#OK to post homework
#George Spahn, 3-27-2022, Assignment 16

#2

IsCondorcet := proc(P)
local sv,i:
	sv := SV(Tour(P)):
	for i from 0 to nops(sv)-1 do
		if not(i in sv) then 
			RETURN (true):
		fi:
	od:
	RETURN (false):
end:

#3

ExactCond := proc(n,v)
local rp,c,r:
	c := 0:
	rp := RP(n,v):
	for r in rp do
		if IsCondorcet(r) then 
			c := c+1:
		fi:
	od:
	c / nops(rp):
end:

#4 
EstCond := proc(n,v,K)
local i,c,r:
	c := 0:
	
	for i from 1 to K do
		r := RandP(n,v):
		if IsCondorcet(r) then 
			c := c+1:
		fi:
	od:
	evalf(c / K):
end:

#5
Borda := proc(P)
local n,i,p,ret:
	n := nops(P[1]):
	for i from 1 to n do ret[i]:=0: od:
	for p in P do
		for i from 1 to n do
			ret[p[i]] := ret[p[i]] + (n-i):
		od:
	od:
	[seq(ret[i],i=1..n)]:
end:

#7
BordaRank := proc(P):
local b,m,ret,i,s1,j:
	b := Borda(P):
	m := max(b):
	ret := []:
	for i from m to 0 by -1 do
		s1 := {}:
		for j from 1 to nops(b) do
			if b[j] = i then
				s1 := s1 union {j}:
			fi:
		od:
		if nops(s1) > 0 then
			ret := [op(ret),s1]:
		fi:
	od:
	ret:
end: