Beta"  .  13634)
    ("Beta"  .  14977)
    ("Beta"  .  15719)
    ("Alpha" .  17075)
    ("Rho"   .  18949)
    ("Gamma" .  21118)
    ("Gamma" .  26923)
    ("Alpha" .  31609))

How can I count the total number of occurrences of the terms in the car of each element in the list? Basically I want:

(("Alpha" . 4)
 ("Beta" . 5)
 ("Gamma" . 3)
 ("Rho" . 1))

No, this is not homework. I just don't have the "thinking in Lisp" thing quite yet.

In C#, I would use LINQ to do this. I can do it in lisp, too, using while loops and such but the way I am thinking of doing it seems overly complicated.

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EDIT

This is what I have:

(defun count-uniq (list)
  "Returns an alist, each item is a cons cell where the car is
a unique element of LIST, and the cdr is the number of occurrences of that
unique element in the list. "
  (flet ((helper (list new)
                 (if (null list)
                     new
                   (let ((elt (assoc (car list) new)))
                     (helper (cdr list)
                             (if elt
                                 (progn (incf (cdr elt)) new)
                               (cons (cons (car list) 1) new)))))))
    (nreverse (helper list nil))))

Answer 1

(defun freqs (list &optional test key)
  (let ((h (make-hash-table :test test)))
    (dolist (x list)
      (let ((key (if key (funcall key x) x)))
        (puthash key (1+ (gethash key h 0)) h)))
    (let ((r nil))
      (maphash #'(lambda (k v) (push (cons k v) r)) h)
      (sort r #'(lambda (x y) (< (cdr x) (cdr y)))))))

(freqs '(("Alpha" .  1538)
         ("Beta"  .  8036)
         ("Gamma" .  8990)
         ("Beta"  .  10052)
         ("Alpha" .  12837)
         ("Beta"  .  13634)
         ("Beta"  .  14977)
         ("Beta"  .  15719)
         ("Alpha" .  17075)
         ("Rho"   .  18949)
         ("Gamma" .  21118)
         ("Gamma" .  26923)
         ("Alpha" .  31609))
       #'equal #'car)