How do you call a situation or a point at wich statistics data stops changing? When I calculate a prediction, for instance I am trying to find out who is going to win elections and I do that by asking people who they voted on. After a certain number of answers my data will stop changing. The chance percentage of being elected will stop changing. 
Is there a special analytical or statistical definition of such situation where no more data is necessary to give proper results?
 A: Partially answered in comments: 
convergence? /// – Jeff
You'll want to look into standard errors. For example, for your case what's relevant is the standard error of a proportion. As the sample size doubles, the standard error decreases by a factor of the square root of two. The larger the sample, and the smaller the standard error, the greater the precision of your point estimate, and the smaller your uncertainty (margin or error or confidence interval around that point estimate). All of this assumes that you have taken random samples from the population, though. – rolando2 
Your data have not stopped changing, because each new point adds to it. What you are observing is that an estimate formed from the data changes by less and less as more and more data come in. But it will keep changing, as you will see if you just increase the number of decimal points in your estimate of the percentage chance of being elected. – Peter Ellis
In your example the estimate (the proportion of people who told you they voted for X) is always changing as you add new data points. The changes are just getting smaller and smaller until you don't notice them (see also rolando2's comment). Consequently, there is no single point at which the proportion stops changing, it depends on the level of precision you are considering (the number of figures after the decimal mark, if you will). – Gala
A: In qualitative methods, this 'point' is termed "data saturation". This is conventionally defined as the point when “no new information or themes are observed in the data” (Guest, Bunce, & Johnson, 2006, p. 59). Personally I see no reason why this term (and the general concept) cannot also be used with quantitative methods as well.
Reference: Guest, G., Bunce, A. & Johnson, L. (2006). How Many Interviews Are Enough?: An Experiment with Data Saturation and Variability. Field Methods, 18(1), 59-81. doi:10.1177/1525822X05279903
