We have the same sort of thing at my work (about 150 of us pay �1 a week).
Because the elected committee are dealing with other peoples money we also have written rules.
Basically it covers what the committee will/will not spend our money on, who is eligible to join etc....
If you type "Social Committee Constitution" into Google you can see how other people deal with this.
for example:
http://www.postdoc.ucla.edu/constitution
A written constution means that everybody has a clear understanding of the committee's responsibility.
We had an issue somtime ago where all the keen fishermen gained places on the committee, we saw all of our money being spent on fishing days, bait and fishing licences, changes were made to the constitution to stop this happening again. A properly written set of rules will stop any arguing/ill feeling.