(define-module (deliberate borda)
  #:use-module (deliberate utils)
  #:export (borda-score social-choice-borda social-preference-borda))

(define (borda-score alternatives ranked)
  ;; Check whether all alternatives have been scored
  (if (nil? alternatives)
      '()
      ;; Check whether all ranked alternatives have been scored
      (if (nil? ranked)
	  (let* ((n (length alternatives))
		 (score (/ (- n 1) 2)))
	    ;; Assign average remaining score to all unranked alternatives
	    (map cons alternatives (const-list n score)))
	  ;; Just use next rank
	  (let* ((alt (car ranked))
		(remaining (delete alt alternatives)))
	    (cons (cons alt (length remaining))
		  (borda-score remaining (cdr ranked))))
	  )))

(define (profile->scores alternatives profile)
  (apply append
	 (map (lambda (pair)
		(borda-score alternatives (cdr pair)))
	      profile)))

(define (groups->totals groups)
  (map (lambda (elt)
	 (cons (car elt)
	       (reduce + 0 (map cdr (cdr elt)))))
       groups))

(define (profile-borda-totals alternatives profile)
  (let* ((scores (profile->scores alternatives profile))
	 (groups (group-by car scores))
	 (totals (groups->totals groups)))
    totals))

;; TODO - handle ties
(define (social-preference-borda alternatives profile)
  (let ((totals (profile-borda-totals alternatives profile)))
    ;; We use > instead of < for to rank in decreasing score order
    (map (compose list car) (sort totals (lambda (x y) (> (cdr x) (cdr y)))))))

(define (social-choice-borda alternatives profile)
  (car (social-preference-borda alternatives profile)))