Determining Winning Combinations of Parties with >50% Votes

[Ryan_m_b]

This is born out of musings around coalition governments that arise from the party with the most votes not achieving ≥50% of the votes (as opposed to emergency coalitions).

Taking the figures below how would one go about determining all the possible combinations of parties who combined have >50% of the votes without sitting down and working them out one by one?

Kid gloves please I haven't studied maths for the better part of a decade...

Parties / Percentage of votes

Pink / 21
Orange / 19
Brown / 16
Blue / 10
Green / 10
Tan / 8
Red / 5
Black / 4
Purple / 4
White / 3

 

[oli4]

Brute force my friend !
Here is a groovy script that answers your question:

def X=[Pink:21, Orange:19, Brown:16, Blue:10, Green:10, Tan:8, Red:5, Black:4, Purple:4, White:3]
def XS=X.keySet() as List
def N=XS.size()
def F; F={ ix,n ->
	def L0=[XS[ix]]
	if(n==1) return [L0]
	def L=[]
	for(def j=ix; j<N-1; j++) { 
		F(j+1, n-1).each{ L<<(L0+it) }
	}
	L
}
def OK=[:]
for(def i=0;i<N;i++) {
	for(def j=1;j<=N-i;j++) {
		def c=F(i,j)
		c.each{ 
			def s=0; it.each { s+=X[it]} 
			if(s>50) OK[it]=s 
		}
	}
}
OK.keySet().sort{x,y->OK[y]<=>OK[x]}.each{ println "$it: ${OK[it]}%" }

I don't post the result since there are 502 winning combinations going all the way from 51% up to 100%

 

[Ryan_m_b]

Brute force my friend !
Here is a groovy script that answers your question:
I don't post the result since there are 502 winning combinations going all the way from 51% up to 100%

Wow thanks a lot! To be honest I'm not really sure how to work code lol but it's good to know that there's a relatively simple way to get it done. Thanks!