## Example A5

A large group of citizens, always the same persons, are asked regularly whether or not they support a certain political issue. It is recorded how many YES and how many NO there are; these numbers are denoted .v„ and xl2, respectively at poll number / = 0,1,2, The persons asked cannot refuse to answer, nor can they answer DON'T KNOW. Furthermore it has been established from previous experience that a person who says YES has probability 70% of giving the same answer next time (and 30% of saying NO), and a NO has probability 20% of saying YES next time (and 80 of saying NO again). From this information we conclude that

a' , f +1 =0.3.v„ +0.8.v;, or in vector-matrix formulation

Suppose the polls involve 1000 persons of which 800 said YES and 200 said NO at the first poll. Iteration of (A.40)/(A.41) yields

 t 0 1 2 3 4 5 xu 800 600 500 450 425 413 200 400 500 550 575 There seems to be a tendency to stabilize near* = (400, 600)T. This distribution is in fact stationary in the sense that*, = (400,600)T impliesjc,+ ] =xl+2 = ... = (400,600)T.
0 0