Question

Let's use the results of the 2012 presidential election as our x0. Looking up the popular vote totals, we find that our initial distribution vector should be (0.5106, 0.4720, 0.0075, 0.0099)T. Enter the matrix P and this vector x0 in MATLAB: >> P = [0.8100 0.0800 0.1600 0.1000; 0.0900 0.8400 0.0500 0.0800; 0.0600 0.0400 0.7400 0.0400; 0.0400 0.0400 0.0500 0.7800] >> x0 = [0.5106; 0.4720; 0.0075; 0.0099] According to our model, what should the party distribution vector be after three, six, and ten elections? What about 30, 60, and 100 elections from now? How different are these three results from each other? Summarize what is happening with xk as k gets big.

Answer 1

Explanation:

Explanation:

The code for the problem is as follows:

%Defining the given matrices:

%P is the matrix showing the percentage of changes in voterbase

P = [ 0.8100 0.0800 0.1600 0.1000;

0.0900 0.8400 0.0500 0.0800;

0.0600 0.0400 0.7400 0.0400;

0.0400 0.0400 0.0500 0.7800];

%x0 is the vector representing the current voterbase

x0 = [0.5106; 0.4720; 0.0075; 0.0099];

%In MATLAB, the power(exponent) operator is defined by ^

%After 3 elections..

x3 = P^3 * x0;

disp("The voterbase after 3 elections is:");

disp(x3);

%After 6 elections..

x3 = P^6 * x0;

disp("The voterbase after 6 elections is:");

disp(x3);

%After 10 elections..

x10 = P^10 * x0;

disp("The voterbase after 10 elections is:");

disp(x10);

%After 30 elections..

x30 = P^30 * x0;

disp("The voterbase after 30 elections is:");

disp(x30);

%After 60 elections.

x60 = P^60 * x0;

disp("The voterbase after 60 elections is:");

disp(x60);

%After 100 elections.

x100 = P^100 * x0;

disp("The voterbase after 100 elections is:");

disp(x100);

The output is as well as the code in the matlab is as attached.

The output will be as follows:

The voter-base after 3 elections is therefore:

0.392565, 0.400734, 0.109855, 0.096846

The voter-base after 6 elections is therefore:

0.36168, 0.36294, 0.14176, 0.13362

The voter-base after 10 elections is therefore:

0.35405, 0.34074, 0.15342, 0.15178

The voter-base after 30 elections is therefore:

0.35463, 0.32854, 0.15697, 0.15986

The voter-base after 60 elections is therefore:

0.35465, 0.32849, 0.15698, 0.15988

The voter-base after 100 elections is therefore:

0.35465, 0.32849, 0.15698, 0.15988