# Code for simulations to produce Figure 3 in Humphreys and Laver 2009.
# Written for R 2.9 
#
# Simulate the size of the winset for 3 players, dimensions 2, 3, 4 
# and Minkowski exponents between 1 and 2.


Y = function(steps, sims1, sims2, n , d){

PDEFEAT<- 	matrix(-1,steps) 	# OUTPUT VECTOR -- PROB DDM DEFEATED BY AN ARBITRARY POINT			

for(k in 1:steps){					
	mink<- 1 + (k-1)/(steps-1)	# Minkowski exponent			
	Z<-matrix(0,sims1)		# VECTOR TO STORE FREQUENCY OF DEFEATS FOR EACH POLITY in 1:SIMS1		
	for(j in 1:sims1){				
			x <- matrix(runif(n*d), nrow=n)		
			DDM<-t(matrix(-1,d))			
			for(s in 1:d){DDM[s]<-(median(x[,s]))}			
			X<-rbind(x, DDM)			
			mX <- as.matrix(dist(X,method="minkowski", p=mink))[n+1,]			
			simx <- matrix(runif(sims2*d), nrow=sims2)			
			output<-matrix(NA,sims2)			
				for(i in 1:sims2){		
				Y<-rbind(x, simx[i,])		
				mY <- as.matrix(dist(Y,method="minkowski", p=mink))[n+1,]		
				output[i]<-(sum(mX>mY))>(n/2)}		
			Z[j]<-mean(output)}			
					
			PDEFEAT[k]<-mean(Z)				
			}				
	PDEFEAT}


# GRAPH

n<- 		3	 		# SIZE OF THE COMMITTEE
d<- 		2	 		# NUMBER OF DIMENSIONS
steps<- 	5	 		# NUMBER OF METRICS EXAMINED BETWEEN CITYBLOCK AND EUCLIDEAN	
sims1<- 	1000	 		# NUMBER OF DEMOGRAPHIES DRAWN EACH TIME	
sims2<- 	1000	 		# NUMBER OF POLICIES RIVAL TO SQ EXAMINED FOR EACH DEMOGRAPHY	


k 	=1:steps
mink 	<- 1 + (k-1)/(steps-1)

D3 = Y(steps,sims1,sims2,n,2)
D4 = Y(steps,sims1,sims2,n,3)
D5 = Y(steps,sims1,sims2,n,4)

pdf("fig3.pdf")
plot(mink, D3, type = "o", xlab="Minkowski Exponent", ylab = "Measure of Points that Beat the DDM", pch=19)
lines(mink, D4, type = "o", pch=19) 
lines(mink, D5, type = "o", pch=19) 
text(mink[3], D3[3]+.002, "d=2")
text(mink[3], D4[3]+.002, "d=3")
text(mink[3], D5[3]+.002, "d=4")
dev.off()

plot(mink, D3, type = "o", xlab="Minkowski Exponent", ylab = "Measure of Points that Beat the DDM", pch=19)
lines(mink, D4, type = "o", pch=19) 
lines(mink, D5, type = "o", pch=19) 
text(mink[3], D3[3]+.002, "d=2")
text(mink[3], D4[3]+.002, "d=3")
text(mink[3], D5[3]+.002, "d=4")