his article considers a social system where a political decision is to be made. Only two alternatives are permitted: YES or NO. Within the total population A there are two groups, one (X) campaigns for a YES decision, the other one (Y) argues for a NO decision. It is assumed that every individual within the total population has the same opportunities in the field of communications. The question to be answered is as follows: How are the opinions within the total population A distributed after a certain length of time. In our model we use a quantitative concept: The 'Influence of Opinion in a Two-Party-System'. It is assumed that the relative influence of a group of people having a certain opinion is the stronger, the faster they are able to publicize their decision within the total population A. This and other assumptions (axioms) are formulated more precisely in the following discussion.
First of all I shall attempt to formulate the theory Tin every-day-language. Thereby I shall use terms that can be interpreted in various ways. I shall add in parenthesis a definite interpretation. The term 'contact' e.g. can be interpreted as a greeting with handshake, as a conversation, or as contacting an infectious illness, provided that the term 'element' was interpreted as person. AXIOM 1. The set A (totalpopulation) is finite and constant. AXIOM 2. The set A contains two subsets: X and Y. X represents those elements (persons) which have the property F (opting for the YES decision). Y contains those elements (persons) which have the property G (representing the NO position). AXIOM 3. At the time t =0, A is not a subset of the union ofXand Y. (The population A is larger than X and Y combined.) AXIOM 4. The intersection of X and Y is always an empty set. AXIOM 5. During the time interval t 2 --tl each element in X has an average of c 1 contacts (conversations initiated by X) with elements of the set A.