Appendix 1

The actual routine scripts are provided and shown below, however links to ".txt "files are more useful and given first:

1)    Banzhaf index calculator
2)    Shapley-Shubik index calculator
3)    Randomized Shapley-Shubik index calculator
4)    Johnston index calculator

The Banzhaf power index routine

//  Start of the Banzhaf index calculator function

function  banzhaf_index = banzhaf_pir(weights,quota)

totalwinning =0;

for i = 1:length(weights)

tally(i)=0,

end

for i=1:(2^(length(weights))-1)

total(i)=0;

for k=1:length(weights)

total(i)=total(i)+bitget(i,k)*weights(k);

end

if (total(i)>=quota) then

totalwinning=totalwinning+1,

       for k=1:length(weights)

               if (((total(i)-bitget(i,k)*weights(k))

                  tally(k)=tally(k)+bitget(i,k),

               end

       end

end

end

crit_sum=0;

for k=1:length(weights)

crit_sum=crit_sum+tally(k);

end

banzhaf_index=tally;

for k=1:length(weights)

banzhaf_index(k)=banzhaf_index(k)/crit_sum;

end

endfunction

//  End of the Banzhaf index calculator function

//**************************************

//**************************************

// Enter the weights and quota here

// Be sure the weights and quota are non-negative and that there are no more than 10 weights

weights = [4 2 1 ];

quota =5;

// You have entered the weights and quota

//**************************************

//**************************************

banzhaf_voting_index="Null--Invalid input.Check that the quota and weights are non-negative and that there are no more than 10 candidates";

good_input=((quota>0)&(length(weights)<11 amp="" min="" weights="">0));

if (good_input) then  banzhaf_voting_index=banzhaf_pir(weights,quota);

end

banzhaf_voting_index

The Shapley-Shubik power index routine

//  Start of the Shapley-Shubik index calculator function

function shapley_index = shapley_pir(weights, quota)

for i= 1:length(weights)

totals(i)=0,

x(i)=i,

end

y=perms(x);

for j = 1:size(y,"r")

permutation=y(j,:);

i=1;

total=0;

decider(j) =0;

while (decider(j)==0)

total=total+weights(permutation(i)),

if (total>=quota) then

decider(j) = i,

else

i=i+1,

end

end

decider(j) = permutation(i);

end

for i = 1:length(decider)

totals(decider(i))=totals(decider(i))+1,

end

crit_sum=0;

for k=1:length(weights)

crit_sum=crit_sum+totals(k);

end

shapley_index=totals;

for k=1:length(weights)

shapley_index(k)=shapley_index(k)/crit_sum;

end

endfunction

//  End of the Shapley-Shubik index calculator function

//**************************************

//**************************************

// Enter the weights and quota here

// Be sure the weights and quota are non-negative and that there are no more than 10 weights

weights = [4 2 1 ];

quota =5;

// You have entered the weights and quota

//**************************************

//**************************************

shapley_voting_index="Null--Invalid input.Check that the quota and weights are non-negative and that there are no more than 8 candidates";

good_input=((quota>0)&(length(weights)<9 amp="" min="" weights="">0));

if (good_input) then  shapley_voting_index=shapley_pir(weights,quota);

end

shapley_voting_index

The randomized Shapley-Shubik power index routine

//  Start of the randomized Shapley-Shubik index calculator function

function r_shapley_index = r_shapley_pir(weights, quota)

for i= 1:length(weights)

totals(i)=0,

x(i)=i,

end

//**************************************

//**************************************

//  Enter the sample size here

Sample_Size=100000;

//**************************************

//**************************************

for j = 1:Sample_Size

permutation=grand(1,'prm',x);

i=1;

total=0;

decider(j) =0;

while (decider(j)==0)

total=total+weights(permutation(i)),

if (total>=quota) then

decider(j) = i,

else

i=i+1,

end

end

decider(j) = permutation(i);

end

for i = 1:length(decider)

totals(decider(i))=totals(decider(i))+1,

end

crit_sum=0;

for k=1:length(weights)

crit_sum=crit_sum+totals(k);

end

r_shapley_index=totals;

for k=1:length(weights)

r_shapley_index(k)=r_shapley_index(k)/crit_sum;

end

endfunction

//  End of the randomized Shapley-Shubik index calculator function

//**************************************

//**************************************

//  Enter the weights and quota here

// Be sure the weights and quota are non-negative and that there are between 9 and 20 weights

weights = [9 9 9 9 8 8 8 6 5 5 4 3  ];

quota =12;

// You have entered the weights and quota

//**************************************

//**************************************

r_shapley_voting_index="Null--Invalid input.Check that the quota and weights are non-negative and that there are between 9 and 20";

good_input=((quota>0)&(length(weights)<21 amp="" length="" weights="">8)&(min(weights)>0));

if (good_input) then  r_shapley_voting_index=r_shapley_pir(weights, quota);

end

r_shapley_voting_index

The Johnston power index routine

//  Start of the Johnston index calculator function

function johnston_index = johnston_pir(weights,quota)

totalwinning =0;

temp=0;

for i = 1:length(weights)

tally(i)=0,

end

for i=1:(2^(length(weights))-1)

  total(i)=0;

  for k=1:length(weights)

       total(i)=total(i)+bitget(i,k)*weights(k);

 end

if (total(i)>=quota) then

totalwinning=totalwinning+1,

       for k=1:length(weights)

               if (((total(i)-bitget(i,k)*weights(k))

  temp=0;

                  for l=1:length(weights)

               temp=temp+bitget(i,l),

                  end

                  tally(k)=tally(k)+1/temp,

               end

       end

  end

end

crit_sum=0;

for k=1:length(weights)

crit_sum=crit_sum+tally(k);

end

johnston_index=tally;

for k=1:length(weights)

johnston_index(k)=johnston_index(k)/crit_sum;

end

endfunction

//  End of the Johnston  index calculator function

//**************************************

//**************************************

//  Enter the weights and quota here

// Be sure the weights and quota are non-negative and that there are between 9 and 20 weights

weights = [4 2 1 ];

quota =5;

// You have entered the weights and quota

//**************************************

//**************************************

johnston_voting_index="Null--Invalid input.Check that the quota and weights are non-negative and that there are no more than 10 candidates";

good_input=((quota>0)&(length(weights)<11 amp="" min="" weights="">0));

if (good_input) then  johnston_voting_index=johnston_pir(weights,quota);

end

johnston_voting_index