OK, I found a plugin that does seem to want to do what I want and it's called "kk_ratings". I installed the plugin and after looking up on the support blog I found this bit of code:
Replace query_posts; with
query_posts('meta_key=_kk_ratings_avg&orderby=meta_value&order=DESC');
My theme only had:
suffusion_query_posts; (shows the theme name first)
So I added it like this:
suffusion_query_posts('meta_key=_kk_ratings_avg&orderby=meta_value&order=DESC');
but it does not sort the post on the category page by rating.
So I then tried it without the "suffusion_" part like this:
query_posts('meta_key=_kk_ratings_avg&orderby=meta_value&order=DESC');
that does show the rated posts but ONLY the rated posts and not all the others. It also does not show the rating stars like it would normally on the posts in the category page.
Any ideas please? I have left the plugin installed and you will see two of the posts have ratings on this page http://bantayan.info/category/accommodation/ (they are currently half way down the page, I want these rated ones to be at the top).