1. The problem statement, all variables and given/known data We are given a matrix with the following data Democrats Republicans Independents Libertarians Democrats 0.81 0.08 0.16 0.10 Republicans 0.09 0.84 0.05 0.08 Independent 0.06 0.04 0.74 0.04 Libertarians 0.04 0.04 0.05 0.78 2. Relevant equations Let xn be the vector (Dn, Rn, In, Ln)T. It represents the percentage of representatives of each party after n presidential elections and we shall call it the party distribution in general xn = (Pn)(x0) Why is it that for for a significantly large n, say n approaches infinity, no matter what your initial distribution of the electorate is, it does not seem to affect the distribution in the long term. 3. The attempt at a solution Say, you can choose any vector in R4 for x0 so long as all the entries sum up to 100 and multiplying this by Pinf = 0.3548 0.3548 0.3548 0.3548 0.3286 0.3286 0.3286 0.3286 0.1570 0.1570 0.1570 0.1570 0.1600 0.1600 0.1600 0.1600 will always give you the following vector: 35.4809 32.8634 15.7046 15.9955 Why is this? I notice this is true for any Matrix P whose first row has entries that are all the same value second row has entries that are all the same value etc.