Downsian convergence (I believe that's how you spell it) is the theory that, in a two-party system, parties will tend to the centre.
It has just struck me that the tendency to the centre does not work. Moving to the centre from (say) the left will lose the extreme left. Put another way, where n is the normal distribution on a notional left-right axis and m is the dropoff of a party's support due to distance from the party's stated position, yn>ym.
Equally, the distribution is not necessarily normal (assuming it can be meaningfully boiled down to a single axis). People won't distribute themselves on a normal distribution for three reasons. Firstly, I see no evidence as to why politics should be considered organic or why it should be boiled down to a statistical function.
Secondly, people have to express themselves through political action. This is done by political parties and, increasingly of late, through single- or narrow- issue groups. People are attracted to these groups because they are close to their own opinion on a given issue, set of issues or general outlook. Once in that group, they will be 'educated' by the group to some degree, and will move towards the norm of that group. This does mean that parties &c. are dynamic poles.
Thirdly, some issues are particularly intellectually or emotionally powerful, so they act as other poles of attraction. Even if someone is generally (say) economically liberal, they might have a particular attraction to (say) nationalised healthcare. Particularly if the issue of healthcare funding is prominent in an election, this might move their position on the scale. People also retain loyalty to a given party, and so they can be discounted except in terms of a 'get out the vote' operation so long as they are not alienated by the party's changed position. The very few who hold views strongly enough to do something about them are better considered as agents in the process.
Does anyone know of any papers done on this? Is this complete rot?