Electoral Stability and Rigidity

Some argue that political stability is best served through a two-party system. This study refutes this. The author mathematically defines the stability and rigidity of electoral systems comprised of any quantity of electors and parties. In fact, stability is a function of the quantity of electors - i.e., the number of occupied seats at the table. As the number of electors increases, the properties of an electorate are increasingly well resolved, and well described by those of an electorate that is least excessive -- that is to say an electorate that is closest to equilibrium. Further, electoral rigidity is a function of the quantity of parties and their probabilities of representation. An absolutely rigid system admits no fluctuations -- whatever happens to one elector will happen to all electors. As the quantity of parties increases so does the number of party lines, and with it the quantity of alternatives with which to respond to an external stimulus. Rigidity is significant in a social system that places high value on party loyalty. In conclusion, (i) electoral stability is best served by increasing the quantity of electors; (ii) electoral rigidity is best served by decreasing the quantity of parties, and by increasing the representation of some parties at the expense of others; and (iii) the less stable a branch of government, the more concern is placed on those who would hold those offices for the people.