By the time you have walked half way along the beach to the icecream stalls, the distance between them will be negligible. If I walk up to three icecream stalls, I'll be right infront of three icecream stalls, so location won't matter.

I'm not sure how this aspect applies to the political senario, which is the more interesting one.

In politics what it usually means that while there can be advantages for two parties to tend towards the political centre, they always tend to keep enough distance between themselves to be clearly differentiated. The same logic still applies more or less - although the further towards the extremes the parties get, the larger the gap between them will tend to have to be.

> I'm not sure how this aspect applies to the political senario, which is the more interesting one.

That's more difficult. For in most voting systems you have to take strategic voting into account. E.g. in a winner-takes-all systems people don't want to waste their votes, and thus the system tends towards two parties.

How about moving to the edge in the center? Then he'll capture the whole side until someone else claims his place, rinse and repeat.