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THE PURPOSE OF THIS ARTICLE IS TO EXPLORE THE CONNECTION BETWEEN IDEOLOGY AND ISSUES IN THE MINDS OF VOTERS AND THE RELATIONSHIP BETWEEN THIS CONNECTION AND THE ELECTORAL PROSPECTS OF CANDIDATES ENGAGED IN TWO-CANDIDATE COMPETITION. TOWARD THIS END WE EXAMINE THE EFFECTS ON ELECTORAL COMPETITION OF EITHER MAGNIFYING OR COLLAPSING THE EXPECTED POLICY DIFFERENCE THAT VOTERS ASSOCIATE WITH A FIXED IDEOLOGICAL DIFFERENCE. THE AUTHORS FIND THAT MAGNIFYING THIS DIFFERENCE AIDS THE INCUMBENT, WHEREAS COLLAPSING IT AIDS THE CHALLENGER. THEY GO ON TO POINT OUT HOW THIS SECOND RESULT PROVIDES AN EXPLANATION FOR THE ELECTORAL APPEAL OF EXTREMIST CANDIDATES AND AN IMPORTANT INSIGHT INTO THE QUESTION OF STATE STABILITY.

The aggregation of individual preferences into a soc preference ordering is one of the most fundamental of the problems in soc sci. The general problem is non-trivial even for a small group of individuals. Only in the special case of 2 alternatives is the device of decision by majority rule proven to provide a generally satisfactory soc preference ordering for an arbitrary number of individuals. Presented here is a mathematical model of elections which allows certain aspects of the problem of soc choice to be systematically explored. Basically, it consists of 2 parts. 1st, there is a simple rule which is taken to represent the decision mechanism of a voter confronted with choosing between competing candidates who are viewed as being nothing more than a set of policies. 2nd, there is a probabilistic representation of the distribution of preferences across the pop. IPSA.